Ecology

1.Westerling, A. L. R. Increasing western US forest wildfire activity: sensitivity to changes in the timing of spring. Phil. Trans. R. Soc. B 371, 20150178 (2016).PubMed 
PubMed Central 

Google Scholar 
2.Abatzoglou, J. T. & Williams, A. P. Impact of anthropogenic climate change on wildfire across western US forests. Proc. Natl Acad. Sci. USA 113, 11770–11775 (2016).CAS 
PubMed 
PubMed Central 

Google Scholar 
3.Gonzalez, P. et al. Southwest: Impacts, Risks, and Adaptation in the United States: Fourth National Climate Assessment (U.S. Global Change Research Program, 2018).4.McLauchlan, K. K. et al. Fire as a fundamental ecological process: research advances and frontiers. J. Ecol. 108, 2047–2069 (2020).
Google Scholar 
5.Bowman, D. M. J. S. et al. Fire in the Earth system. Science 324, 481–484 (2009).6.Davis, K. T. et al. Wildfires and climate change push low-elevation forests across a critical climate threshold for tree regeneration. Proc. Natl Acad. Sci. USA 116, 6193–6198 (2019).CAS 
PubMed 
PubMed Central 

Google Scholar 
7.Stephens, S. L. et al. Drought, tree mortality, and wildfire in forests adapted to frequent fire. Bioscience 68, 77–88 (2018).
Google Scholar 
8.Radeloff, V. C. et al. Rapid growth of the US wildland–urban interface raises wildfire risk. Proc. Natl Acad. Sci. USA 115, 3314–3319 (2018).CAS 
PubMed 
PubMed Central 

Google Scholar 
9.Syphard, A. D., Keeley, J. E., Pfaff, A. H. & Ferschweiler, K. Human presence diminishes the importance of climate in driving fire activity across the United States. Proc. Natl Acad. Sci. USA 114, 13750–13755 (2017).CAS 
PubMed 
PubMed Central 

Google Scholar 
10.Mietkiewicz, N. et al. In the line of fire: consequences of human-ignited wildfires to homes in the U.S. (1992–2015). Fire 3, 50 (2020).11.Balch, J. K. et al. Human-started wildfires expand the fire niche across the United States. Proc. Natl Acad. Sci. USA 114, 2946–2951 (2017).CAS 
PubMed 
PubMed Central 

Google Scholar 
12.McKenzie, D. & Littell, J. S. Climate change and the eco-hydrology of fire: will area burned increase in a warming western USA. Ecol. Appl. 27, 26–36 (2017).PubMed 

Google Scholar 
13.Littell, J. S., Mckenzie, D., Peterson, D. L. & Westerling, A. L. Climate and wildfire area burned in western U.S. ecoprovinces, 1916–2003. Ecol. Appl. 19, 1003–1021 (2009).PubMed 

Google Scholar 
14.Jensen, D. et al. The sensitivity of US wildfire occurrence to pre-season soil moisture conditions across ecosystems. Environ. Res. Lett. 13, 014021 (2018).PubMed 
PubMed Central 

Google Scholar 
15.Vicente-Serrano, S. M., Quiring, S. M., Peña-Gallardo, M., Yuan, S. & Domínguez-Castro, F. A review of environmental droughts: increased risk under global warming? Earth Sci. Rev. 201, 102953 (2020).
Google Scholar 
16.Ficklin, D. L. & Novick, K. A. Historic and projected changes in vapor pressure deficit suggest a continental-scale drying of the United States atmosphere. J. Geophys. Res. 122, 2061–2079 (2017).
Google Scholar 
17.Sarhadi, A., Ausín, M. C., Wiper, M. P., Touma, D. & Diffenbaugh, N. S. Multidimensional risk in a nonstationary climate: joint probability of increasingly severe warm and dry conditions. Sci. Adv. 4, eaau3487 (2018).PubMed 
PubMed Central 

Google Scholar 
18.Abatzoglou, J. T., Williams, A. P., Boschetti, L., Zubkova, M. & Kolden, C. A. Global patterns of interannual climate–fire relationships. Glob. Change Biol. 24, 5164–5175 (2018).
Google Scholar 
19.Williams, A. P. & Abatzoglou, J. T. Recent advances and remaining uncertainties in resolving past and future climate effects on global fire activity. Curr. Clim. Change Rep. 2, 1–14 (2016).
Google Scholar 
20.Bradstock, R. A. A biogeographic model of fire regimes in Australia: current and future implications. Glob. Ecol. Biogeogr. 19, 145–158 (2010).
Google Scholar 
21.Krawchuk, M. A. & Moritz, M. A. Constraints on global fire activity vary across a resource gradient. Ecology 92, 121–132 (2011).PubMed 

Google Scholar 
22.Scarff, F. R. et al. Effects of plant hydraulic traits on the flammability of live fine canopy fuels. Funct. Ecol. 35, 835–846 (2021).23.Ruffault, J., Martin-StPaul, N., Pimont, F. & Dupuy, J. L. How well do meteorological drought indices predict live fuel moisture content (LFMC)? An assessment for wildfire research and operations in Mediterranean ecosystems. Agric. For. Meteorol. 262, 391–401 (2018).
Google Scholar 
24.Pivovaro, A. L. et al. The effect of ecophysiological traits on live fuel moisture content. Fire 2, 28 (2019).25.Nolan, R. H., Hedo, J., Arteaga, C., Sugai, T. & Resco de Dios, V. Physiological drought responses improve predictions of live fuel moisture dynamics in a Mediterranean forest. Agric. For. Meteorol. 263, 417–427 (2018).26.Skelton, R. P., West, A. G. & Dawson, T. E. Predicting plant vulnerability to drought in biodiverse regions using functional traits. Proc. Natl Acad. Sci. USA 112, 5744–5749 (2015).CAS 
PubMed 
PubMed Central 

Google Scholar 
27.Ma, W. et al. Assessing climate change impacts on live fuel moisture and wildfire risk using a hydrodynamic vegetation model. Biogeosciences 18, 4005–4020 (2021).CAS 

Google Scholar 
28.McColl, K. A. et al. The global distribution and dynamics of surface soil moisture. Nat. Geosci. 10, 100–104 (2017).CAS 

Google Scholar 
29.Chuvieco, E., González, I., Verdú, F., Aguado, I. & Yebra, M. Prediction of fire occurrence from live fuel moisture content measurements in a Mediterranean ecosystem. Int. J. Wildland Fire 18, 430–441 (2009).30.Rao, K., Williams, A. P., Flefil, J. F. & Konings, A. G. SAR-enhanced mapping of live fuel moisture content. Remote Sens. Environ. 245, 111797 (2020).
Google Scholar 
31.Nolan, R. H., Boer, M. M., Resco De Dios, V., Caccamo, G. & Bradstock, R. A. Large-scale, dynamic transformations in fuel moisture drive wildfire activity across southeastern Australia. Geophys. Res. Lett. 43, 4229–4238 (2016).
Google Scholar 
32.Dennison, P. E. & Moritz, M. A. Critical live fuel moisture in chaparral ecosystems: a threshold for fire activity and its relationship to antecedent precipitation. Int. J. Wildland Fire 18, 1021–1027 (2009).
Google Scholar 
33.Tumino, B. J., Duff, T. J., Goodger, J. Q. D. & Cawson, J. G. Plant traits linked to field-scale flammability metrics in prescribed burns in Eucalyptus forest. PLoS ONE 14, e0221403 (2019).34.Rodman, K. C. et al. A trait-based approach to assessing resistance and resilience to wildfire in two iconic North American conifers. J. Ecol. 109, 313–326 (2021).
Google Scholar 
35.Resco de Dios, V. Plant–Fire Interactions (Springer, 2020).36.Hurteau, M. D., Liang, S., Westerling, A. L. R. & Wiedinmyer, C. Vegetation–fire feedback reduces projected area burned under climate change. Sci. Rep. 9, 2838 (2019).37.Littell, J. S., McKenzie, D., Wan, H. Y. & Cushman, S. A. Climate change and future wildfire in the western United States: an ecological approach to nonstationarity. Earths Future 6, 1097–1111 (2018).38.Abatzoglou, J. T. & Kolden, C. A. Relationships between climate and macroscale area burned in the western United States. Int. J. Wildland Fire 22, 1003–1020 (2013).
Google Scholar 
39.Goss, M. et al. Climate change is increasing the likelihood of extreme autumn wildfire conditions across California. Environ. Res. Lett. 15, 094016 (2020).40.Bradshaw, L. S., Deeming, J. E., Burgan, R. E. & Cohen, J. D. The 1978 National Fire-Danger Rating System: Technical Documentation General Technical Report INT-169 (US Department of Agriculture, Forest Service, Intermountain Forest and Range Experiment Station,1984); https://doi.org/10.2737/INT-GTR-16941.Hardy, C. C. & Hardy, C. E. Fire danger rating in the United States of America: an evolution since 1916. Int. J. Wildland Fire 16, 217–231 (2007).42.Rabin, S. S. et al. The Fire Modeling Intercomparison Project (FireMIP), phase 1: experimental and analytical protocols with detailed model descriptions. Geosci. Model Dev. 10, 1175–1197 (2017).CAS 

Google Scholar 
43.Hantson, S. et al. The status and challenge of global fire modelling. Biogeosciences 13, 3359–3375 (2016).
Google Scholar 
44.Anderegg, W. R. L. Spatial and temporal variation in plant hydraulic traits and their relevance for climate change impacts on vegetation. New Phytol. 205, 1008–1014 (2015).PubMed 

Google Scholar 
45.Konings, A. G. & Gentine, P. Global variations in ecosystem-scale isohydricity. Glob. Change Biol. 23, 891–905 (2017).
Google Scholar 
46.Forkel, M. et al. Emergent relationships with respect to burned area in global satellite observations and fire-enabled vegetation models. Biogeosciences 16, 57–76 (2019).
Google Scholar 
47.Brodribb, T. J., Powers, J., Cochard, H. & Choat, B. Hanging by a thread? Forests and drought. Science 368, 261–266 (2020).CAS 
PubMed 

Google Scholar 
48.Trugman, A. T., Anderegg, L. D. L., Shaw, J. D. & Anderegg, W. R. L. Trait velocities reveal that mortality has driven widespread coordinated shifts in forest hydraulic trait composition. Proc. Natl Acad. Sci. USA 117, 8532–8538 (2020).CAS 
PubMed 
PubMed Central 

Google Scholar 
49.Williams, A. P. et al. Correlations between components of the water balance and burned area reveal new insights for predicting forest fire area in the southwest United States. Int. J. Wildland Fire 24, 14–26 (2015).
Google Scholar 
50.Knapp, P. A. Spatio-temporal patterns of large grassland fires in the Intermountain West U.S.A. Glob. Ecol. Biogeogr. Lett. 7, 259–272 (1998).
Google Scholar 
51.Keeley, J. & Syphard, A. Climate change and future fire regimes: examples from California. Geosciences 6, 37 (2016).
Google Scholar 
52.Badia, A., Serra, P. & Modugno, S. Identifying dynamics of fire ignition probabilities in two representative Mediterranean wildland–urban interface areas. Appl. Geogr. 31, 930–940 (2011).
Google Scholar 
53.Fusco, E. J., Abatzoglou, J. T., Balch, J. K., Finn, J. T. & Bradley, B. A. Quantifying the human influence on fire ignition across the western USA. Ecol. Appl. 26, 2390–2401 (2016).
Google Scholar 
54.Syphard, A. D. et al. Human influence on California fire regimes. Ecol. Appl. 17, 1388–1402 (2007).PubMed 

Google Scholar 
55.Ager, A. A., Finney, M. A., Kerns, B. K. & Maffei, H. Modeling wildfire risk to northern spotted owl (Strix occidentalis caurina) habitat in central Oregon, USA. For. Ecol. Manage. 246, 45–56 (2007).56.Thomas, D., Butry, D., Gilbert, S., Webb, D. & Fung, J. The Costs and Losses of Wildfires: A Literature Survey NIST Special Publication 1215 (NIST, 2017); https://doi.org/10.6028/NIST.SP.121557.Wang, D. et al. Economic footprint of California wildfires in 2018. Nat. Sustain. 4, 252–260 (2021).
Google Scholar 
58.Burke, M. et al. The changing risk and burden of wildfire in the United States. Proc. Natl Acad. Sci. USA 118, e2011048118 (2021).59.García, M., Chuvieco, E., Nieto, H. & Aguado, I. Combining AVHRR and meteorological data for estimating live fuel moisture content. Remote Sens. Environ. 112, 3618–3627 (2008).
Google Scholar 
60.Matthews, S. Dead fuel moisture research: 1991–2012. Int. J. Wildland Fire 23, 78–92 (2014).
Google Scholar 
61.Cohen, J. D. et al. The National Fire-Danger Rating System: Basic Equations Vol. 82 (US Department of Agriculture, Forest Service, Pacific Southwest Forest and Range Experiment Station, 1985).62.Pellizzaro, G., Cesaraccio, C., Duce, P., Ventura, A. & Zara, P. Relationships between seasonal patterns of live fuel moisture and meteorological drought indices for Mediterranean shrubland species. Int. J. Wildland Fire 16, 232–241 (2007).63.Liu, L., Zhang, Y., Wu, S., Li, S. & Qin, D. Water memory effects and their impacts on global vegetation productivity and resilience. Sci. Rep. 8, 2962 (2018).PubMed 
PubMed Central 

Google Scholar 
64.Anderegg, W. R. L. et al. Woody plants optimise stomatal behaviour relative to hydraulic risk. Ecol. Lett. 21, 968–977 (2018).PubMed 

Google Scholar 
65.Meinzer, F. C., Johnson, D. M., Lachenbruch, B., McCulloh, K. A. & Woodruff, D. R. Xylem hydraulic safety margins in woody plants: coordination of stomatal control of xylem tension with hydraulic capacitance. Funct. Ecol. 23, 922–930 (2009).
Google Scholar 
66.National Fuel Moisture Database (United States Forest Service, 2018); https://www.wfas.net/nfmd/public/index.php67.Abatzoglou, J. T. Development of gridded surface meteorological data for ecological applications and modelling. Int. J. Climatol. 33, 121–131 (2011).
Google Scholar 
68.Homer, C. et al. Completion of the 2006 National Land Cover Database for the conterminous United States. Photogramm. Eng. Remote Sens. 77, 858–864 (2011).69.Williams, A. P. et al. Observed impacts of anthropogenic climate change on wildfire in California. Earths Future 7, 892–910 (2019).
Google Scholar 
70.Boschetti, L., Roy, D., Hoffman, A. A. & Humber, M. Collection 5 MODIS Burned Area Product User Guide Version 3.0.1 (NASA EOSDIS Land Processes DAAC, 2013).71.PRISM Climate Data (Prism Climate Group, Oregon State University, accessed 16 December 2020); https://prism.oregonstate.edu72.Simard, M., Pinto, N., Fisher, J. B. & Baccini, A. Mapping forest canopy height globally with spaceborne lidar. J. Geophys. Res. 116, G04021 (2011).73.Fan, Y., Miguez-Macho, G., Jobbágy, E. G., Jackson, R. B. & Otero-Casal, C. Hydrologic regulation of plant rooting depth. Proc. Natl Acad. Sci. USA 114, 10572–10577 (2017).CAS 
PubMed 
PubMed Central 

Google Scholar 
74.Montzka, C., Herbst, M., Weihermüller, L., Verhoef, A. & Vereecken, H. A global data set of soil hydraulic properties and sub-grid variability of soil water retention and hydraulic conductivity curves. Earth Syst. Sci. Data 9, 529–543 (2017).
Google Scholar 
75.Liu, S. et al. NACP MsTMIP: Unified North American Soil Map (ORNL DAAC, 2014); https://doi.org/10.3334/ornldaac/124276.Pedregosa, F. et al. Scikit-learn: machine learning in Python. J. Mach. Learn. Res. 12, 2825–2830 (2011).
Google Scholar 
77.Martinuzzi, S. et al. The 2010 Wildland–Urban Interface of the Conterminous United States (USDA, 2015).78.Medlyn, B. E. et al. Reconciling the optimal and empirical approaches to modelling stomatal conductance. Glob. Change Biol. 17, 2134–2144 (2011).
Google Scholar  More

1.Le Loeuff, J., Buffetaut, E. & Martin, M. The last stages of dinosaur faunal history in Europe: a succession of Maastrichtian dinosaur assemblages from the Corbières (southern France). Geol. Mag. 131, 625–630 (1994).
Google Scholar 
2.Vila, B., Sellés, A. G. & Brusatte, S. L. Diversity and faunal changes in the latest Cretaceous dinosaur communities of southwestern Europe. Cretac. Res. 57, 552–564 (2016).
Google Scholar 
3.Fondevilla, V. et al. Chronostratigraphic synthesis of the latest Cretaceous dinosaur turnover in south-western Europe. Earth Sci. Rev. 191, 168–189 (2019).
Google Scholar 
4.Sanz, J. L., Powell, J. E., Le Loeuff, J., Martínez, R. & Pereda-Suberbiola, X. Sauropod remains from the Upper Cretaceous of Laño (northcentral Spain). Titanosaur phylogenetic relationships. Est. Mus. Cienc. Nat. Alava 14, 235–255 (1999).
Google Scholar 
5.Garcia, G., Amico, S., Fournier, F., Thouand, E. & Valentin, X. A new titanosaur genus (Dinosauria, Sauropoda) from the Late Cretaceous of southern France and its paleobiogeographic implications. Bull. Soc. Géol. Fr. 181, 269–277 (2010).
Google Scholar 
6.Díez Díaz, V. et al. A new titanosaur (Dinosauria: Sauropoda) from the Upper Cretaceous of Velaux La-Bastide Neuve (southern France). Hist. Biol. https://doi.org/10.1080/08912963.2020.1841184 (2020).7.Le Loeuff, J. Ampelosaurus atacis (nov. gen., nov. sp.), a new titanosaurid (Dinosauria, Sauropoda) from the Late Cretaceous of the Upper Aude Valley (France). C. R. Acad. Sci. II 321, 693–700 (1995).
Google Scholar 
8.Díez Díaz, V. et al. A new titanosaur (Dinosauria, Sauropoda) from the Upper Cretaceous of Lo Hueco (Cuenca, Spain). Cretac. Res. 68, 49–60 (2016).
Google Scholar 
9.Company, J. Bone histology of the titanosaur Lirainosaurus astibiae (Dinosauria: Sauropoda) from the latest Cretaceous of Spain. Naturwissenschaften 98, 67–78 (2011).CAS 
PubMed 

Google Scholar 
10.Klein, N. et al. Modified laminar bone in Ampelosaurus atacis and other titanosaurs (Sauropoda): implications for life history and physiology. PLoS ONE 7, e36907 (2012).CAS 
PubMed 
PubMed Central 

Google Scholar 
11.Díez Díaz, V. et al. The titanosaurian dinosaur Atsinganosaurus velauciensis (Sauropoda) from the Upper Cretaceous of southern France: new material, phylogenetic affinities, and palaeobiogeographical implications. Cretac. Res. 91, 429–456 (2018).
Google Scholar 
12.Benítez-López, A. et al. The island rule explains consistent patterns of body size evolution in terrestrial vertebrates. Nat. Ecol. Evol. 5, 768–786 (2021).PubMed 

Google Scholar 
13.Benton, M. J. et al. Dinosaurs and the island rule: the dwarfed dinosaurs from Haţeg Island. Palaeogeogr. Palaeoclimatol. Palaeoecol. 293, 438–454 (2010).
Google Scholar 
14.Canudo, J. I. Descripción de un fragmento proximal de fémur de Titanosauridae (Dinosauria, Sauropoda) del Maastrichtiense superior de Serraduy (Huesca). In Proc. XVII Jornadas de la Sociedad Española de Paleontología (eds Meléndez, G. et al.) 255–262 (Sociedad Española de Paleontología y Área y Museo de Paleontología de la Universidad de Zaragoza, 2001).15.Vila, B. et al. The diversity of sauropods and their first taxonomic succession from the latest Cretaceous of south-western Europe: clues to demise and extinction. Palaeogeogr. Palaeoclimatol. Palaeoecol. 350–352, 19–38 (2012).
Google Scholar 
16.Sallam, H. M. et al. New Egyptian sauropod reveals Late Cretaceous dinosaur dispersal between Europe and Africa. Nat. Ecol. Evol. 2, 445–451 (2018).PubMed 

Google Scholar 
17.Buffetaut, E. Archosaurian reptiles with Gondwanan affinities in the Upper Cretaceous of Europe. Terra Nova 1, 69–74 (1989).
Google Scholar 
18.Le Loeuff, J. The Campano-Maastrichtian vertebrate faunas from southern Europe and their relationships with other faunas in the world; palaeobiogeographical implications. Cretac. Res. 12, 93–114 (1991).
Google Scholar 
19.Pereda-Suberbiola, X. Biogeographical affinities of Late Cretaceous continental tetrapods of Europe: a review. Bull. Soc. Geol. Fr. 180, 57–71 (2009).
Google Scholar 
20.Csiki-Sava, Z., Buffetaut, E., Ősi, A., Pereda-Suberbiola, X. & Brusatte, S. L. Island life in the Cretaceous – faunal composition, biogeography, evolution, and extinction of land-living vertebrates on the Late Cretaceous European archipelago. ZooKeys 469, 1–161 (2015).
Google Scholar 
21.Ezcurra, M. D. & Agnolín, F. L. A new global palaeobiogeographical model for the late Mesozoic and early Tertiary. Syst. Biol. 61, 553–566 (2012).PubMed 

Google Scholar 
22.Sellés, A. G. & Vila, B. Re-evaluation of the age of some dinosaur localities from the southern Pyrenees by means of megaloolithid oospecies. J. Iber. Geol. 41, 125–139 (2015).
Google Scholar 
23.Bonaparte, J. F. & Coria, R. A. Un nuevo y gigantesco saurópodo titanosaurio de la Formación Río Limay (Albiano–Cenomaniano) de la Provincia del Neuquén, Argentina. Ameghiniana 30, 217–282 (1993).
Google Scholar 
24.Curry Rogers, K. The postcranial osteology of Rapetosaurus krausei (Sauropoda: Titanosauria) from the Late Cretaceous of Madagascar. J. Vertebr. Paleontol. 29, 1046–1086 (2009).
Google Scholar 
25.Zurriaguz, V. & Powell, J. New contributions to the presacral osteology of Saltasaurus loricatus (Sauropoda, Titanosauria) from the Upper Cretaceous of northern Argentina. Cretac. Res. 54, 283–300 (2015).
Google Scholar 
26.Coria, R. A., Filippi, L. S., Chiappe, L. M., García, R. & Arcucci, A. B. Overosaurus paradasorum gen. et sp. nov., a new sauropod dinosaur (Titanosauria: Lithostrotia) from the Late Cretaceous of Neuquén, Patagonia, Argentina. Zootaxa 3683, 357–376 (2013).PubMed 

Google Scholar 
27.Calvo, J. O., González Riga, B. J. & Porfiri, J. D. A new titanosaur sauropod from the Late Cretaceous of Neuquén, Patagonia, Argentina. Arq. Mus. Nac. 65, 485–504 (2007).
Google Scholar 
28.Jain, S. L. & Bandyopadhyay, S. New titanosaurid (Dinosauria: Sauropoda) from the Late Cretaceous of central India. J. Vertebr. Paleontol. 17, 114–136 (1997).
Google Scholar 
29.Gorscak, E. & O’Connor, P. M. A new African titanosaurian sauropod dinosaur from the middle Cretaceous Galula Formation (Mtuka Member), Rukwa Rift Basin, southwestern Tanzania. PLoS ONE 14, e0211412 (2019).CAS 
PubMed 
PubMed Central 

Google Scholar 
30.Kellner, A. W. A. & de Azevedo, S. A. K. A new sauropod dinosaur (Titanosauria) from the Late Cretaceous of Brazil. Nat. Sci. Mus. Monogr. 15, 111–142 (1999).
Google Scholar 
31.Novas, F. E. et al. Paleontological discoveries in the Chorrillo Formation (upper Campanian-lower Maastrichtian, Upper Cretaceous), Santa Cruz Province, Patagonia, Argentina. Rev. Mus. Argent. Cienc. Nat. 21, 217–293 (2019).
Google Scholar 
32.Wilson, J. A., D’Emic, M. D., Curry Rogers, K. A., Mohabey, D. M. & Sen, S. Reassessment of the sauropod dinosaur Jainosaurus (=“Antarctosaurus”) septentrionalis from the Upper Cretaceous of India. Contrib. Mus. Paleontol. Univ. Mich. 32, 17–40 (2009).
Google Scholar 
33.Powell, J. E. Revision of South American titanosaurid dinosaurs: palaeobiological, palaeobiogeographical and phylogenetic aspects. Rec. Queen Vic. Mus. 111, 1–173 (2003).
Google Scholar 
34.Smith, J. B. et al. A giant sauropod dinosaur from an Upper Cretaceous mangrove deposit in Egypt. Science 292, 1704–1706 (2001).CAS 
PubMed 

Google Scholar 
35.Otero, A. & Vizcaíno, S. F. Hindlimb musculature and function of Neuquensaurus australis (Sauropoda: Titanosauria). Ameghiniana 45, 333–348 (2008).
Google Scholar 
36.von Huene, F. Los saurisquios y ornitisquios del Cretáceo Argentino. Mus. La Plata 3, 1–196 (1929).
Google Scholar 
37.Mannion, P. D. & Otero, A. A reappraisal of the Late Cretaceous Argentinean sauropod dinosaur Argyrosaurus superbus, with a description of a new titanosaur genus. J. Vertebr. Paleontol. 32, 614–638 (2012).
Google Scholar 
38.Mocho, P., Pérez-García, A., Martín Jiménez, M. & Ortega, F. New remains from the Spanish Cenomanian shed light on the Gondwanan origin of European Early Cretaceous titanosaurs. Cretac. Res. 95, 164–190 (2019).
Google Scholar 
39.Díez Díaz, V., Pereda Suberbiola, X. & Sanz, J. L. Appendicular skeleton and dermal armour of the Late Cretaceous titanosaur Lirainosaurus astibiae (Dinosauria: Sauropoda) from Spain. Palaeontol. Electronica 16, 19A (2013).
Google Scholar 
40.Le Loeuff, J. in Thunder-Lizards: The Sauropodomorph Dinosaurs (eds Tidwell, V. & Carpenter, K.) 115–137 (Indiana Univ. Press, 2005).41.Borsuk-Bialynicka, M. A new camarasaurid sauropod Opisthocoelicaudia skarzynskii gen. n., sp. n. from the Upper Cretaceous of Mongolia. Acta Palaeontol. Pol. 37, 5–63 (1977).
Google Scholar 
42.Filippi, L. S., García, R. A. & Garrido, A. A new sauropod titanosaur from the Plottier Formation (Upper Cretaceous) of Patagonia (Argentina). Geol. Acta 9, 1–12 (2011).
Google Scholar 
43.Salgado, L., Coria, R. A. & Calvo, J. O. Evolution of titanosaurid sauropods. I: phylogenetic analysis based on the postcranial evidence. Ameghiniana 34, 3–32 (1997).
Google Scholar 
44.D’Emic, M. D. The early evolution of titanosauriform sauropod dinosaurs. Zool. J. Linn. Soc. 166, 624–671 (2012).
Google Scholar 
45.Tschopp, E. & Mateus, O. Clavicles, interclavicles, gastralia, and sternal ribs in sauropod dinosaurs: new reports from Diplodocidae and their morphological, functional and evolutionary implications. J. Anat. 222, 321–340 (2013).PubMed 

Google Scholar 
46.Wilson, J. A. Sauropod dinosaur phylogeny: critique and cladistic analysis. Zool. J. Linn. Soc. 136, 217–276 (2002).
Google Scholar 
47.Powell, J. E. in Los Dinosaurios y Su Entorno Biótico (eds Sanz, J. L. & Buscalioni, A. D.) 165–230 (Instituto ‘Juan de Valdés’, 1992).48.Otero, A. The appendicular skeleton of Neuquensaurus, a Late Cretaceous saltasaurine sauropod from Patagonia, Argentina. Acta Palaeontol. Pol. 55, 399–426 (2010).
Google Scholar 
49.Gilmore, C. W. Reptilian Fauna of the North Horn Formation of Central Utah Professional Paper 210-C (USGS Numbered Series, 1946).50.Ullmann, P. V. & Lacovara, K. J. Appendicular osteology of Dreadnoughtus schrani, a giant titanosaurian (Sauropoda, Titanosauria) from the Upper Cretaceous of Patagonia, Argentina. J. Vertebr. Paleontol. 36, e1225303 (2016).
Google Scholar 
51.Poropat, S. F. Carl Wiman’s sauropods: the Uppsala Museum of Evolution’s collection. GFF 135, 104–119 (2013).CAS 

Google Scholar 
52.Cerda, I. A., Salgado, L. & Powell, J. E. Extreme postcranial pneumaticity in sauropod dinosaurs from South America. Paläontol. Z. 86, 441–449 (2012).
Google Scholar 
53.Wilson, J. A. & Carrano, M. T. Titanosaurs and the origin of “wide-gauge” trackways: a biomechanical and systematic perspective on sauropod locomotion. Paleobiol. 25, 252–267 (1999).
Google Scholar 
54.Upchurch, P., Barrett, P. & Dodson, P. in The Dinosauria (eds Weishampel, D. B. et al.) 259–324 (Univ. California Press, 2004).55.Lehman, T. M. & Coulson, A. B. A juvenile specimen of the sauropod dinosaur Alamosaurus sanjuanensis from the Upper Cretaceous of Big Bend National Park, Texas. J. Paleontol. 76, 156–172 (2002).
Google Scholar 
56.Gallina, P. A. & Otero, A. Reassessment of Laplatasaurus araukanicus (Sauropoda: Titanosauria) from the Upper Cretaceous of Patagonia, Argentina. Ameghiniana 52, 487–501 (2015).
Google Scholar 
57.Wilson, J. A. & Upchurch, P. Redescription and reassessment of the phylogenetic affinities of Euhelopus zdanskyi (Dinosauria: Sauropoda) from the Early Cretaceous of China. J. Syst. Palaeontol. 7, 199–239 (2009).
Google Scholar 
58.Sereno, P. C. A rationale for phylogenetic definitions, with application to the higher-level taxonomy of Dinosauria. Neues Jahrb. Geol. Paläontol. Abh. 210, 41–83 (1998).
Google Scholar 
59.Chiappe, L. M. et al. Sauropod dinosaur embryos from the Late Cretaceous of Patagonia. Nature 396, 258–261 (1998).CAS 

Google Scholar 
60.Haq, B. U. Cretaceous eustasy revisited. Glob. Planet. Change 113, 44–58 (2014).
Google Scholar 
61.Gheerbrant, E. & Rage, J.-C. Paleobiogeography of Africa: how distinct from Gondwana and Laurasia? Palaeogeogr. Palaeoclimatol. Palaeoecol. 241, 224–246 (2006).
Google Scholar 
62.Canudo, J. I. et al. What Iberian dinosaurs reveal about the bridge said to exist between Gondwana and Laurasia in the Early Cretaceous. Bull. Soc. Géol. Fr. 180, 5–11 (2009).
Google Scholar 
63.Dal Sasso, C., Pierangelini, G., Famiani, F., Cau, A. & Nicosia, U. First sauropod bones from Italy offer new insights on the radiation of Titanosauria between Africa and Europe. Cretac. Res. 64, 88–109 (2016).
Google Scholar 
64.Stein, K. et al. Small body size and extreme cortical bone remodeling indicate phyletic dwarfism in Magyarosaurus dacus (Sauropoda: Titanosauria). Proc. Natl Acad. Sci. USA 107, 9258–9263 (2010).CAS 
PubMed 
PubMed Central 

Google Scholar 
65.Botfalvai, G. et al. ‘X’ marks the spot! Sedimentological, geochemical and palaeontological investigations of Upper Cretaceous (Maastrichtian) vertebrate fossil localities from the Vălioara valley (Densuş-Ciula Formation, Hațeg Basin, Romania). Cretac. Res. 123, 104781 (2021).
Google Scholar 
66.Csiki-Sava, Z. et al. The east side story–the Transylvanian latest Cretaceous continental vertebrate record and its implications for understanding Cretaceous–Paleogene boundary events. Cretac. Res. 57, 662–698 (2016).
Google Scholar 
67.Campione, N. E. & Evans, D. C. A universal scaling relationship between body mass and proximal limb bone dimensions in quadrupedal terrestrial tetrapods. BMC Biol. 10, 60 (2012).PubMed 
PubMed Central 

Google Scholar 
68.González Riga, B. J., Lamanna, M. C., Ortiz David, L. D., Calvo, J. O. & Coria, J. P. A gigantic new dinosaur from Argentina and the evolution of the sauropod hind foot. Sci. Rep. 6, 19165 (2016).PubMed 
PubMed Central 

Google Scholar 
69.Seebacher, F. New method to calculate allometric length–mass relationships of dinosaurs. J. Vertebr. Paleontol. 21, 51–60 (2001).
Google Scholar 
70.Mallison, H. & Wings, O. Photogrammetry in paleontology— a practical guide. J. Paleontol. Tech. 12, 1–31 (2014).
Google Scholar 
71.Matthews, N., Noble, T. & Breithaupt, B. H. in Dinosaur Tracks—The Next Steps (eds Falkingham, P. L. et al.) 28–55 (Indiana Univ. Press, 2016).72.Falkingham, P. L. et al. A standard protocol for documenting modern and fossil ichnological data. Palaeontology 61, 469–480 (2018).
Google Scholar 
73.Huelsenbeck, J. P. & Ronquist, F. MRBAYES: Bayesian inference of phylogeny. Bioinformatics 17, 754–755 (2001).CAS 

Google Scholar 
74.Stadler, T., Kühnert, D., Bonhoeffer, S. & Drummond, A. J. Birth–death skyline plot reveals temporal changes of epidemic spread in HIV and hepatitis C virus (HCV). Proc. Natl Acad. Sci. USA 110, 228–233 (2013).CAS 
PubMed 

Google Scholar 
75.Matzke, N. J. Probabilistic historical biogeography: new models for founder-event speciation, imperfect detection, and fossils allow improved accuracy and model-testing. Front. Biogeogr. 5, 242–248 (2013).
Google Scholar 
76.Ogg, J. G. & Hinnov, L. A. in The Geological Time Scale (eds Gradstein, F. M. et al.) 793–853 (Elsevier, 2012).77.Vianey-Liaud, M., Khosla, A. & Garcia, G. Relationships between European and Indian dinosaur eggshells of the oofamily Megaloolithidae. J. Vertebr. Paleontol. 23, 575–585 (2003).
Google Scholar  More

Comprehensive parks in small towns generally serve the urban residents within a few kilometers of the park. Parks are generally in an area with a large flow of people in a small town15. However, the geographical blockage indicates that the users of parks in small towns are generally of limited educational level, so the investigation process is more complicated. This study adopts a multimethod design with DPOE (diagnostic post-use evaluation) as the main research method, supplemented by the analytic hierarchy process (AHP) and GIS technology, to quantitatively evaluate the current use of comprehensive parks in small cities and towns, and make a decision based on the evaluation results regarding the corresponding optimization and promotion strategy. The research was divided into the following three stages.EvaluateBasis of evaluationBased on the perspective of “human body—movement—space—place—environment”21, stimulation theory and control theory in environmental psychology are used as the main directions for setting up and investigating recreational behaviors. Field investigations were conducted on the current environment, region, culture and other relevant factors of Central Park in Qingkou Town from April to May 2020. The survey covered weekdays, weekends and holidays, sunny/rainy days and mornings and evenings. The main task of the survey was to supervise the development and use of parks in small towns, the number of users, the types of facilities, and the appearance and maintenance of the park22 and to list the problems related to the environment and its ecology, the benefits provided by groups of parks, or the benefits provided to the surrounding enterprises and schools. Especially after the epidemic, residents have had a more active and urgent need for the participation of green space. To cover a wider range of weather and time conditions, data were collected in sequence during the observation period according to a preset scheme for four periods of the day, alternating between two working days and one weekend each week23. Two team members (interviewers) were in contact with tourists at different times in the park from 8 am to 8 pm. In order to minimize selection errors, each respondent was invited to participate in the survey (the targets included adults, children, and adolescents). Elderly people who agreed to participate in the survey were asked about their visit activities and usage behaviors in the park, such as the frequency of visits, distance, and satisfaction with respect to park maintenance, safety, and infrastructure construction24. Finally, the survey requested relevant social demographic information, such as age, highest education level, and marital status (with or without children).Construction of a performance evaluation index system for comprehensive park landscapes in small townsThe evaluation index of the general applicability of small-town parks was established using a field investigation and the combination of the American landscape performance series (LPS)25. The index system was divided into three levels. The first level was the target level, that is, the evaluation index system of the comprehensive landscape performance of small-town parks. The second level was the criterion level, including environmental performance, health performance and economic performance. As the embodiment of the second level, the three-level index layer mainly includes park construction, infrastructure setting, landscape quality, garden atmosphere, and tourist behavior. Considering the accuracy of comprehensive park evaluation in small towns, the three-level index layer was used to obtain 19 related indexes after expert advice and screening20.Questionnaire designSince this study is aimed at parks in small towns and the surrounding residents generally have a low level of education, to obtain more effective data, the questionnaire was in the form of ticking. In terms of content, the questionnaire was divided into two parts. The first part collected basic information about tourists, such as the mode of transportation to the park and visit frequency. Second, there were 19 evaluation index factors. The Likert method was used to evaluate the index26, and the answers each had five levels: very satisfied, satisfied, average, dissatisfied and very dissatisfied.Combination weight analysisSome papers in the past ten years have discussed the limitations of the AHP in dealing with the complexity and uncertainty of evaluation indicators and used fuzzy comprehensive evaluation methods to deal with the problem of uncertainty27,28,29,30. However, the fuzzy evaluation method has gradually been eliminated due to its inability to quickly determine the evaluation content31. Therefore, this study used indicator weights for analysis and evaluation. On the basis of the AHP analytic hierarchy process, the coefficient of variation (CV) is added to the weight of each indicator32. The main purpose of adopting this method is to establish a landscape performance evaluation system for Qingkou Central Park, refer to the satisfaction evaluation of tourists through the DPOE, and determine the content that the park needs to be optimized.SurveyThe places where tourists gather or where tourists are the most often have a certain reference significance for the planning and design of parks. Therefore, collecting data on tourist gathering places is needed in the research process33. An increasing number of studies have pointed to the use of social media to examine users’ daily life behaviors and spatial distribution relationships. Wood et al. attempted to evaluate the access rate of entertainment venues based on the location of photos posted on Flickr34. Hamstead et al. use geolocation data from Flickr and Twitter to assess changes in the use of all parks in New York city35. Because the identification system for comprehensive parks in most small towns is not clear, tourists cannot clearly identify a place to visit or a location they often visit. Therefore, the following attempts were made: (1) A total of 182 points of interest of tourists in Qingkou Central Park were collected through Octopus Aata Collector 8, Six-Feet and other software. (2) The distribution of interest points and on-site observations were used to identify five gathering points that cover most of the park landscape. They were named A, B, C, D and E (Table 1) for fixed video recording. The average weekday traffic and weekend traffic information was obtained. (3) The collected data were imported into Excel for sorting, and the utilization of parks was visually expressed in different time periods through GIS. (4) From May to August 2020, 300 copies of paper questionnaires were distributed at nodes A, B, C, D and E. (5) In addition, the questionnaire content was imported into Excel for simple processing, classification and deletion of duplicate data. (6) Finally, the spatial and temporal distribution results and comprehensive evaluation results of tourists in comprehensive parks in small towns were obtained, and optimization suggestions were summarized.Table 1 Landscape node and application of the Central Park.Full size tableSpatial distribution and experience of respondentsThe behavior track, gathering area and spatial distribution of tourists in the park affect the evaluation of the park. However, due to the different behavioral habits of tourists, some areas of the park will have a crowd gathering effect36. As a result, the use of environmental resources in the park is uneven, resulting in the waste of environmental resources and ecological damage.During the study, to make the data more accurate, a total of six samples were randomly selected from three working days and three weekends from May to July 2020 for data collection. The collection method consisted of five people at five important nodes in the park that basically cover the popular areas (including A. Northeast Main Entrance Square, B. Southwest Main Entrance Square, C. West Secondary Entrance Square, D. Sports Theme Square, and E. Waterfront wooden platform); the sites were filmed from 06:00 to 20:00 (fifteen minutes were taken from 06:00–08:00, 08:00–11:00, 11:00–13:00, 13:00–17:00 and 17:00–20:00 for each time period) to record the activity track of tourists in a day. Then, the average weekday samples and weekend samples were averaged, and the data of the flow of people and the length of stay were processed. The flow of people in the different periods of each node of the two samples was sorted using Excel, and coordinate marks were made on the construction drawings according to the image data to screen out repeated and unreasonable data37,38. Then, ArcGIS was used to perform data visualization (scenic spot heat), and the following conclusions could be drawn: there was a significant difference in the stay time of tourists at different nodes (Fig. 2).Figure 2Schematic diagram of the flow of people in different times and spaces.Full size imageThrough node analysis, it was found that tourists stayed in the park for at least 30 min. Compared with the research process, it took approximately 1 h and 10 min to complete the whole track through the Six-Foot app, which showed that tourists stayed in the park for a longer time. Among them, the passenger flow peaks were during 06:00–08:00, 11:00–13:00 and 17:00–20:00, while the passenger flow was lower at other times. In addition, according to observation and survey data summary, passenger flow was not evenly concentrated among the five node areas6. Overall, node A and node B had a large flow of tourists and a longer stay time. Node D was ranked next, while node C and node E had less traffic and shorter stay times.Overview of respondentsAccording to the POE field survey and questionnaire survey, 292 valid questionnaires (recovery rate 97.3%) were obtained, among which 58.2% (169 persons) were female, slightly higher than the 41.8% (123 persons) that were male. Among them, 40.5% (118 persons) were carrying children under 8 years old. In terms of age, young people between 30 and 39 years old accounted for 43.7% (128 people), most of whom carried children, followed by younger people between 19 and 29 years old and young people between 40 and 49 years old, which fully showed that the urban center where the park is located was dominated by young people. Among the visitors, 71.9% (210 people) were local residents, 18.5% (54 people) were temporary residents, and 9.6% (28 people) were foreign tourists. In terms of how people arrived at the park, most of them came by walking (116 people), accounting for 38.9%, followed by electric vehicles and private cars (61 people each), accounting for 21.6%. Among them, 53% (154 people) chose to come to the park when they were free, and 24% (70 people) came to the park three or four times a week. In the park system of this small town, the public green space served the local residents to a large extent and gradually became a recreational place for the real-time entertainment of nearby residents (Table 2).AHP-CV comprehensive weight analysisThe development of the AHP-CV combined weights has led to a change in the method of determining indicator weights from a single subjectiveness to a comprehensive objectivity39. In order to avoid the evolution of the AHP to a single weighting method, the AHP method is combined with the SW and CV methods here to calculate objective weight, based on the principle of minimum information entropy combining two kinds of weighted information40.

1.

To ensure the reliability of the data, first, check the consistency of the paired comparison matrix:$${text{RC }} = {text{ IC}}/{text{IR}}$$
If RC  More

1.Trivers, R. L. Parent-offspring conflict. Am. Zool. 14, 249–264 (1974).
Google Scholar 
2.Trivers, R. L. Parental investment and sexual selection. In Sexual Selection and the Descent of Man 1871–1971 (ed. Campbell, B.) 136–179 (Routledge, 1972).
Google Scholar 
3.Godfray, H. C. J. Evolutionary theory of parent–offspring conflict. Nature 376, 133–138 (1995).CAS 
PubMed 
ADS 

Google Scholar 
4.Parker, G. A. & Macnair, M. R. Models of parent-offspring conflict. IV. Suppression: Evolutionary retaliation by the parent. Anim. Behav. 27, 1210–1235 (1979).
Google Scholar 
5.Wells, J. C. K. Parent-offspring conflict theory, signaling of need, and weight gain in early life. Q. Rev. Biol. 78, 169–202 (2003).PubMed 

Google Scholar 
6.Godfray, H. C. J. & Johnstone, R. A. Begging and bleating: The evolution of parent-offspring signalling. Philos. Trans. R. Soc. B 355, 1581–1591 (2000).CAS 

Google Scholar 
7.Mock, D. W. & Parker, G. A. Siblicide, family confilct and the evolutionary limits of selfishness. Anim. Behav. 56, 1–10 (1997).
Google Scholar 
8.Wilson, A. J. et al. Selection on mothers and offspring: Whose phenotype is it and does it matter?. Evolution 59, 451–463 (2005).PubMed 

Google Scholar 
9.Janzen, F. J. & Warner, D. A. Parent-offspring conflict and selection on egg size in turtles. J. Evol. Biol. 22, 2222–2230 (2009).CAS 
PubMed 

Google Scholar 
10.Hinde, C. A., Johnstone, R. A. & Kilner, R. M. Parent-offspring conflict and coadaptation. Science 327, 1373–1376 (2010).CAS 
PubMed 
ADS 

Google Scholar 
11.Kölliker, M. et al. Parent-offspring conflict and the genetic trade-offs shaping parental investment. Nat. Commun. 6, 1–8 (2015).
Google Scholar 
12.Kilner, R. M. & Hinde, C. A. Parent–offspring conflict. In The Evolution of Parental Care (eds Royle, N. J. et al.) 119–132 (Oxford University Press, 2012).
Google Scholar 
13.Mas, F. & Kölliker, M. Maternal care and offspring begging in social insects: Chemical signalling, hormonal regulation and evolution. Anim. Behav. 76, 1121–1131 (2008).
Google Scholar 
14.Hale, R. E. & Travis, J. The evolution of developmental dependence, or ‘Why do my kids need me so much?’. Evol. Ecol. Res. 14, 207–221 (2012).
Google Scholar 
15.Gomendio, M. Suckling behaviour and fertility in rhesus macaques (Macaca multatta). J. Zool. 217, 449–467 (1989).
Google Scholar 
16.Hamada, Y., Murata, T., Watanabe, S. & Kanda, I. Inhibitory effect of prolactin on ovulation in the in vitro perfused rabbit ovary. Nature 285, 161–163 (1980).CAS 
PubMed 
ADS 

Google Scholar 
17.Short, R. V. Breast feeding. Sci. Am. 250, 35–41 (1984).CAS 
PubMed 

Google Scholar 
18.Traynor, K. S., Le Conte, Y. & Page, R. E. Age matters: Pheromone profiles of larvae differentially influence foraging behaviour in the honeybee, Apis mellifera. Anim. Behav. 99, 1–8 (2015).
Google Scholar 
19.Maisonnasse, A., Lenoir, J. C., Beslay, D., Crauser, D. & Le Conte, Y. E-β-ocimene, a volatile brood pheromone involved in social regulation in the honey bee colony (Apis mellifera). PLoS ONE 5, 1–7 (2010).
Google Scholar 
20.Capodeanu-Nägler, A., De La Torre, E. R., Eggert, A. K., Sakaluk, S. K. & Steiger, S. Divergent coevolutionary trajectories in parent–ofspring interactions and discrimination against brood parasites revealed by interspecifc cross-fostering. R. Soc. Open Sci. 5, 180819 (2018).
Google Scholar 
21.Smiseth, P. T. & Moore, A. J. Behavioral dynamics between caring males and females in a beetle with facultative biparental care. Behav. Ecol. 15, 621–628 (2004).
Google Scholar 
22.Eggert, A. K. Alternative male mate-finding tactics in burying beetles. Behav. Ecol. 3, 243–254 (1992).
Google Scholar 
23.Pukowski, E. Ökologische untersuchungen an Necrophorus F. Z. Morphol. Ökol. Tiere 27, 518–586 (1933).
Google Scholar 
24.Eggert, A.-K. & Müller, J. K. Biparental care and social evolution in burying beetles: Lessons from the larder. Soc. Behav. Insects Arachn. (1997).25.Royle, N. J., Hopwood, P. E. & Head, M. L. Burying beetles. Curr. Biol. 23, R907 (2013).CAS 
PubMed 

Google Scholar 
26.Scott, M. P. The ecology and behavior of burying beetles. Annu. Rev. Entomol. 43, 595–618 (1998).CAS 
PubMed 

Google Scholar 
27.Arce, A. N., Johnston, P. R., Smiseth, P. T. & Rozen, D. E. Mechanisms and fitness effects of antibacterial defences in a carrion beetle. J. Evol. Biol. 25, 930–937 (2012).CAS 
PubMed 

Google Scholar 
28.Cotter, S. C. & Kilner, R. M. Sexual division of antibacterial resource defence in breeding burying beetles, Nicrophorus vespilloides. J. Anim. Ecol. 79, 35–43 (2010).PubMed 

Google Scholar 
29.Vogel, H. et al. The digestive and defensive basis of carcass utilization by the burying beetle and its microbiota. Nat. Commun. 6, 1–10 (2017).
Google Scholar 
30.Shukla, S. P. et al. Microbiome-assisted carrion preservation aids larval development in a burying beetle. Proc. Natl. Acad. Sci. USA. 115, 11274–11279 (2018).CAS 
PubMed 
PubMed Central 

Google Scholar 
31.Duarte, A., Welch, M., Swannack, C., Wagner, J. & Kilner, R. M. Strategies for managing rival bacterial communities: Lessons from burying beetles. J. Anim. Ecol. 87, 414–427 (2018).PubMed 

Google Scholar 
32.Miller, C. J., Bates, S. T., Gielda, L. M. & CurtisCreighton, J. Examining transmission of gut bacteria to preserved carcass via anal secretions in Nicrophorus defodiens. PLoS ONE 14, 1–13 (2019).
Google Scholar 
33.Suzuki, S. Suppression of fungal development on carcasses the burying beetle Nicrophorus quadripunctatus (Coleoptera: Silphidae). Entomol. Sci. 4, 403–405 (2001).
Google Scholar 
34.Eggert, A. K., Reinking, M. & Müller, J. K. Parental care improves offspring survival and growth in burying beetles. Anim. Behav. 55, 97–107 (1998).CAS 
PubMed 

Google Scholar 
35.Trumbo, S. T. Feeding upon and preserving a carcass: The function of prehatch parental care in a burying beetle. Anim. Behav. 130, 241–249 (2017).
Google Scholar 
36.Smiseth, P. T., Darwell, C. T. & Moore, A. J. Partial begging: An empirical model for the early evolution of offspring signalling. Proc. R. Soc. B Biol. Sci. 270, 1773–1777 (2003).
Google Scholar 
37.Rauter, C. M. & Moore, A. J. Do honest signalling models of offspring solicitation apply to insects?. Proc. R. Soc. B Biol. Sci. 266, 1691–1696 (1999).
Google Scholar 
38.Royle, N. J., Russell, A. F. & Wilson, A. J. The evolution of flexible parenting. Science 345, 776–781 (2014).CAS 
PubMed 
ADS 

Google Scholar 
39.Capodeanu-Nägler, A., Eggert, A. K., Vogel, H., Sakaluk, S. K. & Steiger, S. Species divergence in offspring begging and parental provisioning is linked to nutritional dependency. Behav. Ecol. 29, 42–50 (2018).
Google Scholar 
40.Müller, J. K. Replacement of a lost clutch: A strategy for optimal resource utilization in Necrophorus vespilloides (Coleoptera: Silphidae). Ethology 76, 74–80 (1987).
Google Scholar 
41.Müller, J. K., Braunisch, V., Hwang, W. & Eggert, A. K. Alternative tactics and individual reproductive success in natural associations of the burying beetle, Nicrophorus vespilloides. Behav. Ecol. 18, 196–203 (2007).
Google Scholar 
42.Müller, J. K. & Eggert, A. K. Time-dependent shifts between infanticidal and parental behavior in female burying beetles a mechanism of indirect mother-offspring recognition. Behav. Ecol. Sociobiol. 27, 11–16 (1990).
Google Scholar 
43.Smiseth, P. T. & Parker, H. J. Is there a cost to larval begging in the burying beetle Nicrophorus vespilloides?. Behav. Ecol. 19, 1111–1115 (2008).
Google Scholar 
44.Steiger, S. Bigger mothers are better mothers: Disentangling size-related prenatal and postnatal maternal effects. Proc. R. Soc. B. 280, 1225 (2013).
Google Scholar 
45.Keppner, E. M. et al. Beyond cuticular hydrocarbons: Chemically mediated mate recognition in the subsocial burying beetle Nicrophorus vespilloides. J. Chem. Ecol. 43, 84–93 (2017).CAS 
PubMed 

Google Scholar 
46.Schrader, M. & Galanek, J. Stridulation is unimportant for effective parental care in two species of burying beetle. Ecol. Entomol. 47, 1–18 (2021).
Google Scholar 
47.Curtis Creighton, J., Heflin, N. D. & Belk, M. C. Cost of reproduction, resource quality, and terminal investment in a burying beetle. Am. Nat. 174, 673–684 (2009).PubMed 

Google Scholar 
48.Engel, K. C. et al. A hormone-related female anti-aphrodisiac signals temporary infertility and causes sexual abstinence to synchronize parental care. Nat. Commun. 7, 1–10 (2016).
Google Scholar 
49.Trumbo, S. T. Reproductive benefits of infanticide in a biparental burying beetle Nicrophorus orbicollis. Behav. Ecol. Sociobiol. 27, 269–273 (1990).
Google Scholar 
50.Skinner, S. W. Clutch size as an optimal foraging problem for insects. Behav. Ecol. Sociobiol. 17, 231–238 (1985).
Google Scholar 
51.Lack, D. The significance of clutch-size. Ibis 89, 302–352 (1946).
Google Scholar 
52.Lyon, B. E. Optimal clutch size and conspecific brood parasitism. Nature 392, 380–383 (1998).CAS 
ADS 

Google Scholar 
53.Parker, G. A. & Courtney, S. P. Models of clutch size in insect oviposition. Theor. Popul. Biol. 26, 27–48 (1984).MATH 

Google Scholar 
54.Godfray, H. C. J., Partridge, L. & Harvey, P. H. Clutch size. Annu. Rev. Ecol. Syst. 22, 409–429 (1991).
Google Scholar 
55.Hardy, I. C. W., Griffiths, N. T. & Godfray, H. C. J. Clutch size in a parasitoid wasp: a manipulation experiment. J. Anim. Ecol. 61, 121–129 (1992).
Google Scholar 
56.Zaviezo, T. & Mills, N. Factors influencing the evolution of clutch size in a gregarious insect parasitoid. J. Anim. Ecol. 69, 1047–1057 (2000).
Google Scholar 
57.Bezemer, T. M. & Mills, N. J. Clutch size decisions of a gregarious parasitoid under laboratory and field conditions. Anim. Behav. 66, 1119–1128 (2003).
Google Scholar 
58.Parker, G. A., Royle, N. J. & Hartley, I. R. Intrafamilial conflict and parental investment: a synthesis. Philos. Trans. R. Soc. B 357, 295–307 (2002).
Google Scholar 
59.Godfray, H. C. J. & Parker, G. A. Clutch size, fecundity and parent-offspring conflict. Philos. Trans. R. Soc. Lond. B 332, 67–79 (1991).ADS 

Google Scholar 
60.Alexander, R. D. The evolution of social behavior. Annu. Rev. Ecol. Syst. 5, 325–383 (1974).
Google Scholar 
61.Kilner, R. M. & Hinde, C. A. Information warfare and parent-offspring conflict. Adv. Stud. Behav. 38, 283–336 (2008).
Google Scholar 
62.Kilner, R. M. & Johnstone, R. A. Begging the question: are offspring solicitation behaviours signals of need?. Trends Ecol. Evol. 12, 11–15 (1997).CAS 
PubMed 

Google Scholar 
63.Godfray, H. C. J. Signalling of need by offspring to their parents. Lett. Nat. 352, 328–330 (1991).
Google Scholar 
64.Johnstone, R. A. Begging signals and parent-offspring conflict: Do parents always win?. Proc. R. Soc. B. 263, 1677–1681 (1996).ADS 

Google Scholar 
65.Parker, G. A., Royle, N. J. & Hartley, I. R. Begging scrambles with unequal chicks: Interactions between need and competitive ability. Ecol. Lett. 5, 206–215 (2002).
Google Scholar 
66.Keller, L. & Nonacs, P. The role of queen pheromones in social insects: Queen control or queen signal?. Anim. Behav. 45, 787–794 (1993).
Google Scholar 
67.Kocher, S. D. & Grozinger, C. M. Cooperation, conflict, and the evolution of queen pheromones. J. Chem. Ecol. 37, 1263–1275 (2011).CAS 
PubMed 

Google Scholar 
68.Oi, C. A. et al. The origin and evolution of social insect queen pheromones: Novel hypotheses and outstanding problems. BioEssays 37, 808–821 (2015).CAS 
PubMed 

Google Scholar 
69.Smiseth, P. T. & Moore, A. J. Does resource availability affect offspring begging and parental provisioning in a partially begging species?. Anim. Behav. 63, 577–585 (2002).
Google Scholar 
70.Andrews, C. P. & Smiseth, P. T. Differentiating among alternative models for the resolution of parent-offspring conflict. Behav. Ecol. 24, 1185–1191 (2013).
Google Scholar 
71.Steiger, S., Peschke, K., Francke, W. & Müller, J. K. The smell of parents: Breeding status influences cuticular hydrocarbon pattern in the burying beetle Nicrophorus vespilloides. Proc. R. Soc. B Biol. Sci. 274, 2211–2220 (2007).CAS 

Google Scholar 
72.Steiger, S., Franz, R., Eggert, A. K. & Müller, J. K. The Coolidge effect, individual recognition and selection for distinctive cuticular signatures in a burying beetle. Proc. R. Soc. B Biol. Sci. 275, 1831–1838 (2008).
Google Scholar 
73.Chemnitz, J., Jentschke, P. C., Ayasse, M. & Steiger, S. Beyond species recognition: somatic state affects long-distance sex pheromone communication. Proc. R. Soc. B 282, 1–9 (2015).CAS 

Google Scholar 
74.Steiger, S. Recognition and family life: Recognition mechanisms in the biparental burying beetle. in Social Recognition in Invertebrates: The Knowns and the Unknowns (eds. Aquiloni, L. & Tricarico, E.) 249–266 (2015).75.Takata, M., Mitaka, Y., Steiger, S. & Mori, N. A parental volatile pheromone triggers offspring begging in a burying beetle. Science 19, 1260–1278 (2019).
Google Scholar 
76.Mäenpää, M. I. & Smiseth, P. T. Resource allocation is determined by both parents and offspring in a burying beetle. J. Evol. Biol. 33(11), 1567–1578 (2020).PubMed 
PubMed Central 

Google Scholar 
77.Mattey, S. N., Richardson, J., Ratz, T. & Smiseth, P. T. Effects of offspring and parental inbreeding on parent-offspring communication. Am. Nat. 191, 716–725 (2018).PubMed 

Google Scholar 
78.Steiger, S. & Stökl, J. Pheromones regulating reproduction in subsocial beetles: insights with references to eusocial insects. J. Chem. Ecol. 44, 785–795 (2018).CAS 
PubMed 

Google Scholar 
79.Haig, D. Genetic conflict in human pregnancy. Q. Rev. Biol. 68, 495–532 (1993).CAS 
PubMed 

Google Scholar 
80.Paquet, M., Drummond, H. & Smiseth, P. T. Offspring are predisposed to beg more towards females in the burying beetle Nicrophorus vespilloides. Anim. Behav. 141, 195–201 (2018).
Google Scholar 
81.Sakaluk, S. K., Eggert, A.-K. & Müller, J. K. The ‘widow effect’ and its consequences for reproduction in burying beetles, Nicrophorus vespilloides (Coleoptera: Silphidae). Ethology 104, 553–564 (1998).
Google Scholar 
82.De Gasperin, O., Duarte, A., Troscianko, J. & Kilner, R. M. Fitness costs associated with building and maintaining the burying beetle’s carrion nest. Sci. Rep. 6, 1–6 (2016).
Google Scholar 
83.Bartlett, J. Male mating success and paternal care in Nicrophorus vespilloides (Coleoptera: Silphidae). Behav. Ecol. Sociobiol. 23, 297–303 (1988).
Google Scholar 
84.Müller, J. K., Eggert, A. K. & Sakaluk, S. K. Carcass maintenance and biparental brood care in burying beetles: are males redundant?. Ecol. Entomol. 23, 195–200 (1998).
Google Scholar 
85.Smiseth, P. T., Dawson, C., Varley, E. & Moore, A. J. How do caring parents respond to mate loss? Differential response by males and females. Anim. Behav. 69, 551–559 (2005).
Google Scholar 
86.Parker, D. J. et al. Transcriptomes of parents identify parenting strategies and sexual conflict in a subsocial beetle. Nat. Commun. 6, 1–10 (2015).CAS 

Google Scholar 
87.Keppner, E. M., Ayasse, M. & Steiger, S. Contribution of males to brood care can compensate for their food consumption from a shared resource. Ecol. Evol. 10, 3535–3543 (2020).PubMed 
PubMed Central 

Google Scholar 
88.Schedwill, P., Paschkewitz, S., Teubner, H. & Steinmetz, N. From the host’ s point of view: Effects of variation in burying beetle brood care and brood size on the interaction with parasitic mites. Plosone 15, 1–14 (2020).
Google Scholar 
89.Pilakouta, N., Hanlon, E. J. H. & Smiseth, P. T. Biparental care is more than the sum of its parts: Experimental evidence for synergistic effects on offspring fitness. Proc. R. Soc. B. 285, 875 (2018).
Google Scholar 
90.Chemnitz, J., Bagrii, N., Ayasse, M. & Steiger, S. Staying with the young enhances the fathers’ attractiveness in burying beetles. Evolution 71, 985–994 (2017).PubMed 

Google Scholar  More

1.Cardinale, B. et al. Biodiversity loss and its impact on humanity. Nature 486, 59–67 (2012).ADS 
CAS 
PubMed 

Google Scholar 
2.Kouba, A., Petrusek, A. & Kozák, P. Continental-wide distribution of crayfish species in Europe: Update and maps. Knowl. Manag. Aquat. Ecosyst. 413, 05. https://doi.org/10.1051/kmae/2014007 (2014).Article 

Google Scholar 
3.Chucholl, C. The bad and the super-bad: Prioritising the threat of six invasive alien to three imperilled native crayfishes. Biol. Invasions 18, 1967–1988 (2016).
Google Scholar 
4.Richman, N. I. et al. Multiple drivers of decline in the global status of freshwater crayfish (Decapoda: Astacidea). Phil. Trans. R. Soc. B. 370, 20140060. https://doi.org/10.1098/rstb.2014.0060 (2015).Article 
PubMed 
PubMed Central 

Google Scholar 
5.Jussila, J., Edsman, L., Maguire, I., Diéguez-Uribeondo, J. & Theissinger, K. Money kills native ecosystems: European crayfish as an example. Front. Ecol. Evol. (2021) (accepted).6.Maguire, I. et al. Recent changes in distribution pattern of freshwater crayfish in Croatia—Threats and perspectives. Knowl. Manag. Aquatic Ecosyst. 409, 2. https://doi.org/10.1051/kmae/2017053 (2018).Article 

Google Scholar 
7.Schrimpf, A. et al. Phylogeography of noble crayfish (Astacus astacus) reveals multiple refugia. Freshw. Biol. 59, 761–776 (2014).CAS 

Google Scholar 
8.Laggis, A. et al. Microevolution of the noble crayfish (Astacus astacus) in the Southern Balkan Peninsula. BMC Evol. Biol. 17, 122. https://doi.org/10.1186/s12862-017-0971-6 (2017).Article 
PubMed 
PubMed Central 

Google Scholar 
9.Gross, R. et al. Genetic diversity and structure of the noble crayfish populations in the Balkan Peninsula revealed by mitochondrial and microsatellite DNA markers. PeerJ 9, 11838. https://doi.org/10.7717/peerj.11838 (2021).Article 

Google Scholar 
10.Gross, R. et al. Microsatellite markers reveal clear geographic structuring among threatened noble crayfish (Astacus astacus) populations in Northern and Central Europe. Conserv. Genet. 14, 809–821 (2013).CAS 

Google Scholar 
11.Schrimpf, A. et al. Genetic characterization of Western European noble crayfish populations (Astacus astacus) for advanced conservation management strategies. Conserv. Genet. 18, 1299–1315 (2017).CAS 

Google Scholar 
12.Edsman, L., Füreder, L., Gherardi, F. & Souty-Grosset, C. Astacus astacus. in IUCN 2010, IUCN Red List of Threatened Species. http://www.iucnredlist.org (2010).13.Gottstein, S. et al. Red List of Freshwater and Brackish Water Crustaceans of Croatia. (State Institute for Nature Protection, 2011).14.Lowe, S., Browne, M., Boudjelas, S. & De Poorter, M. 100 of the World’s Worst Invasive Alien Species: A Selection from the Global Invasive Species Database. (The Invasive Species Specialist Group (ISSG) a specialist group of the Species Survival Commission (SSC) of the World Conservation Union (IUCN), 2000).15.Dragičević, P., Faller, M., Kutleša, P. & Hudina, S. Update on the signal crayfish, Pacifastacus leniusculus (Dana, 1852) range expansion in Croatia: A 10-year report. BioInvasions Rec. 9, 793–807 (2020).
Google Scholar 
16.Dobrović, A., Maguire, I., Boban, M., Grbin, D. & Hudina, S. Reproduction dynamics of the marbled crayfish Procambarus virginalis Lyko, 2017 from an anthropogenic lake in northern Croatia. Aquat. Invasions 16, 482–498 (2021).
Google Scholar 
17.Lovrenčić, L. et al. New insights into the genetic diversity of the stone crayfish: Taxonomic and conservation implications. BMC Evol. Biol. 20, 146. https://doi.org/10.1186/s12862-020-01709-1 (2020).Article 
PubMed 
PubMed Central 

Google Scholar 
18.Eizaguirre, C. & Baltazar-Soares, M. Evolutionary conservation—Evaluating the adaptive potential of species. Evol. Appl. 7, 963–967 (2014).PubMed Central 

Google Scholar 
19.Ricciardi, A. & Simberloff, D. Assisted colonization is not a viable conservation strategy. Trends Ecol. Evol. 24, 248–253 (2009).PubMed 

Google Scholar 
20.Hewitt, N. et al. Taking stock of the assisted migration debate. Biol. Conserv. 144, 2560–2572 (2011).
Google Scholar 
21.Butt, N. et al. Importance of species translocations under rapid climate change. Biol. Conserv. 35, 775–783 (2021).
Google Scholar 
22.Abdul-Muneer, P. M. Application of microsatellite markers in conservation genetics and fisheries management: Recent advances in population structure analysis and conservation strategies. Genet. Res. Int. https://doi.org/10.1155/2014/691759 (2014).Article 
PubMed 
PubMed Central 

Google Scholar 
23.Bláha, M., Žurovcová, M., Kouba, A., Policar, T. & Kozák, P. Founder event and its effect on genetic variation in translocated populations of noble crayfish (Astacus astacus). J. Appl. Genet. 57, 99–106 (2016).PubMed 

Google Scholar 
24.Panicz, R. et al. Genetic diversity in natural populations of noble crayfish (Astacus astacus L.) in north-western Poland on the basis of combined SSR and AFLP data. PeerJ 7, 7301. https://doi.org/10.7717/peerj.7301 (2019).Article 

Google Scholar 
25.Guisan, A. et al. Predicting species distributions for conservation decisions. Ecol. Lett. 16, 1424–1435 (2013).PubMed 
PubMed Central 

Google Scholar 
26.Markovic, D. et al. Europe’s freshwater biodiversity under climate change: Distribution shifts and conservation needs. Divers. Distrib. 20, 1097–1107 (2014).
Google Scholar 
27.Jiménez-Valverde, A. et al. Use of niche models in invasive species risk assessments. Biol. Invasions 13, 2785–2797 (2011).
Google Scholar 
28.Guisan, A., Petitpierre, B., Broennimann, O., Daehler, C. & Kueffer, C. Unifying niche shift studies: Insights from biological invasions. Trends Ecol. Evol. 29, 260–269 (2014).PubMed 

Google Scholar 
29.Chucholl, C. Niche-based species distribution models and conservation planning for endangered freshwater crayfish in south-western Germany. Aquat. Conserv. 27, 698–705 (2017).
Google Scholar 
30.Préau, C. et al. Niche modelling to guide conservation actions in France for the endangered crayfish Austropotamobius pallipes in relation to the invasive Pacifastacus leniusculus. Freshw. Biol. 65, 304–315 (2020).
Google Scholar 
31.Parmesan, C. Ecological and evolutionary responses to recent climate change. Annu. Rev. Ecol. Evol. Syst. 37, 637–669 (2006).
Google Scholar 
32.Pecl, G. T. et al. Biodiversity redistribution under climate change: Impacts on ecosystems and human well-being. Science 355, eaai9214. https://doi.org/10.1126/science.aai9214 (2017).CAS 
Article 
PubMed 

Google Scholar 
33.Kouba, A. et al. The significance of droughts for hyporheic dwellers: Evidence from freshwater crayfish. Sci. Rep. 6, 1–7 (2016).
Google Scholar 
34.Capinha, C., Larson, E. R., Tricarico, E., Olden, J. D. & Gherardi, F. Effects of climate change, invasive species, and disease on the distribution of native European crayfishes. Conserv. Biol. 27, 731–740 (2013).PubMed 

Google Scholar 
35.Chapuis, M. P. & Estoup, A. Microsatellite null alleles and estimation of population differentiation. Mol. Biol. Evol. 24, 621–631 (2007).CAS 
PubMed 

Google Scholar 
36.Hanley, J. A. & McNeil, B. J. The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology 143, 29–36 (1982).CAS 

Google Scholar 
37.Araújo, M. B., Pearson, R. G., Thuiller, W. & Erhard, M. Validation of species–Climate impact models under climate change. Glob. Chang. Biol. 11, 1504–1513 (2005).ADS 

Google Scholar 
38.Swets, J. A. Measuring the accuracy of diagnostic systems. Science 240, 1285–1293 (1988).ADS 
MathSciNet 
CAS 
MATH 

Google Scholar 
39.Maguire, I. et al. Two distinct evolutionary lineages of the Astacus leptodactylus species-complex (Decapoda: Astacidae) inferred by phylogenetic analyses. Invertebr. Syst. 28, 117–123 (2014).
Google Scholar 
40.Akhan, S., Bektas, Y., Berber, S. & Kalayci, G. Population structure and genetic analysis of narrow-clawed crayfish (Astacus leptodactylus) populations in Turkey. Genetica 142, 381–395 (2014).PubMed 

Google Scholar 
41.Jelić, M. et al. Insights into the molecular phylogeny and historical biogeography of the white-clawed crayfish (Decapoda, Astacidae). Mol. Phylogenet. Evol. 103, 26–40 (2016).PubMed 

Google Scholar 
42.Bláha, M. et al. Genetic diversity, phylogenetic position and morphometric analysis of Astacus colchicus (Decapoda, Astacidae): A new insight into Eastern European crayfish fauna. Integr. Zool. 16, 368–378 (2021).PubMed 

Google Scholar 
43.Hewitt, G. M. Genetic consequences of climatic oscillations in the Quaternary. Philos. Trans. R. Soc. Lond. B. Biol. Sci. 359, 183–195 (2004).CAS 
PubMed 
PubMed Central 

Google Scholar 
44.Maguire, I., Špoljarić, I. & Klobučar, G. The indigenous crayfish of Plitvice Lakes National Park, Croatia. Freshw. Crayfish 19, 91–96 (2013).
Google Scholar 
45.Njegovan, V., Orešković, M., Hudina, S. & Maguire, I. Crayfish fauna of the Maksimir lakes in the urban area of Zagreb. Freshw. Crayfish 23, 1–11 (2017).
Google Scholar 
46.Allendorf, F. W. & Luikart, G. Conservation and the Genetics of Populations (Blackwell Publishing, 2007).47.Frankham, R. Stress and adaptation in conservation genetics. J. Evol. Biol. 18, 750–755 (2005).CAS 
PubMed 

Google Scholar 
48.Karaman, S. Die Potamobiiden Jugoslaviens. Glas. Zemalj. Muz. Bosne Herceg. 41, 147–150 (1929).
Google Scholar 
49.Myers, N., Mittermeier, R. A., Mittermeier, C. G., da Fonseca, G. A. B. & Kent, J. Biodiversity hotspots for conservation priorities. Nature 403, 853–858 (2000).ADS 
CAS 
PubMed 

Google Scholar 
50.Tierno de Figueroa, J. M. et al. Freshwater biodiversity in the rivers of the Mediterranean Basin. Hydrobiologia 719, 137–186 (2013).
Google Scholar 
51.Barnett, Z. C., Adams, S. B., Ochs, C. A. & Garrick, R. C. Crayfish populations genetically fragmented in streams impounded for 36–104 years. Freshw. Biol. 65, 768–785 (2020).
Google Scholar 
52.Hossain, M. A. et al. Assessing the vulnerability of freshwater crayfish to climate change. Divers. Distrib. 24, 1830–1843 (2018).
Google Scholar 
53.Piyapong, C., Tattoni, C., Ciolli, M., Dembski, S. & Paradis, E. Modelling the geographical distributions of one native and two introduced species of crayfish in the French Alps. Ecol. Inform. 60, 101172. https://doi.org/10.1016/j.ecoinf.2020.101172 (2020).Article 

Google Scholar 
54.Gallardo, B. & Aldridge, D. C. Evaluating the combined threat of climate change and biological invasions on endangered species. Biol. Conserv. 160, 225–233 (2013).
Google Scholar 
55.Peterson, K. & Bode, M. Using ensemble modeling to predict the impacts of assisted migration on recipient ecosystems. Conserv. Biol. 35, 678–687 (2021).PubMed 

Google Scholar 
56.Rodríguez-Rey, M., Consuegra, S., Börger, L. & Garcia de Leaniz, C. Improving species distribution modelling of freshwater invasive species for management applications. PLoS ONE 14, 0217896. https://doi.org/10.1371/journal.pone.0217896 (2019).CAS 
Article 

Google Scholar 
57.Elith, J., Kearney, M. & Phillips, S. The art of modelling range-shifting species. Methods Ecol. Evol. 1, 330–342 (2010).
Google Scholar 
58.Zhang, Z. et al. Impacts of climate change on the global potential distribution of two notorious invasive crayfishes. Freshw. Biol. 65, 353–365 (2020).
Google Scholar 
59.Olden, J. D., Kennard, M. J., Lawler, J. J. & Poff, N. L. Challenges and opportunities in implementing managed relocation for conservation of freshwater species. Conserv. Biol. 25, 40–47 (2011).PubMed 

Google Scholar 
60.Weeks, A. R. et al. Assessing the benefits and risks of translocations in changing environments: A genetic perspective. Evol. Appl. 4, 709–725 (2011).PubMed 
PubMed Central 

Google Scholar 
61.Aitken, S. N. & Whitlock, M. C. Assisted gene flow to facilitate local adaptation to climate change. Annu. Rev. Ecol. Evol. Syst. 44, 367–388 (2013).
Google Scholar 
62.Frankham, R. et al. Genetic Management of Fragmented Animal and Plant Populations. Oxford University Press, 2017).63.Schiffers, K., Bourne, E. C., Lavergne, S., Thuiller, W. & Travis, J. M. Limited evolutionary rescue of locally adapted populations facing climate change. Philos. Trans. R. Soc. B. 368, 20120083. https://doi.org/10.1098/rstb.2012.0083 (2013).Article 

Google Scholar 
64.Bucharova, A. Assisted migration within species range ignores biotic interactions and lacks evidence. Restor. Ecol. 25, 14–18 (2017).
Google Scholar 
65.Ghia, D. et al. Modelling environmental niche for the endangered crayfish Austropotamobius pallipes complex in northern and central Italy. Freshw. Crayfish 19, 189–195 (2013).
Google Scholar 
66.Simon, C. et al. Evolution, weighting, and phylogenetic utility of mitochondrial gene sequences and a compilation of conserved polymerase chain reaction primers. Ann. Entomol. Soc. Am. 87, 651–701 (1994).CAS 

Google Scholar 
67.Folmer, O., Black, M., Hoeh, W., Lutz, R. & Vrijenhoek, R. DNA primers for amplification of mitochondrial cytochrome c oxidase subunit I from diverse metazoan invertebrates. Mol. Mar. Biol. Biotechnol. 3, 294–299 (1994).CAS 
PubMed 

Google Scholar 
68.Mrugała, A., Šanda, R., Shumka, S. & Vukić, J. Filling the blank spot: First report on the freshwater crayfish distribution in Albania. Knowl. Manag. Aquat. Ecosyst. 418, 34. https://doi.org/10.1051/kmae/2017024 (2017).Article 

Google Scholar 
69.Hall, T. A. BioEdit: a user-friendly biological sequence alignment editor and analysis program for Windows 95/98/NT. Nucleic Acids Symp. Ser. 41, 95–98 (1999).CAS 

Google Scholar 
70.Villesen, P. FaBox: An online toolbox for fasta sequences. Mol. Ecol. Notes 7, 965–968 (2007).CAS 

Google Scholar 
71.Bandelt, H. J., Forster, P. & Röhl, A. Median-joining networks for inferring intraspecific phylogenies. Mol. Biol. Evol. 16, 37–48 (1999).CAS 
PubMed 

Google Scholar 
72.Leigh, J. W. & Bryant, D. POPART: Full-feature software for haplotype network construction. Methods Ecol. Evol. 6, 1110–1116 (2015).
Google Scholar 
73.Posada, D. & Crandall, K. A. Intraspecific gene genealogies: Trees grafting into networks. Trends Ecol. Evol. 16, 37–45 (2001).CAS 
PubMed 

Google Scholar 
74.Gross, R., Kõiv, K., Pukk, L. & Kaldre, K. Development and characterization of novel tetranucleotide microsatellite markers in the noble crayfish (Astacus astacus) suitable for highly multiplexing and for detecting hybrids between the noble crayfish and narrow-clawed crayfish (A. leptodactylus). Aquaculture 472, 50–56 (2017).CAS 

Google Scholar 
75.Van Oosterhout, C., Hutchinson, W. F., Wills, D. P. M. & Shipley, P. MICRO-CHECKER: Software for identifying and correcting genotyping errors in microsatellite data. Mol. Ecol. Notes 4, 535–538 (2004).
Google Scholar 
76.Rousset, F. genepop’007: A complete reimplementation of the GENEPOP software for Windows and Linux. Mol. Ecol. Resour. 8, 103–106 (2008).PubMed 

Google Scholar 
77.Dempster, A. P., Laird, N. M. & Rubin, D. B. Maximum likelihood from incomplete data via the EM algorithm. J. R. Stat. Soc. Series. B. Stat. Methodol. 39, 1–38 (1977).MathSciNet 
MATH 

Google Scholar 
78.Peakall, R. & Smouse, P. E. GenAlEx 6.5: Genetic analysis in Excel. Population genetic soft-ware for teaching and research—An update. Bioinformatics 28, 2537–2539 (2012).CAS 
PubMed 
PubMed Central 

Google Scholar 
79.Goudet, J. FSTAT version 2. 9. 4: A program to estimate and test population genetics parameters. Updated from Goudet [1995]. http://www.unil.ch/izea/softwares/fstat.html (2003).80.Kalinowski, S. T. hp‐rare 1.0: A computer program for performing rarefaction on measures of allelic richness. Mol. Ecol. Notes 5, 187–189 (2005).81.Piry, S., Luikart, G. & Cornuet, J.-M. BOTTLENECK: A computer program for detecting recent reductions in the effective population size using allele frequency data. J. Hered. 90, 502–503 (1999).
Google Scholar 
82.Pritchard, J. K., Stephens, M. & Donnelly, P. Inference of population structure using multilocus genotype data. Genetics 155, 945–959 (2000).CAS 
PubMed 
PubMed Central 

Google Scholar 
83.Evanno, G., Regnaut, S. & Goudet, J. Detecting the number of clusters of individuals using the software STRUCTURE—A simulation study. Mol. Ecol. 14, 2611–2620 (2005).CAS 
PubMed 

Google Scholar 
84.Earl, D. A. & Von Holdt, B. M. STRUCTURE HARVESTER: A website and program for visualizing STRUCTURE output and implementing the Evanno method. Conserv. Genet. Resour. 4, 359–361 (2012).
Google Scholar 
85.Kopelman, N. M., Mayzel, J., Jakobsson, M., Rosenberg, N. A. & Mayrose, I. Clumpak: A program for identifying clustering modes and packaging population structure inferences across K. Mol. Ecol. Resour. 15, 1179–1191 (2015).CAS 
PubMed 
PubMed Central 

Google Scholar 
86.Excoffier, L. & Lischer, H. E. L. Arlequin suite ver 3.5: A new series of programs to perform population genetics analyses under Linux and Windows. Mol. Ecol. Resour. 10, 564–567 (2010).PubMed 

Google Scholar 
87.Hijmans, R. J., Cameron, S. E., Parra, J. L., Jones, P. G. & Jarvis, A. Very high resolution interpolated climate surfaces for global land areas. Int. J. Climatol. 25, 1965–1978 (2005).
Google Scholar 
88.Naimi, B., Hamm, N. A., Groen, T. A., Skidmore, A. K. & Toxopeus, A. G. Where is positional uncertainty a problem for species distribution modelling?. Ecography 37, 191–203 (2014).
Google Scholar 
89.Thuiller, W., Lafourcade, B., Engler, R. & Araújo, M. B. BIOMOD—A platform for ensemble forecasting of species distributions. Ecography 32, 369–373 (2009).
Google Scholar 
90.Thuiller, W., Georges, D., Engler, R. & Breiner, F. ‘biomod2’: Ensemble Platform for Species Distribution Modeling. (2016).91.Guisan, A., Thuiller, W. & Zimmermann, N. E. Habitat Suitability and Distribution Models: With Applications in R. (Cambridge University Press, 2017).92.McSweeney, C. F., Jones, R. G., Lee, R. W. & Rowell, D. P. Selecting CMIP5 GCMs for downscaling over multiple regions. Clim. Dyn. 44, 3237–3260 (2015).
Google Scholar 
93.Cvitanović, M., Blackburn, G. A. & Jepsen, M. R. Characteristics and drivers of forest cover change in the post-socialist era in Croatia: Evidence from a mixed-methods approach. Reg. Environ. Change 16, 1751–1763 (2016).
Google Scholar 
94.Thuiller, W., Guéguen, M., Renaud, J., Karger, D. N. & Zimmermann, N. E. Uncertainty in ensembles of global biodiversity scenarios. Nat. Commun. 10, 1446. https://doi.org/10.1038/s41467-019-09519-w (2019).ADS 
CAS 
Article 
PubMed 
PubMed Central 

Google Scholar 
95.Liu, C., White, M. & Newell, G. Selecting thresholds for the prediction of species occurrence with presence only data. J. Biogeogr. 40, 778–789 (2013).
Google Scholar  More

Model frameworkThe capture-recapture model applied here is the hierarchical model for stratified populations proposed by Royle et al.48. The model aims to estimate local population size or community structure49 using capture-recapture data from multiple independent locations. In the following, we briefly describe the model in our context, including addressing heterogeneity in detection probability.Let us consider that we establish S independent camera stations in a survey area. Then, we install K camera traps at each station to monitor exactly the same focal area (totally S × K camera traps will be used). We assume that these camera traps detect animals within the focal areas NT times in total. For animal pass i (i = 1, 2, 3, …, NT), we will obtain (1) at the station where the animal is detected (hereafter station identity; gi), and (2) how many of the K cameras at the station were successful in detecting the animal pass (hereafter detection history; yi). The hierarchal capture-recapture model uses these two data, gi and yi.Let the number of the animal passes at station s be Ns (s = 1, 2, 3, …, S). Then, we assume that Ns follows a Poisson distribution with a parameter λ. In this case, the probability of passage i occurring at station s is expected to be (frac{lambda }{lambda times S}). Thus, station identity, gi, can be modelled as follows:$$g_{i} sim {text{ Categorical}}; left(frac{lambda }{lambda times S}right)$$
When the number of the animal passes at station s, Ns, may have larger variation than expected from the Poisson case, we may assume a negative binomial distribution model or may give a random effect to the parameter of the Poisson distribution at the camera station level.The detection history Y with elements yi can be modelled using a data augmentation procedure47. Specifically, the original detection Y is artificially augmented by many M – n passes with all-zero histories (i.e. not detected by any camera). The augmented data W with elements wi (y1, y2…yNT, 0, 0, … 0) will consist of the passage that occurred but was not detected by any camera (false zero), which occurs with probability ψ, and the passage that did not occur (structural zeros) with the probability 1 − ψ. A set of latent augmentation binary variables, z1, z2, … zM, is introduced, which denotes the false zero (z = 1) and the structural zero (z = 0). That is$$z_{i} sim {text{ Bernoulli }}left( psi right).$$The elements of the augmented data, wi, can be modelled conditional on the latent variables zi. There would be two alternative approaches to modelling the wi.The simplest one may regard wi as random binomial variables. That is$$w_{i} |z_{i} = , 1sim {text{ Binomial }}left( {K,p} right)$$When accounting for the heterogeneity of detection among animal passes, it can be accommodated using a beta distribution as follows;$$w_{i} |z_{i} = , 1sim {text{ Binomial }}left( {K,p_{i} } right)$$$$p_{i} sim {text{ Beta}}left( {alpha ,beta } right)$$The expected detection probability can be derived from (widehat{alpha }/(widehat{alpha }+widehat{beta })) and the correlation coefficients can be calculated by (1/(widehat{alpha }+widehat{beta }+1)).Alternatively, we can regard wi as a categorical variable that takes values from zero to K.$$w_{i} sim {text{ Categorical }}left( pi right)$$
where π is a probability vector of length K + 1. For simplicity, let us consider two camera traps installed at each station, and those cameras have equal detection probability. Then, wi can take either 0 (i.e. zi = 0 or both camera traps missed animals with conditional on zi = 1), 1 (i.e. only one camera trap detected animals with conditional on zi = 1), or 2 (i.e. both camera traps detected animals with conditional on zi = 1). Thus, when we define the probability that wi takes 0, 1, 2 with conditional on zi = 1, as φm (m = 1, 2, 3), the elements of π is equal to {zi × φ0 + (1 − zi)}, {zi × φ1}, {zi × φ2}, respectively.We then take different modelling approaches depending on whether detection probability among animal passes is heterogeneous or not. When two camera traps at a station detect animals independently with the same probability ρ, φ0, φ1, and φ2 can be expressed as a function of ρ, i.e. (1 − ρ)2, 2 × ρ × (1 − ρ)2, ρ2, respectively (Clare et al.47). On the other hand, when detections by the two camera traps are correlated, we need to estimate three real parameters φm that designate the probabilities of all outcomes wi|zi = 1. We assume that ρm follows the Dirichlet distribution with the parameter γm (m = 1, 2, 3). That is$$varphi_{m} sim {text{ Dirichlet}}left( {gamma_{1} ,gamma_{2} , , gamma_{3} } right)$$In this approach, the expected detection probability can be derived from ({widehat{varphi }}_{1}/2+{widehat{varphi }}_{2}) and the correlation coefficients can be calculated by ({widehat{varphi }}_{2}-{({widehat{varphi }}_{1}/2+{widehat{varphi }}_{2})}^{2}).Compared to the beta-binomial distribution approach, the approach using categorical-Dirichlet distribution might be more flexible in accommodating detection heterogeneity while it might be more challenging to estimate the model parameters. In either approach, the expected total number of animal passes can be expressed as (lambda times S). Thus, ψ can be fixed as follows:$$psi = frac{lambda times S}{M}$$For more details of the models, see Royle et al.48 and Clare et al.44.Testing the effectiveness of the hierarchical capture-recapture modelWe performed Monte Carlo simulations to evaluate the effectiveness of the hierarchical capture-recapture model. Because the model reliability has been confirmed well48, we here focused on the effects of heterogeneity in detection probability on the accuracy and precision of the estimates.We assumed that the number of detections by camera traps followed a negative binomial distribution with a mean of 5.0 and dispersion parameter 1.27, which derived the actual data on an ungulate in African rainforests34. We also assumed two camera traps each at 30 stations (i.e. 60 camera traps in total). We generated detection histories (i.e. the number of camera traps successfully detecting animals in each animal passage) using a beta-binomial distribution with the expected detection probability at 0.8 or 0.4. We varied the correlation coefficients (= 1/(α + β + 1)), from 0.1 to 0.5 in 0.1 increments. The scale parameters of the beta distributions for each scenario are shown in Table 1. Additionally, to determine the effects of sample sizes on the accuracy and precision of estimates, we increased the number of camera stations at 100. Since this setting requires much computation time, we only assumed a detection probability of 0.4 and a correlation coefficient of 0.3.We estimated the parameters of the hierarchical capture-recapture models assuming a beta-binomial distribution and a categorical-Dirichlet distribution using the Markov chain Monte Carlo (MCMC) implemented in JAGS (version 3.4.0) in all the simulations. We assumed that the number of animal passes followed a negative binomial distribution. For the model assuming a beta-binomial distribution, we transformed the scale parameters, α and β as p*phi and p*(1 − phi), respectively (p is an expected detection probability). Then we used a weakly informative prior (gamma distribution with shape = 10 and rate = 2) for phi and a non-informative uniform distribution from 0 to 1 for the detection probability49. For the model assuming a categorical-Dirichlet distribution, the Dirichlet prior distribution was induced by treating each γm ~ Gamma(1, 1) and calculating each probability by ({varphi }_{m}={{gamma }_{m}}/{sum }_{m=1}^{M}{gamma }_{m}) followingv and Clare et al.44. We generated three chains of 3000 iterations after a burn-in of 1000 and thinned by 5. The convergence of models was determined using the Gelman–Rubin statistic, where values  More

Timeseries imaging tracks gene expression in spatial systemsRecent studies have shown it possible to identify the members of microbial consortia as well as their gene expression within spatially-structured systems30,33,34. However, these methods capture data cross-sectionally and are unable to provide temporal insight into gene expression patterning as it emerges in these cell populations. To bridge this gap, we built a fluorescent imager inside an incubator (Supplementary Fig. 1). Our framework characterizes cellular growth and gene expression in spatially-structured environments with previously unattainable time-resolution and throughput. Fluorescently labeled cells are illuminated using LEDs connected to a custom-built control system (see methods). The images are background corrected and analyzed, tracking colony growth and gene expression information (Supplementary Figs. 2, 3) straight from the spatially-structured system.In our experiments, we utilized a dual-labeled P. aeruginosa PA14 strain harboring PBad-DsRed(EC2)35 driven by L-arabinose in the plate media, which cannot be metabolized by the cells36, and PrhlAB-GFP28,37. When grown in spatial structure, the constitutive expression of DsRed provided a measure of the local density of bacteria (Supplementary Fig. 4). In all our experiments, the dynamical expression of GFP, validated by RT-qPCR (Supplementary Fig. 5) (see methods), reported on the expression of rhlAB.Using these data, we were able to characterize how the surroundings experienced by these microbes influence the dynamics of their cooperative behavior directly in a spatially-structured setting.Rhamnolipid production differs in liquid and spatial environmentsRhamnolipids are necessary for cooperative swarming behavior in P. aeruginosa and for other traits related to virulence26. Rhamnolipids can be produced in liquid culture10,20,28,38, thus rhamnolipid production is often studied in detail there. Despite recent work indicating that gene expression related to quorum signaling systems in P. aeruginosa may differ in spatial structure29, no studies assess how downstream genes, such as rhlAB, may be affected in spatially-structured colonies. Given the relevance of these diffusible inputs to the rhlAB system, we hypothesized that there could be differences between gene expression patterns in liquid and spatial environments.We compared P. aeruginosa biomass growth and gene expression in the liquid and spatial environments (Fig. 1a). Liquid culture data was collected following prior methods28. To interrogate the spatial system, we used the protocol from the classic Colony Forming Unit (CFU) assay. Cells were seeded with extreme dilution and we observed the behavior of the resultant colonies (cCFUs) across time and within the random configurations generated.Fig. 1: Rhamnolipid production differs between liquid culture and surface-attached P. aeruginosa.a Cartoon depictions of liquid and spatially-structured environments used in this study. b Optical density timeseries describing P. aeruginosa growth in liquid culture. [Blue] Biomass growth without exogenous quorum signals. [Purple] Biomass growth with exogenous quorum signals. c DsRed fluorescent timeseries generated from a custom-built imager (Supplementary Fig. 1) and custom software (Supplementary Fig. 3) describing P. aeruginosa growth in colony forming units (CFU). [Blue] Biomass growth without exogenous quorum signals [Purple] Biomass growth with exogenous quorum signals added to the plate media. [Inset] Example plate showing colonies at 48 h. Scale bar 1 cm. d Promoter activity (left[frac{{dGFP}}{{dt}}cdot frac{1}{{{OD}}_{600}}right]) of PrhlAB with respect to culture growth rate (left[frac{d{{OD}}_{600}}{{dt}}cdot frac{1}{{{OD}}_{600}}right]). [Blue] without exogenous quorum signals [Purple] with exogenous quorum signals. e Promoter activity (left[frac{{dGFP}}{{dt}}cdot frac{1}{{DsRed}}right]) of PrhlAB with respect to CFU growth rate (left[frac{{dDsRed}}{{dt}}cdot frac{1}{{DsRed}}right]). [Blue] without exogenous quorum signals [Purple] with exogenous quorum signals provided in the plate media.Full size imageWe observed differences in growth between cells grown in liquid culture (Fig. 1b) and spatial structure (Fig. 1c) with the same media composition. The growth pattern observed in liquid culture recapitulates previously reported data22,28. In comparing WT growth (dark blue data in Fig. 1b, c) between environments, we observed that both achieve a period of exponential growth, followed by a period of slowed growth. This sub-exponential growth is prolonged and no period of biomass decay is observed in the spatially-structured environment during our observation window.Quorum signal perturbation has long been an experimental tool to determine if a phenotype is responsive to social signaling9,10. rhlAB gene expression in particular is known to be downstream of both the las and rhl quorum signal systems39,40. However, it has previously been shown that liquid culture perturbation with additional C4-HSL and 3-oxo-C12-HSL, the rhl and las quorum signal system auto-inducers respectively, do not illicit significant change in growth or PrhlAB dynamics in this strain of P. aeruginosa22. We replicated this liquid culture result (Fig. 1b, purple data). In the spatially-structured system, we performed this perturbation by including both quorum signal molecules in the plate media in the same concentration by volume as previously published22. This analysis was done using biological replicates with More

A theoretical framework of interacting bacterial strainsOur mathematical model was motivated by experimental assays used to establish colony biofilms where the founding inoculum is placed on the surface of solidified nutrient agar. Within the inoculum footprint, individual (or small clusters of) bacteria settle at random locations and grow over time into a mature structured macroscale community (Fig. 1A). In the mathematical model, all the founding cells are assumed to have identical properties. However, to track the dynamics of biofilm growth we divided the founding cells into two groups, denoted by ({B}_{1}) (shown in magenta) and ({B}_{2}) (shown in green) (Fig. 1B). Note that we refer to ({B}_{1}) and ({B}_{2}) as strains for brevity, even though they represent two isogenic cell lineages that express different fluorescent proteins in a single-strain biofilm (Fig. 1A). In our theoretical framework, biofilm dynamics were reduced to the fundamental processes of local growth and spatial spread (more details below), which provided a species-independent representation of dual-strain biofilm growth. Suitably nondimensionalised (see Section S3), the model is given by$$frac{partial {B}_{1}}{partial t}=nabla cdot left({Id}left(1-left({B}_{1}+{B}_{2}right)right){nabla B}_{1}right)+{B}_{1}left(1-left({B}_{1}+{B}_{2}right)right),$$$$frac{partial {B}_{2}}{partial t}=nabla cdot left({Id}left(1-left({B}_{1}+{B}_{2}right)right)nabla {B}_{2}right)+{B}_{2}left(1-({B}_{1}+{B}_{2})right),$$
(1)
where, the variables ({0le B}_{1}left({{{{{boldsymbol{x}}}}}},tright),{B}_{2}left({{{{{boldsymbol{x}}}}}},tright)le 1) denote the scaled densities of each strain, respectively at time (t, > ,0) (one nondimensional time unit corresponding to approx. 2.9 h) and at spatial position ({{{{{boldsymbol{x}}}}}}in Omega) (one nondimensional space unit corresponding to approx. 0.15 mm). The spatial domain (Omega ={{{{{{boldsymbol{x}}}}}}in {{mathbb{R}}}^{2}:{||}{{{{{boldsymbol{x}}}}}}{||}le R}) is a two-dimensional disk, representing the biofilm growth medium (Fig. 1C). This simplification provided a significant reduction in computational cost and was motivated by an analysis of a previously published data set, in which we found a two-order of magnitude difference between biofilm diameter and biofilm thickness in B. subtilis NCIB 3610 [27]. The model is therefore unable to explicitly resolve density distributions along the vertical axis, for example, layering of subpopulation caused by gradients in environmental conditions [28,29,30] or topographical features such as ‘wrinkles’ [31]. However, it is fully capable of capturing overlap between subpopulations that are below the environmental carrying capacity and thus can track spatio-temporal coexistence. Moreover, as we show below, we find strong agreement between data obtained from two-dimensional in silico biofilms and data gathered from laboratory grown biofilms, which further supports the model simplification.Fig. 1: Experimental and modelling set-up.A An example of the experimental assay. Founder cells carry either a constitutively produced copy of GFP (green) or mTagBFP (magenta). The bacteria were mixed in a 1:1 ratio and images taken after 24 h and 72 h of incubation. The number of founder cells was approx. 10 CFUs. The scalebars are 5 mm long. B An example realisation of the mathematical model. In the right-hand plots green and magenta are used to differentiate two subsets of the initial patches ((t=0), top) and their subsequent development ((t=25), bottom). Black areas indicate the computational domain, (varOmega). The plot of initial condition is a blow-up of the centre of the whole domain. The scalebars represent 7 nondimensional space units. C Schematic of model initial condition. Initial populations (filled coloured circles) are placed in ({varOmega }_{0}), a small subdomain of the whole computational domain (varOmega) (both centred at the origin (O)).Full size imageThe initial conditions of the theoretical framework were motivated by the random positions at which bacteria settle on the agar within the inoculum footprint (Fig. 1A). In our theoretical framework, we represented the experimental inoculum footprint by a small disk ({Omega }_{0}=left{{{{{{boldsymbol{x}}}}}}in Omega :{||}{{{{{boldsymbol{x}}}}}}{||} ; < ; {R}_{0}right}) in the centre of the computational domain (Fig. 1C). We modelled the random deposition of bacteria by randomly placing ‘microcolonies’ within ({Omega }_{0}) at nodes of a triangulated spatial mesh of linear geometric order, used in the application of a finite element method to numerically solve the model equations (Fig. 1B, C). Each initial microcolony was assumed to only contain one strain and to be at carrying capacity (i.e., ({B}_{1}=1) or ({B}_{2}=1) within each microcolony). Unless otherwise stated, we used an even number ((N)) of initial microcolonies and assigned exactly (N/2) to each strain at random. At spatial locations other than the assigned microcolonies, both densities were set to zero.The size of a spatial mesh element used in the model (approx. (0.008{m}{m}^{2}) in experimental parameters) was much larger than that of a single bacterial cell. This means that the initial conditions represented the experimental assays shortly after inoculation (typically after 24 h of incubation), at which time each bacterium (or small cluster of bacteria) had formed a distinct, spatially separated microcolony. Hence, the number of in silico microcolonies, (N,) represented the number of bacteria used in the initial inoculum. Resolving the initial data at this spatial scale allowed analysis for founder densities (0le Nle 824). Using a selected set of values from that range was sufficient to capture clear trends (see below). The range covers biologically relevant founder densities, which generate mature colony biofilms with broadly similar morphologies (Supplementary Fig. S1). Additionally, to verify whether the observed trends could be extrapolated to (N ; > ; 824), we represented high founder densities by piecewise spatially homogeneous initial conditions ({B}_{1}={B}_{2}=0.5) in ({Omega }_{0}) and ({B}_{1}={B}_{2}=0) otherwise.The strains were assumed to grow logistically, with growth being limited by the total population, which could not exceed unity (after nondimensionalisation). Moreover, spatial propagation was described by diffusion as is common [32]. However, in our model, we employed a diffusion coefficient that decreased with increasing population size. This density dependence prevented merging of initially separated founding patches in the model and was invoked to capture experimental observations that indicated such colonies abut rather than merge on meeting [33, 34]. The indicator function ({Id}=1) if ({B}_{1}+{B}_{2}le 1) and ({Id}=0) otherwise guaranteed nonnegativity of the diffusion coefficients; this constrained the model to the physically relevant case and moreover ensured numerical stability during simulation.Finally, we defined the competitive outcome score (for ({B}_{1})) of the interaction to be the relative mass of strain ({B}_{1}) i.e., ({B}_{1}^{Omega }/({B}_{1}^{Omega }+{B}_{2}^{Omega })) at the chosen end point ((t=T)) of our model simulation, where$${B}_{i}^{Omega }:={int }_{Omega }{B}_{i}({{{{{boldsymbol{x}}}}}},T){{{{{rm{d}}}}}}{{{{{boldsymbol{x}}}}}},,i=1,2.$$The competitive outcome score lies in the interval (left[{{{{mathrm{0,1}}}}}right]) with the value 0.5 signifying a 1:1 ratio between the strains. Note that we could swap the indices without loss of generality to equivalently define the competitive outcome to be the relative mass of strain(,{B}_{2}) at the chosen end point.Low founder densities yield large variability in competitive outcomesIn the absence of spatial dynamics, the mathematical model predicted that the ratio between both strains would always remain constant (left(frac{d}{{dt}}big(frac{{B}_{1}}{{B}_{2}}big)=0right)) and therefore that the competitive outcome would be determined by the initial ratio. To test whether such a relationship continued to hold in the full, spatially extended system, we examined data from simulations over a test range of initial founding cell densities. The initial strain ratio was selected to be 1:1 for each test.Model simulations using homogeneous initial conditions (representing high founder densities) consistently resulted in a competitive outcome score of 0.5 (i.e., strains in 1:1 ratio) with the strains remaining homogeneously distributed in space across the colony (Fig. 2A, Supplementary Movie S1). By contrast, independent model realisations using a specified number of microcolonies placed at randomly chosen locations representing low (({N}=6)) and intermediate (({N}=824)) founder densities, revealed significant variation in competitive outcome (Fig. 2B, C, Supplementary Movies S2 and S3). To explore this observed variability in more detail, we employed a Monte Carlo approach. For each fixed founder density (N) within the selected set, 1000 independent model realisations were conducted. Data from these simulations revealed that the competitive outcome score for each founder density was normally distributed with mean 0.5. The standard deviation was relatively large for low founder densities ((N={{{{mathrm{4,6,8,10}}}}})) and decreased with further increases in (N) (Fig. 2D). (Note the small standard deviation for (N=2); see supplementary information for a discussion of this special case). Finally, our model predicted significant changes in the spatial organisation of the two strains within the biofilm in response to changing founder density, consistent with previous studies [14]. For high founder densities, isogenic in silico strains were predicted to coexist homogenously (Fig. 2A). However, as the founder density was decreased (decreasing (N)), homogeneous coexistence was gradually replaced by the formation of spatial sectors dominated by one strain or the other. Full segregation occurred for low founder densities (Fig. 2B, C).Fig. 2: Spatial structure and variability in competitive outcome depend on founder density.A–C Example model realisations for different founder densities. All plots show the system’s initial conditions ((t=0)) and the outcomes after 25 time units. Plots visualising the systems’ states at (t=0) show a blow-up of the subdomain ({varOmega }_{0}); plots visualising outcomes at (t=25) show the full computational domain (varOmega) (black background). The scalebars are seven unit lengths long. A The outcome of simulations initialised with piecewise spatially homogeneous populations representing high founder density. The ‘Merged’ image channel shows both strains (grey colour corresponds to overlap); the ({B}_{1})(green) and ({B}_{2}) (magenta) channels only show single strain filters of the plot. B The range of outcomes observed for low founder density (number of initial cell patches ({N}=6)). C The range of outcomes for intermediate founder densities ((N=824)). In (B, C) only the ‘Merged’ channel is shown. D Variability in competitive outcome increases with decreasing founder density. Each boxplot contains data from 1000 model realisations. Blue and red boxplots correspond to the founder densities in B and C, respectively.Full size imageAccess to free space determines competitive outcomeNext, we attempted to uncover the mechanism(s) by which low founder densities drive variability in competitive outcome. Motivated by [14], we first tested whether the initial separation between initial microcolonies of different types was the simple determinant. We did not find this to be the case for isogenic strain pairings in the mathematical model (Supplementary Fig. S2).As an alternative, we hypothesised that a microcolony surrounded by others may have little impact on competitive outcome as its contribution to biofilm growth would be ultimately limited. On the other hand, microcolonies located close to the boundary of the biofilm inoculum would be free to expand radially and thus could make a more significant contribution to the competitive outcome (for an example timelapse video see Movie S3). Hence, we explored whether competitive outcome was correlated to a strain’s potential for radial expansion beyond the inoculum. To do so, we assumed the potential for radial expansion to be solely determined by the geographical locations of a strain’s initial microcolonies. We then defined an appropriate score for this potential as follows. First, a circle was drawn that enclosed the initial microcolonies. Second, each point on the circle was associated with the nearest microcolony and assigned to that strain. Third, the total arc length on the circle associated with each strain was computed. Finally, the access to free space score (AFS score) for strain ({B}_{1}), denoted AFS1, was then computed as the ratio of the total arc length associated with ({B}_{1}) to the circumference of the circle. Therefore, (0le {{{{{rm{AF}}}}}}{{{{{{rm{S}}}}}}}_{1}le 1) quantified strain ({B}_{1})’s hypothesised potential to contribute to radial biofilm expansion. It is straightforward to confirm that the AFS score for strain ({B}_{2}), ({{{{{rm{AF}}}}}}{{{{{{rm{S}}}}}}}_{2}=1-{{{{{rm{AF}}}}}}{{{{{{rm{S}}}}}}}_{1}). See Section S4.2 and Supplementary Figs. S3 and S4 for a mathematically rigorous definition of the AFS score.We explored the utility of the AFS score using (N=6) and (N=824) as representatives of low and intermediate founder cell densities, respectively. We increased the number of model realisations to 5000 for each of the selected values of N to ensure improved accuracy of our data analysis. The AFS score was then calculated for each of the 10,000 initial conditions (see examples Fig. 3A, B). On completion of each simulation, the corresponding competitive outcome score was computed. Analysis of these model data confirmed that the AFS score accurately predicts competitive outcome: for each fixed founder density, the AFS score unfolds the variation shown in Fig. 2D, yielding a positive, linear relationship between AFS1 and competitive outcome for ({B}_{1}) (Fig. 3C, D). For each of the selected values of (N), initial configurations of microcolonies with a low AFS1 score predictably generated a low competitive outcome for ({B}_{1}). Correspondingly, initial configurations with a high AFS1 score predictably generated a high competitive outcome for ({B}_{1}). The slope of this linear relationship provided a deterministic quantification of the variability of competitive outcomes for a given founder density (cf. Fig. 3C, D, Supplemental text).Fig. 3: Access to free space determines competitive outcome.A, B Example model realisations for different founder densities. All plots show system initial conditions ((t=0)) with the reference circle used to compute the AFS score (the circle is rescaled for visualisation purposes) and outcomes after 25 time units. The founder densities are (N=824) and (N=6) in A and B, respectively. Plots visualising system states at (t=0) show a blow-up of the subdomain ({varOmega }_{0}); plots visualising outcomes at (t=25) show the full computational domain (varOmega) (black background). The scalebars are seven unit lengths long. C, D The relation between the AFS score ({AF}{S}_{1}), and competitive outcome is shown for intermediate founder density ((N=824)) and low founder density ((N=6)) in C and D, respectively. Data were obtained from 5000 model realisations and cover the continuum of ({AF}{S}_{1}). The observed probability density function for AFS is shown (circular markers); along with the density function of a fitted normal distribution ((mu approx 0.5,sigma approx 0.10) in C, (mu approx 0.5,sigma approx 0.16) in D) (solid line). E The relation between the standard deviations of the AFS score ({AF}{S}_{1}) and the competitive outcome. Each data point (circle) represents a different founder density and contains information from 1000 model realisations.Full size imageWe subsequently established that the predictive power of the AFS score was maintained across the range of founder densities considered in the model. Additionally, the variation in the AFS score was shown to decrease with increasing founder density (cf. Fig. 3C, D). Further, we revealed strong correlation between variation in AFS score and variation in competitive outcome (Fig. 3E). Therefore, for increasing founder density, the observed decrease in variation in competitive outcome can be directly attributed to the decrease in variation in the AFS score.Dual strain single-isolate biofilm assays confirm modelling hypothesesNext, we aimed to test the hypotheses put forward by the mathematical model. We selected an isogenic pair of Bacillus subtilis strains derived from isolate NCIB 3610 that constitutively produced the green fluorescent protein GFP (NRS6942, shown in green, Table S1) and the blue fluorescent protein mTagBFP (NRS6932, shown in magenta, Tables S1 and S2), respectively. In line with the modelling assumption, the isolates were mixed in a 1:1 ratio at a defined initial cell density (we used an OD600 of 1) and this cell culture was serially diluted prior to inoculating the colony biofilms (Section S7). Thus, biofilms were inoculated using ~106 CFUs and dilutions in 10-fold increments to order 1 CFU. For each founder density, 12 technical replicates were performed to provide a meaningful sample size, and the experiment was repeated on three independent occasions. We used a non-destructive colony biofilm image analysis approach, to measure the relative mass (and hence the competitive outcome) of the two isogenic strains at 24 h, 48 h, 72 h after inoculation (see Section S10). We confirmed that the output from the image analysis correlated well with data generated by disruption of the colony biofilm and analysis of the relative strain proportions determined using single cells analysis by flow cytometry (Fig. 4A) (see also [35]). The mTagBFP labelled strain consistently performed marginally worse than the GFP labelled competitor at high founder densities in co-culture, which suggests some impact on competitive fitness (Fig. 4B, C). To allow comparison with results from the mathematical model, we denoted the mTagBFP (NRS6932, shown in magenta) and GFP (NRS6942, shown in green) strains as ({B}_{1}) and ({B}_{2}), respectively, with associate AFS scores AFS1 and AFS2Fig. 4: Experimental data confirm modelling hypotheses.A Comparison of image analysis with flow cytometry. A scatter plot comparing measurements of relative density of the mTagBFP-labelled strain obtained from image analysis and flow cytometry is shown. Each data point corresponds to one biofilm, which was imaged before being analysed by flow cytometry. The data contains measurements taken from all strain pairs, all founder densities, and all time points. The solid blue line shows the identity (x=y), with the coefficient of determination being ({R}^{2}=0.91). B Example images of single-strain biofilms consisting of GFP (green(,{B}_{1})) and mTagBFP (magenta, ({B}_{2})) labelled copies of 3610. Taken after 72 h of incubation and shown for two different founder densities (scalebar 5 mm). C Strain density data. Competitive outcome measurements taken after 24 h, 48 h and 72 h of biofilm incubation. Plotted are technical repeats from one biological repeat of the experiment. The full data set is presented in Fig. S5A. D Example visualisations of AFS score calculations. Three example biofilms images at 24 h (left), 48 h (middle) and 72 h (right). The strains are as described in B. Images at 24 h show the reference circle used for the AFS1 score. E The relationship between AFS1 and competitive outcome for ({B}_{1}). AFS was calculated from images taken at 24 h, and competitive outcome for ({B}_{1}) after 48 h (left, (n=30)) and 72 h (right, (n=25)). The linear correlation coefficient (rho) is indicated.Full size imageOur experimental analysis proved consistent with the model predictions. High founder densities resulted in a broadly homogenous distribution of both strains over the footprint of the biofilm, while low founder densities led to a high degree of spatial segregation of the strains within the mature biofilm (Fig. 4B, see also [14]). Additionally, analysis of experimental data confirmed that variability in competitive outcome increased with decreasing founder density (Fig. 4B, C, Supplementary Fig. S5A). For founder densities equivalent to (sim)103 to (sim)106 CFUs, the competitive outcome was consistent across each set of technical replicates. By contrast, for founder densities equivalent to (sim)1 to (sim)102 CFUs, the competitive outcome was variable across each set of technical replicates. We noted that variability in competitive outcome, at all initial founder densities, was marginally amplified over time.We assumed the process of repeated dilution and selection of the inoculum volume may not guarantee an exact cell count and/or initial strain ratio of 1:1 at lower founder densities. Indeed, for low founder densities after 24 hrs incubation, we observed inconsistencies in the number and ratio of CFUs deposited (Supplementary Fig. S5B). We therefore considered whether these inconsistencies in the biofilm inocula contributed to the observed variability in competitive outcome. To explore this in more detail, we first implemented a combinatorial ‘cell picking’ model that mathematically simulated the process of selecting the small inoculum volume from a larger cell culture (see Section S4.3). This process identified a threshold of ({sim} {10}^{2}) CFUs below which variability in cell number and/or strain ratio could measurably deviate from their intended values in our experimental assay. Above this threshold, the combinatorial argument predicted limited deviation from the intended values (Supplementary Fig. S6A). Coupling these theoretical predictions with our experimental observations (Supplementary Fig. S5B), we concluded that any observed variability in competitive outcome cannot be a consequence of a measurable deviation in the inoculum composition for colony biofilms founded with (sim {10}^{2}) CFUs or higher.We next wanted to determine whether the predictive power of the AFS score could be used to connect experimental initial configurations of the bacteria with the observed competitive outcome. To do this accurately, we required that the founding bacteria remained spatially separated as small colonies until an image was taken at 24 h (the earliest imaging time-point, see Fig. 4D). Therefore, we only used founder densities lower than 102 CFUs. However, the above noted inconsistencies in initial strain ratios and cell counts at these densities raised the question of whether AFS could still accurately predict competitive outcome. To test this, we repeated our Monte Carlo simulations of (1) in which the number of initial microcolonies for each strain was drawn using the combinatorial cell picking model, rather than being a fixed number and in a 1:1 ratio. Analysing the resulting simulation data for model (1) confirmed that the predictive power of the AFS score was robust to any ‘naturally-occurring’ variation in the initial strain ratio (Supplementary Fig. S6B). Correspondingly, our analysis of the experimental data revealed a strong correlation between a strain’s AFS score and the competitive outcome measured at 48 h and 72 h after incubation (Fig. 4E).A modelling framework for non-isogenic strainsWe have established that for isogenic strains, the initial configuration of founding bacteria determines the competitive outcome in a ‘race for space’ and that the AFS score can accurately predict which strain will dominate. A natural question that follows is what would happen if this race for space was influenced by antagonistic interactions such as killing or growth inhibition. Therefore, we considered the effect of introducing a local (e.g., contact-dependent or short-range non-contact dependent) antagonistic mechanism that causes a reduction in strain net growth. In an extension of our theoretical framework (1), constants describing the ratios between the strains’ maximum growth rates in the absence of competition ((r)), diffusion coefficients ((d)) and competition coefficients ((c)) were introduced to allow for the possibility of differences in strain properties. This resulted in the following system obtained after a suitable nondimensionalisation (see Section S3):$$frac{partial {B}_{1}}{partial t}=nabla cdot left({Id}left(1-frac{{B}_{1}+{B}_{2}}{k}right){nabla B}_{1}right)+{B}_{1}left(1-frac{{B}_{1}+{B}_{2}}{k}right)-{B}_{1}{B}_{2},$$$$frac{partial {B}_{2}}{partial t}=nabla cdot left({Id}cdot dleft(1-frac{{B}_{1}+{B}_{2}}{k}right)nabla {B}_{2}right)+{{rB}}_{2}left(1-frac{{B}_{1}+{B}_{2}}{k}right)-c{B}_{1}{B}_{2}.$$
(2)
Here, the indicator function ({Id}=1) if ({B}_{1}+{B}_{2}le k) and ({Id}=0) otherwise, where k is the nondimensional carrying capacity. To start, strains were assumed to possess identical growth dynamics in the absence of competitors (i.e., r (=1,{d}=1)), but to significantly differ in their ability to negatively impact the competitor strain. For the simulations we set (c=0.2) representing a five-fold difference in competition strength, with ({B}_{2}) being the more effective competitor. A linear stability analysis of model [4] confirmed that in this case and for a homogeneous initial distribution of the strains in a 1:1 ratio, ({B}_{2}) wins the interaction. For this reason, we therefore refer to ({B}_{2}) as the (intrinsically) stronger strain and to ({B}_{1}) as the (intrinsically) weaker strain in the following.The assumption of identical growth dynamics allowed us to focus on the impact of antagonistic interactions on competitive outcome. We anticipated that this assumption was unlikely to hold for non-isogenic strains in experimental settings and therefore we examined (as will be discussed later) the impact of changes to the parameters (r,{d}) and (c). Subsequently, we showed the effect of such parameter variation to be limited.Spatial segregation induced by low founder densities enables coexistenceIn the context of local antagonistic interactions, low founder densities were expected to offer protection for the weaker strain by driving spatial segregation and the formation of enclaves. Test simulations supported this hypothesis. Model realisations with high (spatially uniform initial conditions) and intermediate ((N=824)) founder densities consistently led to competitive exclusion of the weaker strain (Fig. 5A, B, Supplementary Movies S4 and S5), while model realisations with low founder densities ((N=6)) resulted in coexistence with the strains being spatially segregated (Fig. 5C). Once established during early stages of the model simulation, spatial segregation was conserved. However, the stronger strain continually invaded its competitor’s clusters along strain-to-strain interfaces and eventually took over the biofilm centre. Simultaneously, the weaker strain enlarged its sectors due to unimpeded growth on the biofilm edge. Coexistence, as measured by competitive outcome was achieved by a balance of these processes (Supplementary Movie S6).Fig. 5: Modelling data for a non-isogenic strain pair with local antagonistic interactions.A–C Example model realisations for high (A), intermediate (B) and low (C) founder density are shown. A the Merged image channel shows both strains (grey colour corresponds to overlap), the ({B}_{1}) and ({B}_{2}) channels only show single strain filters of the plot. In B, C only the Merged channel is shown. Plots visualising system states at (t=0) show a blow-up of the subdomain ({varOmega }_{0}) and the circles used to calculate the AFS scores around the initial conditions are not to scale. Plots visualising outcomes at (t=25) show the full computational domain (varOmega) (black background). The scalebars are seven unit lengths long. D The relation between founder density and competitive outcome. Each boxplot contains data from 1000 model realisations. E The relation between the AFS score ({AF}{S}_{1}), and competitive outcome for one fixed founder density ((N=6)). Data were obtained from 5000 model realisations and covers the continuum of ({AF}{S}_{1}). The observed probability density function for AFS is shown (circular markers); the density function of a fitted normal distribution ((mu approx 0.5,sigma approx 0.16)) as a solid line.Full size imageLow founder densities generated significant variation in competitive outcome (Fig. 5C). In particular, outcomes were observed for which the weaker strain ({B}_{1}) coexisted with, and could even outperform, the stronger strain ({B}_{2}). To better understand the impact of founder density, we performed Monte Carlo simulations with 1000 independent model realisations for each founder density (N) in our test range. Data from these simulations revealed both the mean and variation of competitive outcome for the weaker strain increased with decreasing founder density (Fig. 5D).Access to free space determines competitive outcome for low founder densitiesThe mathematical model consistently predicted competitive exclusion of the weaker strain at intermediate and high founder densities (Fig. 5A, B). Hence, in these cases, the AFS score no longer provided a meaningful predictor of competitive outcome. Rather, the model predicted the outcome to be dominated by the local antagonisms. However, as detailed above, low founder densities ((N) = 6) resulted in a highly variable competitive outcome and therefore we explored whether the AFS score remained an accurate predictor in this case. The simulation data confirmed that for this fixed number (N), the AFS score remained capable of accurately unfolding the observed variation in competitive outcome (Fig. 5E). Thus, initial strain configurations with a low AFS1 predictably generated a low competitive outcome for ({B}_{1}). The reciprocal was also maintained where initial strain configurations with high AFS1 predictably generated high competitive outcome for ({B}_{1}). As for isogenic strains, this relationship was found to be linear with the slope providing a measure of the deterministic range of competitive outcomes for a given founder density. The relationship between AFS and competitive outcome was again shown to be robust to natural variation in the initial strain ratio inherent in low founding cell densities (Supplementary Fig. S6C).Our mathematical model predicted that coexistence remained possible over a range of maximum growth rates, (r) (within a two-fold difference between dimensional strain growth rates in the absence of competition), diffusion coefficients, (d) (within a three-fold difference between dimensional diffusion coefficients), and most surprisingly, any values of the competition coefficient, (c) (Section S6 and Supplementary Fig. S7A–C). In particular, we showed that a strain required extreme competition efficiency ((c) very large) in order to compensate for being slower in growth ((d,r ; > ; 1)) (Supplementary Fig. S7D). Finally, the predictive power of the AFS score was preserved over the parameter range tested (Supplementary Fig. S7E, F).Dual-isolate biofilm assays – selection of a competition partnerTo experimentally test our model predictions, we needed to identify a suitable partner for NCIB 3610. We chose a Bacillus subtilis strain called NRS6153 (hereafter 6153). This selection was made because (i) 6153 is a genetically competent wild type strain with no known auxotrophies [36]); (ii) in liquid culture conditions the generation times of the two strains are within ~1.5-fold of each other (Fig. 6A); (iii) under biofilm conditions, single strain biofilms of both isolates have footprint sizes that are within (sim)2-fold of each other (Fig. 6B); (iv) across a broad range of founder densities, the competitive outcome of an isogenic pairing of 6153 isolates in a colony biofilm is broadly similar to that of an isogenic pairing of 3610 strains, albeit with more variability in the competitive outcome at the 72-h time point for high founder densities (cf. Fig. 4C (Supplementary Fig. S5A) and Fig. 6C (Supplementary Fig. S8A)); (v) when a colony biofilm is founded at high density with marked strains of 3610 and 6153 starting at an initial 1:1 ratio, 6153 is consistently outcompeted by 3610 (and hence defines 3610 as the stronger strain in the context of this study) (Fig. 6D); and (vi) using an antibiosis halo formation assay, interrogation of the interaction between 3610 and 6153 showed no evidence of contact-independent growth inhibition (Fig. 6E). In combination, these data allow us to infer that the mode of competition during co-culture in the colony biofilm is locally antagonistic.Fig. 6: Selection of a competitive strain.A Growth curves of 3610 (black) and 6153 (grey) in MSgg cultures at 30 °C. The three lines shown for each isolate represent separate biological repeats. B Biofilm footprint area of single-strain 3610 and 6153 biofilms. Data from 18 and 16 biofilms are shown for the 24 h and 48 h timepoint, respectively. C Competitive outcome data from colony biofilm assays of isogenic 6153 biofilms are shown after 24 h, 48 h and 72 h of incubation. Plotted are the technical repeats from one biological repeat. The full data set is presented in Supplementary Fig. S8A. D Flow cytometry data of mixed biofilms grown for 24, 48, and 72 h at 30 °C on MSgg media. Isolate names followed by ‘g’ represent strains constitutively producing  GFP, (green on the graph). Isolate names followed by ‘b’ indicate strains constitutively producing mTagBFP, (magenta on the graph). Three biological and three technical replicates were performed for each strain mix and timepoint and all data points are shown. The error bars represent the mean standard deviation. E Halo formation assays on MSgg agar plates at 24 h of growth. Strains producing mTagBFP (magenta) and GFP (green) are shown.Full size imageDual-isolate biofilm assays confirm modelling hypothesesWe performed dual strain biofilm assays competing 3610 and 6153 over a wide range of founder densities. These competitive assays confirmed the modelling prediction that in biofilms inoculated at low founder densities, coexistence within a non-isogenic strain pair is enabled by spatial segregation (Fig. 7A). Under such conditions, the intrinsically weaker strain (6153) formed spatial sectors and thus was able to coexist with the stronger strain (3610) through spatial segregation (Fig. 7A, B). In contrast, and again as predicted by the mathematical model (and reported during the selection of strain 6153 as a competition partner), for biofilms inoculated at high founder density, 3610 competitively excluded 6153 (Fig. 7A, B, Supplementary Fig. S8B). Finally, a computation of AFS scores based on images taken after 24 h of incubation showed strong correlation between a strain’s AFS score and its competitive outcome after both 48 h and 72 h of incubation for both 6153 alone and when in co-culture with 3610 (Supplementary Figs. S9 and 7C).Fig. 7: Experimental data for a non-isogenic strain pair with local antagonistic interactions.A Example dual-strain biofilms (3610 labelled with GFP (green), 6153 labelled with mTagBFP (magenta)). Images taken after 72 h of incubation for two different founder densities. Scalebars as in Fig. 2. B Competitive outcome data for 3610 in the 3610/6153 pair after 24 h, 48 h and 72 h of biofilm incubation. Plotted are technical repeats from one biological repeat of the experiment. The full data set is presented in Supplementary Fig. S8B. C The relationship between AFS and competitive outcome for 6153. AFS1 was calculated based on images taken after 24 h of biofilm incubation, and competitive outcome after 48 h (top, ({n}=22)) and 72 h (bottom, (n=17)).Full size image More