Philippa Kaur

Spatial standardisation workflowTo produce spatially-standardised fossil occurrence datasets which remain geographically consistent through time, we designed a subsampling algorithm which enforces consistent spatial distribution of occurrence data between time bins, while maximising data retention and permitting highly flexible regionalisation (Fig. 8). Our method was developed in light of, and takes some inspiration from, the spatial standardisation procedure of Close et al.2. This method provides, within a given time bin, subsamples of occurrence data with threshold MST lengths. An average diversity estimate can be taken from this ‘forest’ of MSTs, selecting only those of a target tree length to ensure spatially-standardised measurements. It does not produce a single dataset across time bins, however; rather a series of discontinuous, bin-specific datasets which cannot then simply be concatenated as the spatial extents of each bin-specific forest are not standardised (despite each individual MST being so), even when MSTs are assigned to a specific geographic region, e.g. a continent or to a particular latitudinal band. This prevents estimation of rates, because such analyses require datasets that span multiple time bins and remain geographically consistent and spatially standardised through the time span of interest. This is the shortcoming that our method overcomes. The workflow consists of three main steps.Fig. 8: Component steps of our spatial standardisation workflow.A A spatial window (dotted lines) is used to demarcate the spatial region of interest, which may shift in a regular fashion through time to track that region. Data captured in each window is clipped to a target longitude–latitude range (orange lines). B The data forming the longitude–latitude extent is marked, then masked from further subsampling. C Data are binned using a hexagonal grid, the tally of occurrences in each grid cell taken, and a minimum spanning tree constructed from the grid cell centres. D The cells with the smallest amount of data are iteratively removed from the minimum spanning tree until a target tree length is reached.Full size image1. First, the user demarcates a spatially discrete geographic area (herein the spatial window) and a series of time bins into which fossil occurrence data is subdivided. Occurrence data falling outside the window in each time bin are dropped from the dataset, leaving a spatially restricted subsample (Fig. 8A). Spatial polygon demarcation is a compromise between the spatial availability of data to subsample and the region of interest to the user but allows creation of a dataset where regional nuances of biodiversity may be targeted. Careful choice of window extent can even aid subsequent steps by targeting regions that have a consistently sampled fossil record through time, even if the extent of that record fluctuates. To account for spatially non-random changes in the spatial distribution of occurrence data arising from the interlinked effects of continental drift, preservation potential and habitat distribution17, the spatial polygon may slide to track the location of the available sampling data through time. This drift is performed with two conditions. First, the drift is unidirectional so that the sampling of data remains consistent relative to global geography, rather than allowing the window to hop across the globe solely according to data availability and without biogeographic context. Second, spatial window translation is performed in projected coordinates so that its sampling area remains near constant between time bins, avoiding changes in spatial window area that could induce sampling bias from the species-area effect.2. Next, subsampling routines are applied to the data to standardise its spatial extent to a common threshold across all time bins using two metrics: the length of the MST required to connect the locations of the occurrences; and the longitude–latitude extent of the occurrences. MST length has been shown to measure spatial sampling robustly as it captures not just the absolute extent of the data but also the intervening density of points, and so is highly correlated with multiple other geographic metrics16. MSTs with different aspect ratios may show similar total lengths but could sample over very different spatial extents, inducing a bias by uneven sampling across spatially organised diversity gradients16; standardising longitude–latitude extent accounts for this possibility. The standardisation methods can be applied individually or serially if both MST length and longitude–latitude range show substantial fluctuations through time. Data loss is inevitable during subsampling and may risk degrading the signals of origination, extinction and preservation. To address this issue, subsampling is performed to retain the greatest amount of data possible. During longitude–latitude standardisation, the range containing the greatest amount of data is preserved. During MST standardisation, occurrences are spatially binned using a hexagonal grid to reduce computational burden and to permit assessment of spatial density (Fig. 8B). The grid cells containing the occurrences that define the longitude–latitude extent of the data are first masked from the subsampling procedure so that this property of the dataset is unaffected, and then the occurrences within the grid cells at the tips of the MST are tabulated. Tip cells with the least data are iteratively removed (removal of non-tip cells may have little to no effect on the tree topology) until the target MST length is achieved (Fig. 8D), with tree length iteratively re-calculated to include the branch lengths added by the masked grid cells.For both methods, the solution with the smallest difference to the target is selected and so both metrics may fluctuate around this target from bin to bin, with the degree of fluctuation depending upon the availability of data to exclude—larger regions that capture more data are more amenable to the procedure than smaller regions. Similarly, the serial application of both metrics reduces the pool of data available to the second method, although longitude–latitude standardisation is always applied first in the serial case so that the resultant extent will be retained during MST standardisation. Consequently, the choice of standardisation procedure and thresholds must be tailored to the availability and extent of data within the sampling region through time, along with the resulting degree of data loss. This places further emphasis on the careful construction of the spatial window in the first step. Threshold choice is also a compromise between data loss and consistency of standardisation across the dataset and so it may be necessary to choose targets that standardise spatial extent well for the majority of the temporal range of a dataset, rather than imposing a threshold that spans the entire data range but causes unacceptable data loss in some bins.3. Once the time-binned, geographically restricted data have been spatially standardised, the relationship between diversity and spatial extent is scrutinised. After standardisation, it is expected that residual fluctuations in spatial extent should induce little or no change in apparent diversity. Bias arising from temporal variation in sampling intensity may still be present, so diversity is calculated using coverage-based rarefaction (also referred to as shareholder quorum subsampling13,62,63), with a consistent coverage quorum from bin to bin. While coverage-based rarefaction has known biases, it remains the most accurate non-probabilistic means of estimating fossil diversity14. As such, we consider it the most appropriate method to assess the diversity of a region-level fossil dataset. The residual fluctuations in spatial extent may then be tested for correlation with spatially standardised, temporally corrected diversity. If a significant relationship is found, then the user must go back and alter the standardisation parameters, including the spatial window geometry and drift, the longitude–latitude threshold, and the MST threshold. Otherwise, the dataset is considered suitable for further analysis.We implement our subsample standardisation workflow in R with a custom algorithm, spacetimestand, along with a helper function spacetimewind to aid the initial construction of spatial window. spacetimestand can then accept any fossil occurrence data with temporal constraints in millions of years before present and longitude–latitude coordinates in decimal degrees. Spatial polygon construction and binning is handled using the sp library64, MST manipulation using the igraph and ape libraries65,66, spatial metric calculation using the sp, geosphere and GeoRange libraries67,68, hexagonal gridding using the icosa library69, and diversity calculation by coverage-based rarefaction using the estimateD function from the iNEXT library70. Next, we apply our algorithm to marine fossil occurrence data from the Late Permian to Early Triassic.Data acquisition and cleaningFossil occurrence data for the Late Permian (260 Ma) to Early Jurassic (190 Ma) were downloaded from the PBDB on 28/04/21 with the default major overlap setting applied (an occurrence is treated as within the requested time span if 50% or more of its stratigraphic duration intersects with that time span), in order to minimise edge effects resulting from incomplete sampling of taxon ranges within our study interval of interest (the Permo-Triassic to Triassic-Jurassic boundaries). Other filters in the PBDB API were not applied during data download to minimise the risk of data exclusion. Occurrences from terrestrial facies were excluded, along with plant, terrestrial-freshwater invertebrate and terrestrial tetrapod occurrences (as these may still occur in marine deposits from transport) and occurrences from several minor and poorly represented phyla. Finally, non-genus level occurrences were removed, leaving 104,741 occurrences out of the original 168,124. Based on previous findings2, siliceous occurrences were not removed from the dataset, despite their variable preservation potential compared to calcareous fossils. To increase the temporal precision of the dataset, occurrences with stratigraphic information present were revised to substage- or stage-level precision using a stratigraphic database compiled from the primary literature. To increase the spatial and taxonomic coverage of the dataset, the PBDB data were supplemented by an independently compiled genus-level database of Late Permian to Late Triassic marine fossil occurrences36. Prior to merging, occurrences from the same minor phyla were excluded, along with a small number lacking modern coordinate data, leaving 47,661 occurrences out of an original 51,054. Absolute numerical first appearance and last appearance data (FADs and LADs) were then assigned to the occurrences from their first and last stratigraphic intervals, based on the ages given in A Geologic Timescale 202071. Palaeocoordinates were calculated from the occurrence modern-day coordinates and midpoint ages using the Getech plate rotation model. Finally, occurrences with a temporal uncertainty greater than 10 million years and occurrences for which palaeocoordinate reconstruction was not possible were removed from the composite dataset, leaving 145,701 occurrences out of the original 152,402.In the total dataset, we note that the age uncertainty for occurrences is typically well below their parent stage duration, aside for the Wuchiapingian and Rhaetian where the mean and quartile ages are effectively the same as the stage length (Fig. S44). This highlights the chronostratigraphic quality of our composite dataset, particularly for the Norian stage (~18-million-year duration) which has traditionally been an extremely coarse and poorly resolved interval in Triassic-aged macroevolutionary analyses. Taxonomically, most occurrences are molluscs (Fig. 8), which is unsurprising given the abundance of ammonites, gastropods and bivalves in the PBDB, but introduces the caveat that downstream results will be driven primarily by these clades. Foraminiferal and radiolarian occurrences together comprise the next most abundant element of the composite dataset, demonstrating that we nonetheless achieve good coverage of both the macrofossil and microfossil records, along with broad taxonomic coverage in the former despite the preponderance of molluscs.Spatiotemporal standardisationWe chose a largely stage-level binning scheme when applying our spatial standardisation procedure for several reasons. First, the volume of data in each bin is greater than in a substage bin, providing a more stable view of occurrence distributions through time and increasing the availability of data for subsampling. Spatial variation at substage level might still affect the sampling of diversity, but the main goal of this study is to analyse origination and extinction rates where taxonomic ranges are key rather than pointwise taxonomic observations. Consequently, substage level variation in taxon presences likely amounts to noise when examining taxonomic ranges, making stage-level bins preferable in order maximise signal.During exploratory standardisation trials, we found a large crash in diversity and spatial sampling extent during the Hettangian (201.3–199.3 Mya). No significant relationships with spatially-standardised diversity were found when the Hettangian bin was excluded from correlation tests, indicating its disproportionate effect in otherwise well-standardised time series. Standardising the data to the level present in the Hettangian would have resulted in unacceptable data loss so we instead accounted for this issue by merging the Hettangian bin with the succeeding Sinemurian bin, where sampling returns to spatial extents consistent with older intervals. While this highlights a limitation of our method, as the Hettangian is  2: positive support, log BF  > 6: strong support)85 using the -plotRJ function of PyRate.Probabilistic diversity estimationTraditional methods of estimating diversity do not directly address uneven sampling arising from variation in preservation, collection and description rates, and their effectiveness is highly dependent on the structure of the dataset. We present an alternative method to infer corrected diversity trajectories based on the sampled occurrences and on the preservation rates through time and across lineages as inferred by PyRate, which we term mcmcDivE. The method implements a hierarchical Bayesian model to estimate corrected diversity across arbitrarily defined time bins. The method estimates two classes of parameters: the number of unobserved species for each time bin and a parameter quantifying the volatility of the diversity trajectory.We assume the sampled number of taxa (i.e. the number of fossil taxa, here indicated with xt) in a time bin to be a random subset of an unknown total taxon pool, which we indicate with Dt. The goal of mcmcDivE is to estimate the true diversity trajectory ({{{{{bf{D}}}}}},=,left{{D}_{1},{D}_{2},ldots ,{D}_{t}right}), of which the vector of sampled diversity ({{{{{bf{x}}}}}},=,{{x}_{1},{x}_{2},ldots ,{x}_{t}}) is a subset. The sampled diversity is modelled as a random sample from a binomial distribution86 with sampling probability pt:$${x}_{t}, ,sim, {{{{{rm{Bin}}}}}}({D}_{t},{p}_{t})$$
(1)
We obtain the sampling probability from the preservation rate (qt) estimated in the initial PyRate analysis. If the PyRate model assumes no variation across lineages the sampling probability based on a Poisson process is ({p}_{t},=,1,-,{{{{{rm{exp }}}}}}({-q}_{t},times, {delta }_{t})), where δt is the duration of the time bin. When using a Gamma model in PyRate, however, the qt parameter represents the mean rate across lineages at time t and the rate is heterogeneous across lineages based on a gamma distribution with shape and rate parameters equal to an estimated value α.To account for rate heterogeneity across lineages in mcmcDivE, we draw an arbitrarily large vector of gamma-distributed rate multipliers g1, …, gR ~ Γ(α,α) and compute the mean probability of sampling in a time bin as:$${p}_{t},=,frac{1}{R}mathop{sum }limits_{i,=,R}^{R}1,-,{{{{{rm{exp }}}}}}(-{q}_{t},,times, {g}_{i},times, {delta }_{t})$$
(2)
We note that while qt quantifies the mean preservation rate in PyRate (i.e. averaged among taxa in a time bin t), the mean sampling probability pt will be lower than (1,-,{{{{{rm{exp }}}}}}({-q}_{t},times, {delta }_{t})) (i.e. the probability expected under a constant preservation rate equal to qt) especially for high levels of rate heterogeneity, due to the asymmetry of the gamma distribution and the non-linear relationship between rates and probabilities. We sample the corrected diversity from its posterior through MCMC. The likelihood of the sampled number of taxa is computed as the probability mass function of a binomial distribution with Di as the ‘number of trials’ and pi as the ‘success probability’. To account for the expected temporal autocorrelation of a diversity trajectory87, we use a Brownian process as a prior on the log-transformed diversity trajectory through time. Under this model, the prior probability of Dt is:$$Pleft({{{{{rm{log }}}}}}left({D}_{t}right)right),{{{{{mathscr{ sim }}}}}},{{{{{mathscr{N}}}}}}({{{{{rm{log }}}}}}left({D}_{t,-,1}right),,sqrt{{sigma }^{2},,times, ,{delta }_{t}})$$
(3)
where σ2 is the variance of the Brownian process. For the first time bin in the series, Dt = 0, we use a vague prior ({{{{{mathscr{U}}}}}}(0,infty )). Because the variance of the process is itself unknown and may vary among clades as a function of their diversification history, we assign it an exponential hyperprior Exp(1) and estimate it using MCMC. Thus, the full posterior of the mcmcDivE model is:$$underbrace{P(D,{sigma }^{2}|x,q,alpha )}_{{{{{rm{posterior}}}}}}propto underbrace{P(x|D,q,alpha )}_{{{{{rm{likelihood}}}}}}times underbrace{P(D|{sigma }^{2})}_{{{{{rm{prior}}}}}}times underbrace{P({sigma }^{2})}_{{{{{rm{hyperprior}}}}}}$$
(4)
where ({{{{{bf{D}}}}}},=,{{D}_{0},{D}_{1},ldots ,{D}_{t}}) and ({{{{{bf{q}}}}}},=,{{q}_{0},{q}_{1},ldots ,{q}_{t}}) are vectors of estimated diversity, sampled diversity, and preservation rates for each of T time bins. We estimate the parameters D and σ2 using MCMC to obtain samples from their joint posterior distribution. To incorporate uncertainties in q and α we randomly resample them during the MCMC from their posterior distributions obtained from PyRate analyses of the fossil occurrence data. While in mcmcDivE we use a posterior sample of qt and α precomputed in PyRate for computational tractability of the problem, a joint estimation of all PyRate and mcmcDivE parameters is in principle possible, particularly for smaller datasets. mcmcDivE is implemented in Python v.3 and is available as part of the PyRate software package.Simulated and empirical diversity analysesWe assessed the performance of the mcmcDivE method using 600 simulated datasets obtained under different birth-death processes and preservation scenarios. The settings of the six simulations (A–F) are summarised in Table S65 and we simulated 100 datasets from each setting. Since the birth-death process is stochastic and can generate a wide range of outcomes, we only accepted simulations with 100 to 500 species, although the resulting number of sampled species decreased after simulating the preservation process. From each birth-death simulation we sampled fossil occurrences based on a heterogeneous preservation process. Each simulation included six different preservation rates which were drawn randomly within the boundaries 0.25 and 2.5, with rate shifts set to 23, 15, 8, 5.3 and 2.6 Ma. To ensure that most rates were small (i.e. reflecting poor sampling), we randomly sampled preservation rates as:$$q, sim ,exp left({{{{{mathscr{U}}}}}}left(log left(0.25right),,log left(2.5right)right)right)$$
(5)
In two of the five scenarios (D, F), we included strong rate heterogeneity across lineages (additionally to the rate variation through time), by assuming that preservation rates followed a gamma distribution with shape and rate parameters set to 0.5. This indicates that if the mean preservation rate in a time bin was 1, the preservation rate varied across lineages between More

Parasites have frequently been observed on the gills of coleoid cephalopods during ROV dives in the mesopelagic waters of the Monterey Submarine Canyon. Here, we demonstrate that at least two parasite species can be distinguished from ROV-collected specimens. Based on morphology, the first parasite was identified as the protist Hochbergia cf. moroteuthensis. Although the original description of H. moroteuthensis struggled to assign a taxonomic rank, the authors noted that the presence of trichocysts and an apical pore bear similarities to those of dinoflagellates in an encysted life stage29,30. Using Sanger sequencing and dinoflagellate cyst-specific primers, we confirm this parasite to be a dinoflagellate that forms a sister group to members of the Oodinium genus. The second parasite could not be matched to any documented morphological descriptions, and DNA barcoding was only able to resolve a short sequence that does not provide for a reliable identification.Hochbergia moroteuthensis appears to be a common parasite of midwater cephalopods and has previously been collected off the gills of twenty cephalopod species29,30. These include five taxa investigated here (C. calyx, V. infernalis, Galiteuthis spp., Gonatus spp. and Japetella diaphana), with Taonius sp. new to the list. While H. cf. moroteuthensis found in this study was somewhat smaller than the type series (0.5–1.4 mm versus 1.19–1.99)30, it was within the range of those reported by McLean et al.29 on the squids Stigmatoteuthis dofleini Pfeffer, 1912 and Abralia trigonura Berry, 1913 (i.e. 0.56 to 1.10 mm on average in length)29. The latter authors noticed that parasite size, color (i.e. white to yellow) and thecal plate morphology may differ between host species, which could indicate multiple Hochbergia species. It should, however, be noted that it is unknown whether H. moroteuthensis maximum growth is dependent on host size or whether the investigated parasites were simply in different growth stages given the study’s relatively small samples sizes. Although we did not compare H. cf. moroteuthensis morphology across hosts in great detail, the partial 18S rRNA sequences obtained for parasites on Gonatus berryi and Chiroteuthis calyx were identical. Further research is therefore warranted to investigate species-specific parasite differences and speciation among hosts.The genetic relatedness between H. cf. moroteuthensis and its Oodinium sister group is further supported by several morphological features. First, the lack of distinct dinoflagellate characters, ovoid shape and the presence of trichocysts, have also been noted for Oodinium cysts41,42,43. McLean et al.29 further reported that the nucleus of the single-celled H. moroteuthensis cyst contains diffuse chromatin, a feature unlike most dinoflagellates that possess well-defined rod-like chromosomes42. Remarkably, dinoflagellates within Oodinium are known to alternate between both non-dinokaryotic and dinokaryotic nuclei within their life cycles, which could explain H. moroteuthensis’ diffuse chromatin42,43. Similarities between H. moroteuthensis and Oodinium further extend to the parasitic life style with primarily pelagic hosts. Dinoflagellates in the Oodinium genus are all known to be ectoparasitic, infecting ctenophores, chaetognaths, annelids, larvaceans and a hydromedusa41,43,44,45,46.In spite of these similarities, there are also several noteworthy morphological differences between H. moroteuthensis and members of the Oodinium genus. Young Oodinium cysts generally have a white to yellow coloring, with older cysts taking a yellow–brown or dark brown tint41,43,44. Oodinium cysts also possess relatively simple thecal plates and above all, have a distinct peduncle, or stalk, with which they attach to the host and which is thought to serve as feeding apparatus41,43,47. Maximum lengths for Oodinium cysts have been reported up to 0.39 mm43,46. In contrast, cysts in H. moroteuthensis possess a white to yellow coloring, an intricate pattern of triangular plates, reach sizes up to 1.99 mm long, and have a simple holdfast area with an oval aperture that likely anchors them to the host30. Currently, both Oodinium and Hochbergia form a genetically distinct clade within the Dinophyceae and analysis of further specimens and genetic markers might provide more insight into their relatedness and specialization on primarily pelagic hosts. Additionally, analysis of fast- and slow-evolving genetic markers might resolve the polytomy observed in the phylogenetic trees, which were also present in the phylogenetic reconstruction of the DINOREF reference database by Mordret et al.32.The genetic similarity of H. cf. moroteuthensis to an unidentified eukaryote from the water column and the fact that we encountered the protozoans in an encysted stage, strongly suggests that these dinoflagellates infect their cephalopod hosts through a free-living life stage. Many parasitic dinoflagellates, including Oodinium, alternate between a motile free-living stage—the dinospore—that forms a vegetative feeding stage—the trophont—upon attachment to the host41,47,48. During this vegetative stage, the trophont grows greatly in size but without cellular division. Once mature, the trophont detaches from the host to divide into multiple flagellated dinospores. The dinospores disperse into the water column, free to infect new hosts (Fig. 6)41,47,48.Figure 6Theorized life cycle of Hochbergia moroteuthensis. (a) The vegetative trophont (feeding life stage) grows without cellular division on the cephalopod’s gills. (b) The mature trophont detaches and (c) divides into motile dinospores, (d) free to infect new hosts in the water column. Illustration (b) trophont adapted from Shinn & McLean30.Full size imageSuch a free-living life stage is consistent with H. moroteuthensis’ wide geographic distribution. Free-living dinospores are easily dispersed by ocean currents, and observations in both the North Pacific Ocean and the Gulf of Mexico could indicate large-scale ocean connectivity, potentially beyond the distribution reported here29. This dispersal may also offer H. moroteuthensis a wide range of infection possibilities and explain why trophonts are found in twenty-one different cephalopod taxa. Nevertheless, population genetic structure needs to be investigated, as it is currently unknown if the parasites represent multiple species.Free-living dinospores might also explain H. moroteuthensis’ location on the exterior gill tissue. With dinospores free in the water column, the fastest pathway to a cephalopod’s interior is through ‘inhalation’. In this process, cephalopods actively force water through their gills, making these the first organs Hochbergia would encounter. Respiratory organs give direct access to the cephalopod’s blood stream, and therefore offer a suitable environment (i.e. nutrient and oxygen rich) for development into a trophont. Gills also provide interstices that could simply trap dinospores. Either way, there was only one occasion (i.e. out of 355) where trophonts were seen on other body parts besides the gills (Fig. 4e). In comparison, several Oodinium parasites are also known to attach to specific host-body parts, apparently preferring sites involved in locomotor movement. For instance, Oodinium jordani McLean & Nielsen, 1989 is known to attach to the fin of the chaetognath Sagitta elegans Verrill, 187346, while O. pouchetti is mostly found on the tail of appendicularians41, and Oodinium sp. collected off various ctenophores appears to prefer attachment close to or within the beating comb rows44. Whether these surface areas offer highest encounter rates or provide a physical benefit such as enhanced oxygenation remains unknown.The increased prevalence of H. cf. moroteuthensis observed in the most abundant cephalopod, Chiroteuthis, and in the other adult cephalopods is in line with infection dynamics known from other wildlife parasites, where the probability of a parasitic infection increases with host density and age49,50,51. Following this, dinospores in the Monterey Submarine Canyon have more opportunities to encounter common squids like Chiroteuthis52 and longer-lived cephalopods. Alternatively, it is possible that the increased parasite load in adults is simply the result of larger gill surface areas when compared to juveniles. However, when comparing prevalence between host species, it should be noted that the maximum adult sizes for C. calyx (up to 100 mm in mantle length, ML) are smaller than those of Galiteuthis (500 mm ML), Taonius (660 mm ML) and Japetella (144 mm ML) among specimens found in the Monterey Submarine Canyon53,54.Other factors that might explain the observed prevalence include parasite preferences for host physiology (e.g. respiration rates) or confinement to a certain depth range18. Although Chiroteuthis, Galiteuthis, Taonius and Japetella partially overlap in their depth distributions, Chiroteuthis generally remains above the core of the oxygen minimum zone, located around 700 m in Monterey Bay52,55. Galiteuthis, on the other hand, has a bimodal distribution, with older individuals known to migrate below the oxygen minimum core52,55,56. If dinospore viability is restricted to more shallow depths, the probability of infection for Galiteuthis could decrease when living at deeper depths. This is further supported by Taonius, which showed a comparable bimodal distribution to Galiteuthis52 and shared a similar parasite prevalence. Furthermore, Japetella is the deepest living cephalopod investigated and harbored relatively few Hochbergia trophonts. In spite of this, it is unknown how long it takes for H. moroteuthensis dinospores to develop into mature trophonts and over what time frames they may accumulate on their hosts. Lab-based experiments with Oodinium sp. on the ctenophore Beroe abyssicola Mortensen, 1927 showed that trophonts needed approximately 20 days to grow from 35 µm in length to their mature size of 350 µm at 10 °C44. Given that H. moroteuthensis can grow over five times larger and lives at colder temperatures depending on its host distribution, growth periods may be substantially longer.When looking at the prevalence of H. cf. moroteuthensis over time, only Taonius appeared to be showing an increase in infected individuals over the years. Present results, however, are insufficient to determine whether this increase is the result of environmental change or part of natural variability. We therefore recommend continued monitoring to determine long term trends. Based on the monthly prevalence, it is likely that Chiroteuthis acts as a reservoir for Hochbergia parasites throughout the year. Galiteuthis, Japetella and Taonius show more seasonal dynamics. It may be that the reported seasonality is related to upwelling events or environmental cues promoting dinospore formation (e.g. increasing temperatures)50. Alternatively, cephalopods might be more susceptible to infections in certain months, or have higher resistance in others. Taonius, for example, had a markedly lower parasite load on average than Galiteuthis despite similar prevalence estimates (Tables 1 and 2), potentially indicating some sort of resistance mechanism. More research is warranted to confirm any host resistance and the influence of depth or seasonal effects.The other parasite type found in ROV-collected specimens of Vampyroteuthis infernalis and Gonatus spp. needs further characterization. Although DNA barcoding was able to resolve a short sequence that potentially places it within the phylum Apicomplexa, it appears more likely that this genetic material originated from contamination with a different parasite. Apicomplexa reported in cephalopods generally infect the digestive tract and are morphologically different from the parasites observed here19.In conclusion, our findings highlight the need for further investigation of cephalopods and their gill parasites. Considering that parasites influence biodiversity and that cephalopods form key links in pelagic food webs, future research should be focused at assessing potential effects on cephalopod physiology. For example, if H. moroteuthensis limits longevity or reproduction in common squids like C. calyx, then changes in parasite abundance might result in cascading effects on abundance of Chiroteuthis’ prey, predators and competitors. Additionally, baseline estimates of parasite prevalence are crucial to fully understand whether midwater host-parasite systems are at risk from increasing anthropogenic stressors and how they will change over time. While ROV observations have proven key to estimate prevalence and infection intensity here, trawled specimens continue to be valuable for verification of parasite species and obtaining material for genetic analyses, even if slightly damaged. We therefore recommend combining ROV observations with periodic trawling in future studies, since ROVs may not reveal smaller parasites, early infections or parasites in animals with tissue that is not transparent. More

Australia’s tropical rainforests are some of the oldest in the world.Credit: Alexander Schenkin

The rate of tree dying in the old-growth tropical forests of northern Australia each year has doubled since the 1980s, and researchers say climate change is probably to blame.The findings, published today in Nature1, come from an extraordinary record of tree deaths catalogued at 24 sites in the tropical forests of northern Queensland over the past 49 years.“Trees are such long-living organisms that it really requires huge amounts of data to be able to detect changes in such rare events as the death of a tree,” says lead author David Bauman, a plant ecologist at the University of Oxford, UK. The sites were initially surveyed every two years, then every three to four years, he explains, and the analysis focused on 81 key species.Bauman and his team recorded that 2,305 of these trees have died since 1971. But they calculated that, from the mid-1980s, tree mortality risk increased from an average of 1% a year to 2% a year (See ‘Increasing death rate’).

Bauman says that trees help to slow global warming because they absorb carbon dioxide, so an increase in tree deaths reduces forests’ carbon-capturing ability. “Tropical forests are critical to climate change, but they’re also very vulnerable to it,” he explains.Climate changeThe study found that the rise in death rate occurred at the same time as a long-term trend of increases in the atmospheric vapour pressure deficit, which is the difference between the amount of water vapour that the atmosphere can hold and the amount of water it does hold at a given time. The higher the deficit, the more water trees lose through their leaves. “If the evaporative demand at the leaf level can’t be matched by water absorption in fine roots, it can lead to leaves wilting, whole branches dying and, if the stress is sustained, to tree death,” Bauman says.The researchers looked at other climate-related trends — including rising temperatures and an estimate of drought stress in soils — but they found that the drying atmosphere had the strongest effect. “What we show is that this increase [in tree mortality risk] also closely followed the increase in atmospheric water stress, or the drying power of air, which is a consequence of the temperature increase due to climate change,” Bauman explains.Of the 81 tree species that the team studied, 70% showed an increase in mortality risk over the study period, including the Moreton Bay chestnut (Castanospermum australe), white aspen (Medicosma fareana) and satin sycamore (Ceratopetalum succirubrum).The authors also saw differences in mortality in the same tree species across plots, depending on how high the atmospheric vapour pressure deficit was in each plot.“This is one data set where the trees have been monitored in reasonably good detail since the early ’70s, and this is a really top-notch analysis of it,” says Belinda Medlyn, an ecosystem scientist at University of Western Sydney, Australia.But she says that more experiments are needed to determine whether the vapour pressure deficit is the biggest climate-related contributor to the increase in tree deaths. More

Young cerebrospinal fluid probably improves the conductivity of the neurons in ageing mice.Credit: Qilai Shen/Bloomberg/Getty

Young brain fluid improves memory in old miceCerebrospinal fluid (CSF) from young mice can improve memory function in older mice, researchers report in Nature (T. Iram et al. Nature 605, 509–515; 2022).A direct brain infusion of young CSF probably improves the conductivity of the neurons in ageing mice, which improves the process of making and recalling memories.CSF is a cocktail of essential ions and nutrients that cushions the brain and spinal cord and is essential for normal brain development. But as mammals age, CSF loses some of its punch. Those changes might affect cells related to memory, says co-author Tal Iram, a neuroscientist at Stanford University in California.The researchers found that young CSF helps ageing mice to generate more early-stage oligodendrocytes, cells in the brain that produce the insulating sheath around nerve projections and help to maintain brain function.The team suggest that the improvements are largely due to a specific protein in the fluid.“This is super exciting from the perspective of basic science, but also looking towards therapeutic applications,” says Maria Lehtinen, a neurobiologist at Boston Children’s Hospital in Massachusetts.Gender bias worms its way into parasite namingA study examining the names of nearly 3,000 species of parasitic worm discovered in the past 20 years reveals a markedly higher proportion named after male scientists than after female scientists — and a growing appetite for immortalizing friends and family members in scientific names.Robert Poulin, an ecological parasitologist at the University of Otago in Dunedin, New Zealand, and his colleagues combed through papers published between 2000 and 2020 that describe roughly 2,900 new species of parasitic worm (R. Poulin et al. Proc. R. Soc. B https://doi.org/htqn; 2022). The team found that well over 1,500 species were named after their host organism, where they were found or a prominent feature of their anatomy.

Source: R. Poulin et al. Proc. R. Soc. B https://doi.org/htqn (2022)

Many others were named after people, ranging from technical assistants to prominent politicians. But just 19% of the 596 species named after eminent scientists were named after women, a percentage that barely changed over the decades (see ‘Parasite name game’). Poulin and his colleagues also noticed an upward trend in the number of parasites named after friends, family members and even pets of the scientists who formally described them. This practice should be discouraged, Poulin argues.

Sea anemones turn oxybenzone into a light-activated agent that can bleach and kill corals.Credit: Georgette Douwma/Getty

Anemones suggest why sunscreen turns toxic in seaA common but controversial sunscreen ingredient that is thought to harm corals might do so because of a chemical reaction that causes it to damage cells in the presence of ultraviolet light.Researchers have discovered that sea anemones, which are similar to corals, make the sun-blocking molecule oxybenzone water-soluble by tacking a sugar onto it. This inadvertently turns oxybenzone into a molecule that — instead of blocking UV light — is activated by sunlight to produce free radicals that can bleach and kill corals. The animals “convert a sunscreen into something that’s essentially the opposite of a sunscreen”, says Djordje Vuckovic, an environmental engineer at Stanford University in California.It’s not clear how closely these laboratory-based studies mimic the reality of reef ecosystems. The concentration of oxybenzone at a coral reef can vary widely, depending on factors such as tourist activity and water conditions. And other factors threaten the health of coral reefs; these include climate change, ocean acidification, coastal pollution and overfishing. The study, published on 5 May (D. Vuckovic et al. Science 376, 644–648; 2022) does not show where oxybenzone ranks in the list. More

DataAll data was processed and analyzed using R (R Core Team, Version 4.0.3).Dengue case data were collected and shared by the Alcaldía de Medellín, Secretaría de Salud. In Medellin, dengue case surveillance is conducted by public health institutions that classify and report all cases that meet the WHO clinical dengue case criteria for a probable case to Medellin’s Secretaría de Salud through SIVIGILA (“el Sistema Nacional de Vigilancia en Salud Publica). All case data were de-identified and aggregated to the SIT Zone level.Human public transit usage and movement data were collected and shared by the Área Metropolitana del Valle de Aburrá for 50–200 respondents per SIT Zone. The “Encuestas Origen Destino” (Origen Destination Surveys) were conducted in 2005, 2011, and 2016 and published in 2006, 2012, and 2017, with survey methods described by the Área Metropolitana del Valle de Aburrá25. Survey respondents include a randomly selected subset of all Medellin residents in each SIT zone regardless of whether they use public transit or not. Survey respondents reported the start and end locations, purpose for travel, and mode of travel for all movement over the last 24 h from the time the survey was administered. Respondents reported all modes of movement, including public transit, private transit, and movement on foot. The results of the survey published in 2017 are published online by the Área Metropolitana del Valle de Aburrá26, and select data are available through the geodata-Medellin open data portal27. The results and data of the survey published in 2012 are not publicly available and were obtained directly from the Área Metropolitana del Valle de Aburrá.The public transit usage survey data were also used to extract socioeconomic data to the SIT zone; surveyors also reported basic demographic data including household Estrato, which was averaged per SIT zone to estimate zone socioeconomic status. “Estrato” measures socioeconomic status on a scale from 1 (lowest) to 6 (highest). This system is used by the government of Colombia to allocate public services and subsidies (Law 142, 1994). Data from the public transit usage survey were used to extract socioeconomic status data because it is the only location available where the spatial scale of the data matched the spatial scale of the SIT zone.Data on the location of Medellín public transit lines was downloaded as shape files from the geodata-Medellín open data portal27 and subset for each year to the set of transit lines that was available in that year. Data on the opening date of each Medellín public transit line was taken from the Medellín metro website28.Because census data at the zone level were not available for this study and only exists for 2005 and 2018, we used population estimates for each year downloaded from the WorldPop project29 and aggregated by SIT zone. The accuracy of WorldPop estimates were checked against available census data for 2005 and 2018 at the comuna level, accessed via the geodata- Medellín open data portal27.Ethical considerationsNo human subjects research was conducted. All data used was de-identified, and the analysis was conducted on a database of cases meeting the clinical criteria for dengue with no intervention or modification of biological, physical, psychological, or social variables. All methods were performed in accordance with the relevant guidelines and regulations.Data analysisQuantifying public transit usage and distance from nearest transit lineTo quantify public transit usage, we determined if each respondent reported using the metro, metroplus, or ruta alimentadora (supplementary bus route system integrated with the metro system) in the last 24 h. We then calculated the percent of respondents using the public transit system at least once for each SIT zone.To quantify the distance to the nearest public transit line, we calculated the distance from the center point of each zone to the closest metro, metroplus, tranvía, metrocable, ruta alimentadora, or escalera eléctrica. This was recalculated for each year, including new transit lines that were added within that year.Spatial autoregressive models of dengue incidenceDengue incidence per year at the level of the SIT zone was modeled using a fixed effects spatial panel model by maximum likelihood (R package splm30) as described in31. Our fixed effects were socioeconomic status, distance from public transit, a two-way interaction between these factors, and year. To weight dengue cases by population per SIT zone, the model contained a log offset of population per zone per year. Dengue case counts were log transformed after adding one to account for zones with zero dengue cases in a given year. Year was analyzed as a categorical variable to avoid smoothing epidemic years. All continuous variables were scaled to enable comparison of effect size. Because these panel models require balanced data across time, data was truncated to SIT zones that had data for all years available (247 remaining of 291). Spatial dependency was evaluated, and the model was selected using the Hausman specification test and locally robust panel Lagrange Multiplier tests for spatial dependence. Based on a significant Hausman specification test result, which indicates a poor specification of the random effect model, a fixed effect model was chosen. This result is supported by the fact that we had a nearly exhaustive sample of SIT zones in the Medellin metro area. Lagrange multiplier tests were used to determine the most appropriate spatial dependency specifications. Based on the results of the Lagrange multiplier tests, a Spatial Autoregressive (SAR) model was the most appropriate to incorporate spatial dependency; a SAR model considers that the number of dengue cases in a SIT zone depends on the number in neighboring zones.Because public transit usage was a measurement taken during just two of the study years, we constructed an additional fixed effects spatial panel model by maximum likelihood model of dengue incidence in just 2011 and 2016 that included ridership as an additional predictor variable. Our fixed effects were year, socioeconomic status, distance from public transit, a two-way interaction between socioeconomic status and distance from public transit, percent utilizing public transit, and a two-way interaction between socioeconomic status and percent utilizing public transit. As in our model of all years, the model contained a log offset of population per zone per year and dengue case counts were log transformed after adding one to account for zones with zero dengue cases in a given year, year was analyzed as a categorical variable, and all continuous variables were scaled to enable comparison of effect size. The data was truncated to SIT zones that had data for all years available (251 remaining of 291). We used the same model selection process, and again a fixed effect model was chosen, and based on the results of the Lagrange multiplier tests, a Spatial Autoregressive (SAR) model was determined the most appropriate to incorporate spatial dependency. More

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Study areaWith an area of about 2.33 × 105 km2, the Western Sichuan Plateau (27.11°–34.31°N and 97.36°–104.62°E) is located in the transition zone between the Qinghai-Tibet Plateau and the Sichuan Basin, including all of Garze Prefecture and Aba Prefecture, and parts of Liangshan Yi Autonomous Prefecture28 (Fig. 1). With an altitude of 780–7556 m, this area is dominated by mountain and ravine areas and high mountain and plateau areas, and the terrain is high in the west and low in the east. The climate belongs to the subtropical plateau monsoon climate, with large temperature difference between day and night and abundant sunshine. The annual average temperature is about 9.01–10.5 °C, and the precipitation is about 556.8–730 mm28. The study area is rich in water resources, including the Yalong River, Minjiang River and other important river systems in the upper reaches of the Yangtze River, and the Baihe River, Heihe river and other river systems of the Yellow River. The main types of soil are plateau meadow soil dark brown soil, brown soil, cold frozen soil and cinnamon soil, and the main vegetation types are alpine meadow and scrub. With rich and diverse soil vegetation types and distinctive vertical zonal distribution characteristics, it is one of the global biodiversity conservation hotspots29.Figure 1Location of the study area. The map is created in the support of ArcGIS 10.2 (ESRI). The China map and Western Sichuan Plateau boundary data were collected from Resources and Environmental Science and Data Center (http://www.resdc.cn/). The Qinghai-Tibetan Plateau boundary data were collected from the Global Change Research Data Publishing & Repository (http://www.geodoi.ac.cn/WebCn/Default.aspx).Full size imageData source and processingMultisource archival data were used in this study (Table 1). The land use remote sensing monitoring data, administrative boundary data and geological disaster vector data were obtained from Resources and Environmental Science and Data Center. The spatial resolution of land use remote sensing monitoring data is 30 × 30 m, including 6 first-level classification and 26s-level classification. The first-level classification includes cropland, woodland, grassland, water body, built-up land, and unused land. The accuracy of remote sensing classification is not less than 95% for cropland and built-up land, not less than 90% for grassland, woodland, and water body, and not less than 85% for unused land, which meets the need of the research. Landsat remote sensing monitoring data is used as the main information resources, among which Landsat-TM/ETM remote sensing monitoring data is used in 2000, 2005, 2010 and Landsat 8 remote sensing monitoring data is used in 2015 and 2020. In light of actual conditions and the implementation of policies and philosophies including the natural forest protection project, return of farmland to forest, land remediation, ecological civilization, the period from 2000 to 2020 is selected as the study period, and the land use data of each period is cropped using ArcGIS 10.2 to reclassify the 26 secondary classifications into cropland, woodland, grassland, water body, built-up land and unused land.Table 1 Characteristics of data used for the study.Full size tableThe DEM data were obtained from SRTM (Shuttle Radar Topography Mission) of Resources and Environmental Science and Data Center, the spatial resolution of 30 × 30 m, absolute horizontal accuracy ± 20 m, absolute elevation accuracy ± 16 m, elevation and slope are extracted from the downloaded DEM. The Qinghai-Tibetan Plateau boundary data were collected from the Global Change Research Data Publishing & Repository. Data of carbon density of different land types were obtained from Chinese Ecosystem Research Network Data Center (http://www.nesdc.org.cn/).A total of 29,284 evaluation units were collected for spatial grid processing of the Western Sichuan Plateau according to 3 km × 3 km by ArcGIS 10.2. The impact factors obtained in this study include grid data per kilometer of GDP spatial distribution, grid data per kilometer of population spatial distribution, annual mean temperature spatial interpolation data, annual mean rainfall spatial interpolation data, long-term normalized difference vegetation index (NDVI) comes from Resources and Environmental Science and Data Center with a resolution of 1 km × 1 km. The Human Active Index (HAI), with a resolution of 30 m × 30 m, can be calculated by formula30,31, and the factors are discretized into the data type required for the geodetector by the natural breakpoint method.MethodsThe InVEST modelThe InVEST model was developed by Stanford University, the University of Minnesota, the Nature Conservancy and the World Wide Fund for Nature (WWF). The model’s terrestrial ecosystem services assessment includes four modules: soil conservation, water retention, carbon storage and biodiversity assessment, and provides an overall measurement of regional ecosystem services32. The carbon storage model of the InVEST model divides the carbon storage of the ecosystem into 4 basic carbon pools, namely above-ground carbon, underground carbon, soil carbon, dead organic matter carbon7.The calculation formula of total carbon storage in the Western Sichuan Plateau is as follows7:$$C_{total} = C_{above} + C_{below} + C_{soil} + C_{dead}$$
(1)
In formula (1), Ctotal is the total carbon storage; Cabove is the above-ground carbon storage; Cbelow is the underground carbon storage; Csoil is the soil carbon storage, and Cdead is the dead organic matter carbon storage.Based on the carbon density and land use data of different land use type, the carbon storage of each land use type in the Western Sichuan Plateau is calculated by the formula7:$$C_{{text{total}}i} = (C_{{text{above}}i} + C_{{text{below}}i} + C_{{text{soil}}i} + C_{{text{dead}}i}) times A_{i}$$
(2)
In formula (2), i is the average carbon density of each land use, and Ai is the area of this land used.The carbon density data of different land use types in this study were obtained from the shared date of the National Ecological Science Data Center and some documents33,34,35,36,37. Since the carbon density data were collected from the results of studies in different parts of China, the selected documents should be close to or similar to the study area as far as possible to avoid excessive data gap. At the same time, the carbon density varies with climate, soil properties and land use38, so the carbon density should be modified according to the climate characteristics and land use types of the Western Sichuan Plateau. Existing research results show that the carbon density is positively correlated with annual precipitation and weakly correlated with annual average temperature. The quantitative expression of the relationship between carbon density and temperature and precipitation is as follows39,40,41,42:$$C_{SP} = 3.3968 times P + 3996.1;;left( {{text{R}}^{{2}} = 0.{11}} right)$$
(3)
$$C_{BP} = 6.7981e^{0.00541p};;;left( {{text{R}}^{{2}} = 0.{7}0} right)$$
(4)
$$C_{BT} = 28 times {text{T}} + 398;;left( {{text{R}}^{{2}} = 0.{47,};{text{P}} < 0.0{1}} right)$$ (5) In these formula, CSP is the soil carbon density (kg m−2) based on the annual precipitation; CBP is the biomass carbon density (kg m−2) based on the annual precipitation; CBT is the biomass carbon density (kg m−2) based on annual average temperature; P is the average annual precipitation (mm), and T is the annual average temperature (°C). According to the data of China Meteorological Data Service Centre (http://data.cma.cn/), in the past 20 years, the average annual temperature of China and the Western Sichuan Plateau was 9.0 °C and 6.3 °C, and the average annual precipitation was 643.50 mm and 812.65 mm respectively.The modified formula of carbon density in the Western Sichuan Plateau is as follows7:$$K_{BP} = frac{C^{prime}{_{BP}}}{{C^{primeprime}{_{BP}}}}$$ (6) $$K_{BT} = frac{C^{prime}{_{BT}}}{{C^{primeprime}{_{BT}}}}$$ (7) $$C_{BT} = 28 times T + 398;;left( {{text{R}}^{{2}} = 0.{47,};{text{P}} < 0.0{1}} right)$$ (8) $$K_{S} = frac{C^{prime}{_{SP}}}{{C^{primeprime}{_{SP}}}}$$ (9) In these formula, KBP is the modified indices of precipitation factor in biomass carbon density; KBT is the modified indices of temperature factor; C'BP and C''BP are the biomass carbon density obtained from annual precipitation in the Western Sichuan Plateau and the whole country respectively. C'BT and C''BT are the biomass carbon density obtained from annual average temperature; C'SP and C''SP are the soil carbon density data obtained from annual average temperature; KB and KS are the biomass carbon density modified indices and soil carbon density modified indices respectively. The carbon density values of each land use type after modified in the Western Sichuan Plateau are shown in Table 2.Table 2 Carbon density values of different land use types in the Western Sichuan plateau (t hm−2).Full size tableExploratory spatial analysis methodGlobal spatial autocorrelationGlobal Moran’s I was used to describe the spatial differentiation characteristics of carbon storage in the study area, and the expression formula is as follows43:$$I = frac{{nsumnolimits_{i = 1}^{n} {sumnolimits_{j = 1}^{n} {w_{i,j} left( {x_{i} - overline{x} } right)left( {x_{j} - overline{x} } right)} } }}{{sumnolimits_{i = 1}^{n} {sumnolimits_{j = 1}^{n} {omega_{ij} } } sumnolimits_{i = 1}^{n} {left( {x_{i} - overline{x} } right)^{2} } }}$$ (10) wij is the spatial weight; x is the attribute mean; xi and xj are the attribute values of elements i, j, respectively; n is the number of cells, and the correlation is considered significant when |Z|  > 1.96.Local indications of spatial association (LISA)LISA reveals the local cluster characteristics of spatial unit attributes by analyzing the difference and significance between spatial units and surrounding units, and the expression formula is as follows42:$$I_{i} (d) = frac{{n(x_{i} – overline{x} )sumnolimits_{j = 1}^{n} {w_{ij} (x_{j} – overline{x} )} }}{{sumnolimits_{i = 1}^{n} {(x_{j} – overline{x} )^{2} } }}$$
(11)
Correlation analysisIn order to evaluate the influence of natural factors and socioeconomic factors on carbon storage in the study area, the correlation coefficients of temperature, rainfall, NDVI, GDP, population density (PD), HAI and carbon storage were calculated according to the Pearson correlation coefficient method. The calculation formula is as follows44:$$r_{xy} = frac{{sumnolimits_{i = 1}^{n} {(M_{i} – overline{x} )(y_{i} – overline{y} )} }}{{sqrt {sumnolimits_{i = 1}^{n} {(M_{i} – overline{x} )^{2} sumnolimits_{i = 1}^{n} {(y_{i} – overline{y} )} } } }}$$
(12)
rxy represents the correlation coefficient between x and y; Mi represents the carbon storage in the ith year; yi represents the value of the impact factor Y in the ith year, and ({overline{text{x}}}) and ({overline{text{y}}}) respectively represents the average value of carbon storage and impact factor in the research period over several years.Human influence index analysis methodLand use is significantly spatially clustered in the study area31, and LUCC changes will have a certain impact on the structure and process of the ecosystem. HAI has the characteristics of spatial variability, which can reflect the impact of human activities on land use and landscape composition changes. In this study, Human Influence Index Analysis Method (HAI) index was used to analyze the correlation between carbon storage and human interference intensity in the Western Sichuan Plateau. The calculation formula is as follows30,$$HAI = sumlimits_{i = 1}^{n} {left( {A_{i} P_{i} /TA} right)}$$
(13)
HAI is Human Active Index; Ai is the total area of the ith land use type; Pi The intensity parameter of human impact reflected by type i land use type; TA is the total final surface area of land use type in evaluation unit; n is the number of land use types. Combined with the land use type of this study, Pi is assigned by Delphi method, in which cropland is 0.67, woodland is 0.13, grassland is 0.12, water body is 0.10, built-up land is 0.96, and unused land is 0.0530,45.GeodetectorGeodetector is an algorithm that uses spatial heterogeneity principle to detect driving factors of carbon storage, which can quantitatively detect the influence of impact factors on carbon storage and explore the interaction between driving factors. Geodetector includes factor detection, risk detection, interaction detection and ecological detection46.Differentiation and factor detection: the influence factors were discretized, and then the significance test of the difference in the mean values of the impact factors was conducted to detect the relative importance among the factors. The statistical quantity q is used to measure the explanatory power of impact factors on the carbon storage spatial differentiation and the value range of q is between 0 and 1. The larger the value, the stronger the explanatory power of the factor47.$$q = 1{ – }frac{{sumnolimits_{h = 1}^{L} {N_{h} sigma_{h}^{2} } }}{{Nsigma^{2} }}$$
(14)
In this formula, h = 1, 2…, L is the classification or partition of variable (Y) or factor (X); Nh and N are layer h and regional number units respectively; and (sigma_{h}^{2}) and (sigma_{{}}^{2}) are the variance of the layer h and regional value Y respectively.The variance of the regional value Y is calculated as follows,$$sigma^{2} = frac{{sumnolimits_{i = 1}^{n} {(Y_{i} – overline{Y} )^{2} } }}{N – 1}$$
(15)
where, Yi and (overline{Y}) are the mean value of sample j and the region Y, respectively.$$sigma^{2} = frac{{sumnolimits_{i = 1}^{{n_{h} }} {(Y_{h,i} – overline{{Y_{h} }} )^{2} } }}{{N_{h} – 1}}$$
(16)
where, Y and (overline{Y}) are the value and mean value of sample i in layer h, respectively.Interaction detection: it is used to identify the interaction between different impact factors Xs, that is, to evaluate whether the combined action of X1 and X2 will increase or weaken the explanatory power of vegetation coverage Y, or the influence of these factors on Y is independent of each other. The evaluation method is to first calculate the value q of the two factors X1 and X2 for Y respectively: q(X1) and q(X2), and calculate the value q of their interaction (the new polygon distribution formed by the tangent of the two layers of the superimposed variables X1 and X2) : q(X1 ∩ X2) and compare q(X1) and q(X2) with q(X1 ∩ X2)46. More

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