Philippa Kaur

One thing that the team at Los Amigos did not do is peer deeper into the reserve to try to determine where the Mashco Piro are camped out. Gutiérrez says the decision on whether to establish some kind of monitoring system for isolated communities rests with governments and Indigenous groups, but few doubt that it is possible.
Some researchers worry about the implications of this kind of work. Greg Asner, an ecologist at Arizona State University in Tempe, regularly captured evidence of encampments of isolated groups more than a decade ago, when his team was surveying the Peruvian Amazon in a plane equipped with a powerful laser-based system that provides 3D images of the forest. He flagged the images to his sources at Peru’s environment ministry, but never saw the groups themselves as a legitimate research topic. Even today, he doesn’t see the value in actively tracking them.
“It’s creepy, like describing the home range of jaguars, but human rights are different than jaguar rights,” says Asner. “If we know they are in there, why do we need to know exactly where they are sleeping at night?”
Despite the ethical worries about monitoring, some Indigenous leaders are open to the idea. Knowing where isolated groups are could help surrounding Indigenous communities to prevent unintended and dangerous contact, but “it is the Indigenous organizations that should implement and execute any system of control and surveillance of the Indigenous peoples in isolation,” says Julio Cusurichi, president of FENAMAD, which has worked with the Peruvian government to prevent contact and conflict since the Mashco Piro began to emerge.
FENAMAD was also instrumental in pushing for the creation of the Madre de Dios reserve in 2002. Twenty years later, however, the reserve’s borders have yet to be finalized, and the Indigenous organization is still pushing to expand the eastern boundary to cover areas where the Mashco Piro are known to roam. The problem is that these same areas are currently occupied by logging concessions, which would be costly for the government to cancel.

Julio Cusurichi, president of the Native Federation of the Madre de Dios River and Tributaries (FENAMAD).

Julio Cusurichi, president of the Native Federation of the Madre de Dios River and Tributaries (FENAMAD).

For Cusurichi, the killing of the logger in August is yet another reminder of the precarious situation along the border of the reserve and the risks to both outsiders and the Mashco Piro. Too often, he contends, the government is more concerned with protecting economic interests than the rights of isolated peoples.
Tauli-Corpuz, the former UN rapporteur, has little doubt that scientists mean well, but she worries about any efforts to document the precise location of isolated groups. “If this information falls into the wrong hands, these people will be disturbed in ways they could never imagine,” she says.
Officials from the culture ministry acknowledged these dangers in discussions with Nature, and said they were looking at potential regulations to control the flow of information and restrict who can peer into the reserves.
Although Forsyth says the ministry is full of people who want to do the right thing, he is wary of assuming that government officials always mean well. In Brazil, critics have accused President Bolsonaro, a right-wing populist, of sidelining scientists at FUNAI and attempting to appoint a former Christian missionary to head the division that handles isolated peoples. In the Madre de Dios region, the former governor, Luis Hidalgo Okimura, disappeared in February just before he was to be jailed in connection with an investigation into an illegal logging ring.
“In some cases, the government may not be trustworthy,” Forsyth warns. He places more faith in Indigenous organizations and their advocates. “Giving them access to whatever information they would like or can’t generate themselves ought to be the priority.” More

Protein domains show a Gompertzian growthThe protein domain RSA distributions of 3368 bacterial genomes were obtained as detailed in the “Materials and methods” section. Briefly, for each bacterial genome we retrieved all the identifiable protein domains. Then, we computed the RSA by counting the number of protein domains belonging to each protein domain family.Three evolutionary hypotheses were tested by fitting the empirical RSAs with the Log-Series [Eq. (7)], the Negative Binomial (Eq. (6)) and the Poisson Log-Normal (Eq. (4)) distribution (Fig. 1a). According to the Akaike Information Criterion (AIC)30, in (99.97%) of bacteria the selected model was the Poisson Log-Normal (Fig. 1b). This model performed better than both the Log-Series and the Negative Binomial and described the data well, with an average (R^2) of 0.97 (minimum (R^2)=0.86). The selection of the Poisson Log-Normal model instead of the Negative Binomial or the Log-Series, implies that the protein domains evolution process is characterized by a Gompertzian density regulation function ((g(x)=gamma ln (x+epsilon ))) rather than a linear one ((g(x)=eta x)). This suggests an asymmetric process in which the proliferation rate for low abundant protein domains is faster than for the high abundant ones.Figure 1Fit of protein domains RSA. (a) Example of protein domains Preston plot fitted with three different distributions: the Poisson Log-Normal, the Negative Binomial and the Log-Series. Results refer to the bacterial genome (text {GCA}_000717515). The Negative Binomial and the Log-Series fit overlap. This implies that the dispersion parameter (alpha) of the Negative Binomial distribution (see Eq. (6)) is close to zero. The mean and the median of the dispersion parameter obtained for the 3368 bacterial genomes are ({2.67times 10^{-4}}) and ({2.62times 10^{-7}}), in agreement with the observed overlap. (b) Distribution of the difference between the AIC obtained with the Poisson Log-Normal model (PL) and the Log-Series (LS) or the Negative Binomial (NB) model, considering all the 3368 bacterial genomes.Full size imageProtein domains deactivation is faster than duplicationThe examination of the Poisson Log-Normal scale ((mu)) and location ((sigma ^2)) parameters (see Eq. (4) and Supplementary Material) estimated by the fitting procedure for each bacterial genome, allows us to reveal further features of the evolutionary process of protein domains.First of all, Fig. 2 shows that (mu) has negative values in all bacterial genomes. Recalling that (mu =r/gamma), where r is the growth rate and (gamma) is the multiplicative constant of the Gompertzian function, which must be positive, this implies that the growth rate of protein domains, r, is also negative. Notice that the growth rate can be expressed as the difference between the birth and the death rate, (r=b-d). Hence, a negative r means that the death rate is greater than the birth rate ((d > b)). In the evolutionary model of protein domains, the birth rate b has the meaning of duplication rate, while the death rate d is the rate at which protein domains are deactivated. A negative r hence implies that protein domain deactivation, which is related to the accumulation of events which disrupt the coding sequence of protein domains, happens at a faster rate than the duplication of the whole protein domain sequence within the genome.Figure 2Distribution of species according to the model parameters. Scatter plot of Poisson Log-Normal parameters (mu) versus (sigma ^2) obtained fitting the protein domains RSAs. Only species represented by at least 10 different strains were included in the plot, for a total of 1173 bacterial genomes which belong to 48 different species. Different colors represent different species as indicated in the legend.Full size imageFurthermore, the plot of (mu) as a function of (sigma ^2) (Fig. 2) highlights the negative linear relationship between (mu) and (sigma ^2). Such relationship can also be deduced mathematically.Starting from the expressions (mu =r/gamma) and (sigma ^2=sigma _e^2 / 2gamma), and after simple algebraic manipulation, we can in fact obtain that (mu = 2rsigma ^2 / sigma _e^2), which explains the negative linear relationship between the two parameters.Besides the negative relationship, the plot of (mu) versus (sigma ^2) also highlights the presence of clusters of bacterial genomes with similar ecological features, which are pictured in the plot as roughly parallel stripes (Fig. 2). When we depict bacterial strains belonging to the same species using the same color, it emerges that the stripes are related to the bacterial taxonomy. This result motivates us to introduce a new approach to bacterial phylogeny based on the ecological modeling of protein domains and the consequent estimation of the parameters (mu) and (sigma ^2).Protein domain RSA and evolutionary distanceWe propose to calculate the pairwise evolutionary distances between bacteria based on three parameters: the Poisson Log-Normal scale and location parameters discussed above ((mu) and (sigma)), and the density of protein domains in the bacterial genome. Such density describes to which extend the whole bacterial genome is populated with protein domains and it hence constitutes an additional feature of the protein domain ecological dynamics. As detailed in the Materials and Methods, the distance between bacteria is specifically computed as the 3D euclidean distance in the scaled space of (mu), (sigma), and protein domain density. In the following, we refer to such distance as ‘RSA distance’.To evaluate the bacterial interrelationships derived from the RSA distances, we compared our results with both the bacterial taxonomic classification and the 16S rRNA gene-based phylogeny. Specifically, starting from the RSA distance matrix we computed a hierarchical clustering of bacteria and we compared the resulting clusters with those obtained from the 16S rRNA gene-based distance matrix. Both clustering results were then compared with the bacterial taxonomic classification.Notice that the usage of both 16S rRNA phylogeny and bacterial taxonomic classification allows us to exploit the complementary information that these two approaches provide, despite their intrinsic connection. Namely, modern microbial taxonomy is mostly based on 16S rRNA gene6 and, on the other hand, the cutoffs commonly used in 16S rRNA phylogeny originated from phenotype-based taxonomy31. However, while taxonomy allows us to assign human interpretable names to bacteria, to associate such names with phenotypic properties, and to classify bacteria into a predefined hierarchy, 16S rRNA phylogeny provides a quantitative measurement of the evolutionary distance between bacteria that can be compared with the RSA distance without setting any pre-defined threshold. Moreover, the usage of 16S rRNA phylogeny allows us to investigate the bacterial relationships at the intraspecies level, for which the taxonomic classification is not available.As detailed in the Materials and Methods, 16S rRNA distances were calculated based on the bacterial 16S rRNA gene reference sequences, following the standard procedure32. Taxonomic classification, instead, was retrieved from NCBI and included the following levels: phylum, class, order, family, genus and species. In order to obtain a comparable number of clusters from all three methods, we considered separately each taxonomic level and we cut the 16S rRNA and the RSA -based hierarchical trees so as to get a number of clusters equivalent to the number of taxa available at the selected taxonomic level.At each taxonomic level, the Normalized Mutual Information (NMI) was used as a measurement of agreement between different clustering solutions33. Notice that, while the theoretical range of the NMI score is the interval (left[ 0,1right]), NMI is biased towards clustering solutions with more clusters and fewer data points34. Consequently, the baseline of NMI score in practise is not zero and relatively high NMI scores can be an artifact caused by the low ratio between number of bacteria and number of taxonomic groups. To make the comparison fair, we used simulations to calculate the baseline NMI for each taxonomic level (box plots of Fig. 3).As expected by their intrinsic relationship, taxonomy and 16S rRNA phylogeny show high agreement (red dots in Fig. 3). RSA-based clusters, instead, show a certain deviation from both taxonomy (blue dots in Fig. 3) and phylogeny (green dots in Fig. 3). For both comparisons, however, the NMI scores are still evidently higher than the baseline, signifying that the RSA model captures phylogenetic signals to a certain degree. Comparing the obtained NMI scores with the baseline, we notice that the agreement between RSA-based clusters and both taxonomy and phylogeny increases at lower taxonomic levels, reaching the maximum at species level. Taking as ground truth the taxonomic classification, the total purity of the RSA-based clusters at species level is 0.65, signifying that 65% of bacteria are correctly classified.Figure 3Comparison between the three clustering results at different taxonomic levels. NMI scores (y-axis) are calculated as a measurement of agreement between clusters based on: RSA method and taxonomy (blue), 16S rRNA gene and taxonomy (red), RSA method and 16S rRNA gene (green). Different taxonomic levels are considered for the comparison: phylum, class, order, family, genus and species (x-axis). The box plots represent the baselines of NMI score and are based on simulations.Full size imageTo assess the robustness and stability of the RSA-based phylogeny, with regard to the choice of protein domains, we randomly selected subsamples of protein domains in different proportions (from (10%) to 90% of all protein domains). The reconstructed phylogenetic trees were then compared with the phylogenetic tree obtained using all protein domains (see Materials and Methods for details), and the correlation between the trees was calculated (see Supplementary Fig. S6). As expected, with larger proportions of protein domains taken into account, the correlation between subsample-based phylogeny and base phylogeny increases. For larger subsampling proportions, the compared phylogenetic trees are in good agreement: for a subsample with 90% of protein domains, the mean cophenetic correlation is equal to 0.74, and the mean common-nodes-correlation is equal to 0.68. We notice that the common-nodes-correlation is more stable compared to the cophenetic correlation, as expected since cophenetic correlation is affected by the height of the phylogenetic trees. The results suggest that the overall structure of the phylogenies is stable even for smaller subsampling proportions, while subsampling height of the branches correlates with the full-data height only at larger subsampling proportions.To evaluate the intraspecies composition obtained from the RSA-based clustering, we selected the subset of species for which at least 10 different strains were present in our data (48 species). Among them, we selected the species where hierarchical clustering showed a clear separation of clusters (including outliers) and for which published literature characterizing at least some of the strains was available (6 out of 48 species). For these 6 species, we again assessed the robustness and stability of RSA phylogenies, as detailed in the “Materials and methods” section. Our results suggest (see Supplementary Fig. S7) that the subsample-based phylogenies are in good agreement with the full-data phylogenies, especially for larger subsampling proportions. We notice the correlations is larger than in the case of phylogenetic trees for randomly selected 100 bacteria (Supplementary Fig. S6), especially for certain species (i.e., Xanthomonas citri). This could be attributed to the smaller size of the phylogenetic tree. However, the species with similar phylogenetic tree size still show differences in correlation (i.e., Xanthomonas citri and Francisella tularensis), suggesting that the RSA-based distance matrix between the strains of Xanthomonas citri carries stronger phylogenetic signal. Comparing 6 observed species with the randomly sampled subsets of 100 bacteria, we can analogously conclude that the RSA-captured phylogenetic signal is stronger within the species. In the following, we discuss the results obtained for the 6 selected bacterial species in more details.Figure 4(Previous page.) Hierarchical clustering of bacteria at the intraspecies level, comparing solutions obtained by RSA and 16S rRNA method. Each subplot shows a tanglegram with RSA-based dendrogram on the left and 16S rRNA-based dendrogram on the right. Lines connect the same bacteria from two dendrograms. The color/type of the line represents the feature of the bacterium it connects. (a) 22 strains of Xanthomonas citri belong to two different pathovars: A (orange) and (hbox {A}^{mathrm{W}}) (purple). (b) 10 strains of Chlamydia pneumoniae are isolated from different tissues: conjuctival (yellow), respiratory (magenta) and vascular (violet). 9 strains represented with solid line are human (Homo sapiens) pathogens while the one strain represented by dashed line is koala (Phascolarctos cinereus) pathogen. (c) 14 strains of Vibrio cholerae are colored based on their karyotype. 11 strains have two circular chromosomes Chr1 ((sim 3) Mb) and Chr2 ((sim 1) Mb) (magenta). 2 strains have one (sim)4 Mb long circular chromosome (yellow). One strain has three chromosomes Chr1 ((sim)3 Mb), Chr2 ((sim)1 Mb) and Chr3 ((sim)1 Mb) (violet).Full size imageRSA-based method distinguishes subspecies infecting different hostsXanthomonas citri subsp. citri (XCC) and Chlamydia pneumoniae (Cpn) are two species whose subspecies can infect different hosts. Here we show that the RSA-based method correctly discriminates such subspecies even when their divergence is not detected comparing the 16S rRNA gene sequences.Xanthomonas citri subsp. citri (XCC) is a causal agent of citrus canker type A, a bacterial disease affecting different plants from the genus Citrus. While citrus canker A infects most citrus species, two of its variants, A* and (hbox {A}^{mathrm{W}}), have a much more limited host range with XCC pathotype (hbox {A}^{mathrm{W}}) infecting only Key lime (C. aurantifolia) and alemow (C. macrophylla)2. Our data set includes 17 strains of XCC pathotype A and 5 strains of XCC pathotype (hbox {A}^{mathrm{W}})2. RSA-based clustering of the 22 XCC strains identifies two separated clusters (Fig. 4a, left) which coincide with the two XCC pathotypes. Concurrently, clustering based on 16S rRNA gene fails to identify the two pathotypes of XCC (Fig. 4a, right). This suggests that even though pathotypes A and (hbox {A}^{mathrm{W}}) have different hosts, their diversification is not reflected in the variability of the 16S rRNA gene. On the other hand, modeling the protein domain RSA of the two pathotypes succesfully captures the different functions of their proteomes.Another important aspect of the citrus canker is the geographical spread of the disease. The 22 strains of XCC included in our data set have diverse geographical origin. While all (hbox {A}^{mathrm{W}}) strains were sampled from USA, strains of pathotype A originate from USA, Brazil and China. RSA clustering of 17 A-type strains colored by their sampling location shows a geographical pattern (Supplementary Fig. S2) similar to the one obtained by Patané et al.2 using a maximum likelihood tree based on 1785 concatenated unicopy genes, with the only exception of strain jx-6 ((text {GCA}_001028285)) coming from China.For what concerns Chlamydia pneumoniae (Cpn), this is an obligate intercellular parasite which is widespread in human population and causes acute respiratory disease. Besides humans, different animal species can be infected with Chlamydia pneumoniae. Our data set includes 9 strains which infect humans (Homo sapiens) and 1 strain isolated from koala (Phascolarctos cinereus). RSA-based clustering clearly separates such isolate from the group of highly similar human isolates (Fig. 4b, left). This result is confirmed by 16S rRNA-based clustering (Fig. 4b, right) and is in agreeement with previous results in which the comparison of four human-derived isolates and the koala strain LPCoLN ((text {GCA}_000024145)) through whole-genome sequencing showed a much higher variation between human and koala-derived strains than within the human-derived strains35.Another peculiarity of Chlamydia pneumoniae is tissue tropism. The human-derived strains of Chlamydia pneumoniae can in fact be divided into conjuctival, raspiratory and vascular based on their tissue of origin. Cpn tissue tropism was the focus of the study conducted by Weinmaier et al., where whole-genome sequences of multiple Cpn strains isolated from different human anatomical sites were compared and animal isolates were used as outgroup3. Weinmaier et al. found a good agreement between the anatomical origin of strains and the maximum likelihood phylogenetic tree based on all SNPs. However, they could not obtain a clear separation between anatomical subgroups of Cpn. Our results show that the RSA-based method partially succeeds in separating subspecies related to different tissues (Fig. 4b, left). The RSA-based dendrogram, in fact, shows a cluster of four respiratory bacteria. However, it does not separate the other subspecies by infection site, suggesting that tissue tropism is not entirely captured by our method.RSA-based method discriminates subspecies with different genome compositionIn some cases, subspecies of the same species are characterized by global differences in the genome composition. This is, for example, the case of Vibrio cholerae and Buchnera aphidicola. Here, we show that the RSA-based model is able to capture such differences and to discriminate subspecies with known different genomic peculiarities.Vibrio cholerae is the causative agent of cholera disease. Its genome is normally composed of two chromosomes: Chr1 ((sim 3) Mb) and Chr2 ((sim 1) Mb). However, some strains show a different karyotype. The two strains (1154text {-}74) ((text {GCA}_000969235)) and (10432text {-}62) ((text {GCA}_000969265)), for instance, underwent the process of chromosomal fusion and possess only one (sim 4) Mb long circular chromosome, which shows a high degree of synteny with the two chromosomes of the more common strains36. The strain (text {TSY}216) ((text {GCA}001045415)), on the other hand, besides having the original two chromosomes, also contains an additional (sim 1) Mb long replicon, which does not share any conserved region with Chr1 and Chr237. For these reasons, we expect the single- and two-chromosome strains to be phylogenetically closer to each other than to the three-chromosome strain, which contains the extra replicon. The 16S rRNA gene-based clustering, however, does not identify any clear separation between the three types of strains (Fig. 4c, right). As a matter of fact, all the 16S rRNA gene copies of all the Vibrio cholerae strains included in our data set are located on (sim 3) Mb long chromosome, which shows high synteny across all strains. It is therefore not surprising that the comparison of the 16S rRNA genes does not capture the global genomic differences that exist between the considered strains. On the other hand, the results obtained with the RSA-based clustering show a clear distinction of the strains with different genomic structure (Fig. 4c, left). The reason for the success of the RSA-based method lies in the theoretical definition of RSA-based distance. In fact, the RSA-based distance depends on the Poisson Log-Normal location parameter (sigma ^2), which increases with the genome length (Supplementary Fig. S1): by definition, (sigma ^2 = sigma _e^2 / 2gamma), and, while the environmental noise (sigma _e^2) can be reasonably considered independent of the genome length, the density regulation (gamma) is expected to be stronger for smaller genomes, which repesent a scarcer environment with less resources.Buchnera aphidicola is a bacterial species in mutualistic endosymbiotic relationship with different aphids (members of superfamily Aphidoidea). As many endosymbionts, Buchnera aphidicola underwent the process of genome reduction as an adaptation to the host-associated lifestyle and has a genome with length ( More

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As the Italian probe LICIACube whizzed past asteroids Didymos (bottom) and Dimorphos (top), it captured a debris plume spraying out from the DART spacecraft as it smashed into Dimorphos.Credit: ASI/NASA

Astronomers see fireworks as spacecraft ploughs into asteroidTelescopes in space and across Earth captured the spectacular aftermath of NASA’s Double Asteroid Redirection Test (DART) spacecraft crashing into the asteroid Dimorphos on 26 September.The goal was to knock the harmless space rock into a slightly different orbit to test whether humanity could do such a thing if a dangerous asteroid were ever detected heading for Earth. The smash-up was “the first human experiment to deflect a celestial body”, says Thomas Zurbuchen, NASA’s associate administrator for science, and “an enormous success”.A ringside view came from LICIACube, a tiny Italian spacecraft that flew along with DART and photographed the impact, which took place 11 million kilometres from Earth. LICIACube’s first images, released by the Italian Space Agency on 27 September, show a large fireworks-like plume of rocks and other debris coming off Dimorphos (pictured, top) after DART had ploughed into it.It will take days to weeks before mission scientists can confirm whether the test worked, and did in fact cut the time it takes Dimorphos to orbit its partner asteroid, Didymos (pictured, bottom), by 10–15 minutes.

The shell of the endangered hawksbill sea turtle (pictured) is prized for trinkets and jewellery.Credit: Reinhard Dirscherl/SPL

Sea turtles swim more freely as poaching declinesPoaching is less of a threat to the survival of sea turtles than it once was, an analysis suggests (J. F. Senko et al. Glob. Change Biol. https://doi.org/gqrzzn; 2022). Illegal sea-turtle catch has dropped sharply since 2000, and most current exploitation occurs in areas with relatively healthy turtle populations.The analysis is the first worldwide estimate of the number of adult sea turtles that are moved on the black market. The authors surveyed sea-turtle specialists and sifted through documents to derive an estimate that around 1.1 million sea turtles were illegally harvested between 1990 and 2020. Nearly 90% of them were funnelled into China and Japan. Of the species that could be identified, the critically endangered hawksbill turtle (Eretmochelys imbricata; pictured), prized for its beautiful shell, was among the most frequently exploited.But the team also found that the illegal catch from 2010 to 2020 was nearly 30% lower than in the previous decade. “The silver lining is that, despite the seemingly large illegal take, exploitation is not having a negative impact on sea-turtle populations on a global scale,” says co-author Jesse Senko, a marine-conservation scientist at Arizona State University in Tempe. More

National Center for Theoretical Sciences, Taipei, 10617, TaiwanChun-Wei Chang & Chih-hao HsiehResearch Center for Environmental Changes, Academia Sinica, Taipei, 11529, TaiwanChun-Wei Chang, Fuh-Kwo Shiah & Chih-hao HsiehFaculty of Advanced Science and Technology, Ryukoku University, Otsu, Shiga, 520-2194, JapanTakeshi MikiInstitute of Oceanography, National Taiwan University, Taipei, 10617, TaiwanTakeshi Miki, Fuh-Kwo Shiah & Chih-hao HsiehCenter for Biodiversity Science, Ryukoku University, Otsu, Shiga, 520-2194, JapanTakeshi MikiHealth Science Center Libraries, University of Florida, Gainesville, FL, 32611, USAHao YeUniv. Lille, CNRS, Univ, Littoral Côte D’Opale, IRD, UMR 8187, LOG— Laboratoire D’Océanologie et de Géosciences, Station Marine de Wimereux, F- 59000, Lille, FranceSami SouissiLeibniz Institute of Freshwater Ecology and Inland Fisheries, IGB, 12587, Berlin, GermanyRita AdrianFreie Universität Berlin, Department of Biology, Chemistry and Pharmacy, 14195, Berlin, GermanyRita AdrianNational Research Institute for Agriculture, Food and Environment (INRAE), CARRTEL, Université Savoie Mont Blanc, 74200, Thonon les Bains, FranceOrlane AnnevilleCentre for Limnology, Institute of Agricultural and Environmental Sciences, Estonian University of Life Sciences, Kreutzwaldi 5D, 51014, Tartu, EstoniaHelen Agasild & Peeter NõgesDepartment of Ecosystem Studies, School of Environmental Science, The University of Shiga Prefecture, Hikone, 522-8533, Shiga, JapanSyuhei Ban & Xin LiuKinneret Limnological Laboratory, Israel Oceanographic & Limnological Research, P.O. Box 447, 14950, Migdal, IsraelYaron Be’eri-Shlevin, Gideon Gal & Tamar ZoharyBiodiversity Research Center, Academia Sinica, Taipei, 11529, TaiwanYin-Ru Chiang & Jiunn-Tzong WuUK Centre for Ecology & Hydrology, Lancaster Environment Centre, Library Avenue, Bailrigg, Lancaster, Lancashire, LA1 4AP, UKHeidrun Feuchtmayr & Stephen J. ThackerayLake Biwa Environmental Research Institute, Otsu, 520-0022, JapanSatoshi Ichise & Michio KumagaiFaculty of Environment and Information Sciences, Yokohama National University, Yokohama, 240-8502, Kanagawa, JapanMaiko KagamiDepartment of Environmental Science, Faculty of Science, Toho University, Funabashi, Chiba, 274-8510, JapanMaiko KagamiResearch Center for Lake Biwa & Environmental Innovation, Ritsumeikan University, Kusatsu, 525-0058, Shiga, JapanMichio KumagaiBiodiversity Division, National Institute for Environmental Studies, 16-2 Onogawa, Tsukuba, Ibaraki, 305-8506, JapanShin-Ichiro S. MatsuzakiCNR Water Research Institute (IRSA), L.go Tonolli 50, 28922, Verbania, Pallanza, ItalyMarina M. Manca, Roberta Piscia & Michela RogoraPlymouth Marine Laboratory, Prospect Place, West Hoe, Plymouth, PL1 3DH, UKClaire E. WiddicombeInstitute of Ecology and Evolutionary Biology, Department of Life Science, National Taiwan University, Taipei, 10617, TaiwanChih-hao Hsieh More

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Calculation of flight-step headings and movementTerms defining flight-step movement, precision and geophysical orientation cues are listed in Table 1. Since seasonal migration nearly ubiquitously proceeds from higher to lower latitudes, it is convenient to define headings clockwise from geographic South (counter-clockwise from geographic North for migration commencing in the Southern Hemisphere). Assuming a spherical Earth, a sequence of N migratory flight-steps with corresponding headings, αi, i = 0,…, N−1, the latitudes, ∅i+1, and longitudes, λi+1, on completion of each flight-step can be calculated using the Haversine Equation76, which we approximated by stepwise planar movement using Eqs. (1) and (2). For improved computational accuracy and to accommodate within flight-step effects, we updated simulated headings and corresponding locations hourly. A migrant’s flight-step distance ({R}_{{{mathrm {step}}}}=3.6{V}_{{mathrm {a}}}{cdot n}_{{mathrm {H}}}/{R}_{{{mathrm {Earth}}}}) (in radians), depends on its flight speed, Va (m/s) relative to the mean Earth radius REarth (km), and flight-step hours, nH. With a geomagnetic in-flight compass, expected hourly geographic headings are modulated by changes in magnetic declination, i.e., the clockwise difference between geographic and geomagnetic South10,32.Formulation of compass coursesFor simplicity, we consider the case of a single inherited or imprinted heading. This can be extended to include sequences of preferred headings. Expected geographic loxodrome headings remain unchanged en route, i.e.,$${bar{{{{{{rm{alpha }}}}}}}}_{i}={bar{{{{{{rm{alpha }}}}}}}}_{0}$$
(5)
Relative to geographic axes, expected geomagnetic loxodrome headings remain unchanged relative to proximate geomagnetic South, i.e., are offset by geomagnetic declination on departure (updated hourly in simulations)$${bar{{{{{{rm{alpha }}}}}}}}_{i}={bar{{{{{{rm{alpha }}}}}}}}_{0}+{delta }_{{mathrm {m}},i}$$
(6)
As described and illustrated in detail by Kiepenheuer13, the magnetoclinic compass was hypothesized to explain the prevalence of “curved” migratory bird routes, i.e., for which local geographic headings shift gradually but substantially en route. A migrant with a magnetoclinic compass adjusts its heading at each flight-step to maintain a constant transverse component, γ′, of the experienced inclination angle, γ, so that error-free headings are (see Fig. S5 in ref. 34)$${{bar{{{{{{rm{alpha }}}}}}}}_{i}={{sin }}}^{-1}left(frac{{{tan }}{gamma }_{i}}{{{tan }}{gamma }^{{prime} }}right){={{sin }}}^{-1}left(frac{{{tan }}{gamma }_{i}{{sin }}{bar{{{{{{rm{alpha }}}}}}}}_{0}}{{{tan }}{gamma }_{0}}right).$$
(7)
In a geomagnetic dipole field, the horizontal (Bh) and vertical (Bz) field, and therefore also inclination, each depends solely on geomagnetic latitude, ∅m:(gamma ={{{tan }}}^{-1}left({B}_{{mathrm {z}}}/{B}_{{mathrm {h}}}right)={{{tan }}}^{-1}left(2{{sin }}{phi }_{{mathrm {m}}}/{{cos }}{phi }_{{mathrm {m}}}right)={{{tan }}}^{-1}left(2{{tan }}{phi }_{{mathrm {m}}}right).) The projected transverse component, therefore, becomes$${gamma }^{{prime} }={{{tan }}}^{-1}left(frac{{{tan }}{gamma }_{0}}{{{sin }}{bar{{{alpha }}}}_{0}}right)={{{tan }}}^{-1}left(frac{2{{tan }}{{{phi }}}_{{mathrm {m}},0}}{{{sin }}{bar{{{{{{rm{alpha }}}}}}}}_{0}}right),$$which can be substituted into Eq. (7) to produce a closed formula for magnetoclinic headings in a dipole as a function of geomagnetic latitude$${bar{{{{{{rm{alpha }}}}}}}}_{i}left({{{phi }}}_{{mathrm {m}},i}right)={{{sin }}}^{-1}left(frac{{{sin }}{bar{{{{{{rm{alpha }}}}}}}}_{0}}{{{tan }}{{{phi }}}_{{mathrm {m}},0}}cdot {{tan }}{{{phi }}}_{{mathrm {m}},i}right),$$
(8)
with the expected initial heading, ({bar{{{{{{rm{alpha }}}}}}}}_{0}), and initial geomagnetic latitude, ∅m,0, being constants. Equations (7) and (8) have no solution when inclination increases en route, which could occur following substantial orientation error or in strongly non-dipolar fields. We followed previous studies in allowing magnetoclinic migrants to head towards magnetic East or West until inclination decreased sufficiently33,34,46, but also included orientation error based on the modelled compass precision.To assess sun-compass sensitivity algebraically, and also to improve computational efficiency, we used a closed-form equation for sunset azimuth, θs (derived in Supplementary Note 3 and see ref. 23),$${theta }_{{mathrm {s}}}={{{cos }}}^{-1}left(frac{-{{sin }}{delta }_{{mathrm {s}}}}{{{cos }}{{phi }}}right),$$
(9)
where δs is the solar declination, which varies between −23.4° and 23.4° with season and latitude23. Sunset azimuth is the positive and sunrise azimuth is the negative solution to Eq. (9) (relative to geographic N–S).Fixed sun-compass headings represent a uniform (clockwise) offset, ({bar{{{{{{rm{alpha }}}}}}}}_{{mathrm {s}}}) to sunrise or sunset azimuth, θs,i (calculated using Eq. (9))$${{bar{{{{{{rm{alpha }}}}}}}}_{i}={bar{{{{{{rm{alpha }}}}}}}}_{{mathrm {s}}}+theta }_{{mathrm {s}},i}$$
(10)
where the preferred heading on commencement of migration, ({bar{{{{{{rm{alpha }}}}}}}}_{{mathrm {s}}}={bar{{{{{{rm{alpha }}}}}}}}_{0}-{theta }_{{mathrm {s}},0}), is presumed to be imprinted using an inherited geographic or geomagnetic heading2,10,30.With a TCSC, preferred headings relative to sun azimuth are adjusted according to the time of day. In the context of sun-compass use during migration, Alerstam and Pettersson22 related the hourly “clock-shift” induced by crossing bands of longitude (∆h = 12 ∆λ/π), to a migrant’s time-compensated adjustment given the rate of change (i.e., angular speed) of sun azimuth close to sunset$$frac{partial {theta }_{{mathrm {s}}}}{partial h}cong frac{2pi {{sin }}{{phi }}}{24},$$
(11)
resulting in a “time-compensated” offset in heading on departure ((varDelta bar{{{{{{rm{alpha }}}}}}}cong varDelta {{{{{rm{lambda }}}}}},sin phi), which Eq.(4)). Equation (4) results in near-great-circle trajectories for small ranges in latitude, ∅, until inner clocks are reset. The feasibility of TCSC courses over longer distances (latitude ranges) relies on two critical but little-explored assumptions: (1) time-compensated orientation adjustments are presumed to follow the angular speed of sun azimuth (Eq. (11)) retained from the most recent clock-reset site, and (2) to negotiate unpredictable migratory schedules, migrants are presumed to retain their preferred geographic heading on arrival at extended stopovers22.Regarding the first assumption, time-compensated adjustments could also be influenced by proximate speeds of sun azimuth even when inner clocks are not fully reset. We, therefore, use distinct indices to keep track of “reference” flight-steps for clock-resets (cref,i) and time-compensated adjustments (sref,i). TCSC flight-step headings can then be written as$${bar{{{{{{rm{alpha }}}}}}}}_{i}=left{begin{array}{cc}{bar{{{{{{rm{alpha }}}}}}}}_{{c}_{{{mathrm {ref}}},i}}+left({theta }_{{mathrm {s}},i}-{theta }_{{mathrm {s}},{c}_{{{mathrm {ref}}},i}}right)+left({{{{{{rm{lambda }}}}}}}_{i}-{{{{{{rm{lambda }}}}}}}_{{c}_{{{mathrm {ref}}},i}}right){{sin }}{phi }_{{s}_{{{mathrm {ref}}},i}}, & {i,ne, c}_{{{mathrm {ref}}},i} ; (12a)\ {{{{{{rm{alpha }}}}}}}_{i-1}, & {i=c}_{{{mathrm {ref}}},i} ; (12b)end{array}right.,$$where θs,i represents the sunset azimuth on departures, cref,i specifies the most recent clock-reset site (during which geographic headings are also retained, i.e., ({bar{{{{{{rm{alpha }}}}}}}}_{i}={{{{{{rm{alpha }}}}}}}_{i-1})), and sref,i specifies the site defining the migrant’s temporal (hourly) rate of “time-compensated” adjustments (Eq. (11)). For TCSC courses as conceived by Alerstam and Pettersson22, reference rates of adjustment to sun azimuth are reset in tandem during stopovers, i.e., ({s}_{{{mathrm {ref}}},i}={c}_{{{mathrm {ref}}},i}), but we also considered a proximately gauged TCSC, where migrants gauge their adjustments to currently experienced speed of sun azimuth, i.e., ({s}_{{{mathrm {ref}}},i}=i).Regarding the second assumption, retaining geographic headings on arrival at stopovers is not consistent with ignoring geographic headings between consecutive nightly flight-steps, and may be difficult to achieve while landing. We, therefore, examined a more parsimonious alternative (Fig. 7d, Supplementary Fig. 3) where migrants retain their (usual) TCSC heading from the first night of stopovers, i.e., as if they would have departed on the first night. This alternative also simplifies Eq. (12) to$${bar{{{{{{rm{alpha }}}}}}}}_{i}={bar{{{{{{rm{alpha }}}}}}}}_{{c}_{{{mathrm {ref}}},i}}+left({theta }_{{mathrm {s}},({t}_{i-1}+1)}-{theta }_{{mathrm {s}},{t}_{i-1}}right)+left({{{{{{rm{lambda }}}}}}}_{i}-{{{{{{rm{lambda }}}}}}}_{{c}_{{{mathrm {ref}}},i}}right){{sin }}{{{phi }}}_{{s}_{{{mathrm {ref}}},i}}$$
(12c)
where the index ti−1 here represents the departure date from the previous flight.Sensitivity of compass-course headingsSensitivity was assessed by the marginal change in expected heading from previous (imprecise) headings, (partial {bar{alpha }}_{i}/partial {alpha }_{i-1}). When this is positive, small errors in headings will perpetuate, and therefore expected errors in migratory trajectories will grow iteratively. Conversely, negative sensitivity implies self-correction between successive flight-steps. Geographic and geomagnetic loxodromes are per definition constant relative to their respective axes so have “zero” sensitivity, as long as cue-detection errors are stochastically independent.For magnetoclinic compass courses in a dipole field, sensitivity can be calculated by differentiating Eq. (8) with respect to previous headings:$$frac{{mathrm {d}}{bar{{{{{{rm{alpha }}}}}}}}_{i}}{{mathrm {d}}{{{{{{rm{alpha }}}}}}}_{i-1}}=frac{{sin bar{{{{{{rm{alpha }}}}}}}}_{0}}{tan {phi }_{{mathrm {m}},0}}cdot frac{1}{cos {bar{alpha }}_{i}{cos }^{2}{phi }_{{mathrm {m}},i}}frac{partial {phi }_{{mathrm {m}},i}}{partial {alpha }_{i-1}}=frac{{R}_{{mathrm {step}}},sin {alpha }_{i-1}{sin bar{{{{{{rm{alpha }}}}}}}}_{0}}{cos {bar{alpha }}_{i}{cos }^{2}{phi }_{{mathrm {m}},i},tan {phi }_{{mathrm {m}},0}}$$
(13)
All three terms in the denominator indicate, as illustrated in Fig. 3b, that magnetoclinic courses become unstably sensitive at both high and low latitudes, and any heading with a significantly East–West component.Sensitivity of fixed sun compass headings is non-zero due to sun azimuth dependence on location (Eq. (9)):$$frac{{mathrm {d}}{bar{{{{{{rm{alpha }}}}}}}}_{i}}{{mathrm {d}}{{{{{{rm{alpha }}}}}}}_{i-1}} = , frac{sin {delta }_{{mathrm {s}},i}}{sin {theta }_{{mathrm {s}},i}}cdot frac{sin {phi }_{i}}{{cos }^{2}{phi }_{i}}frac{partial {phi }_{i}}{partial {alpha }_{i-1}}=frac{sin {delta }_{{mathrm {s}},i}}{sin {theta }_{{mathrm {s}},i}}cdot frac{{R}_{{mathrm {step}}},sin {phi }_{i},sin {alpha }_{i-1}}{{cos }^{2}{phi }_{i}}\ = , {R}_{{mathrm {step}}}cdot ,sin {alpha }_{i-1}frac{tan {phi }_{i}}{tan {theta }_{{mathrm {s}},i}}$$
(14)
The sine factor on the right-hand side in Eq. (14) causes the sign of (partial {bar{alpha }}_{i}/partial {alpha }_{i-1}) to be opposite for East to West or West to East headings, and tan θs also change sign at the fall equinox (due to solar declination changing sign). The azimuth term in the denominator indicates heightened sensitivity closer to the summer or winter equinox and at high latitudes, and, conversely, heightened robustness to errors closer to the spring or autumnal equinox (since ({{tan }}{theta }_{{mathrm {s}},0}to pm infty)). This seasonal and directional asymmetry is illustrated in Fig. 3c, e.TCSC courses (Eq. (12)) involve up to three sensitivity terms, due to dependencies on sun azimuth, longitude and latitude:$$ frac{{mathrm {d}}{bar{{{{{{rm{alpha }}}}}}}}_{i}}{{mathrm {d}}{{{{{{rm{alpha }}}}}}}_{i-1}} = , {R}_{{{mathrm {step}}}}cdot {{sin }}{alpha }_{i-1}frac{{{tan }}{phi }_{i}}{{{tan }}{theta }_{{mathrm {s}},i}}+frac{{mathrm {d}}{lambda }_{i}}{{mathrm {d}}{{{{{{rm{alpha }}}}}}}_{i-1}}{{sin }}{{{phi }}}_{{c}_{{{mathrm {ref}}}},i}+left({{{{{{rm{lambda }}}}}}}_{i}-{{{{{{rm{lambda }}}}}}}_{{c}_{{{mathrm {ref}}}},i}right)frac{{mathrm {d}}{{sin }}{phi }_{{s}_{{{mathrm {ref}}}},i}}{{mathrm {d}}{{{{{{rm{alpha }}}}}}}_{i-1}}\ =, left{begin{array}{cc}{R}_{{{mathrm {step}}}}cdot left[{{sin }}{alpha }_{i-1}frac{{{tan }}{phi }_{i}}{{{tan }}{theta }_{{mathrm {s}},i}}-frac{{{cos }}{{{{{{rm{alpha }}}}}}}_{i-1}{{sin }}{phi }_{{s}_{{{mathrm {ref}}}},i}}{{{cos }}{phi }_{i-1}}right],hfill & {{{{{rm{classic}}}}}} ; (15{{{{{rm{a}}}}}})\ {R}_{{{mathrm {step}}}}left[{{sin }}{alpha }_{i-1}frac{{{tan }}{phi }_{i}}{{{tan }}{theta }_{{mathrm {s}},i}}-frac{{{cos }}{{{{{{rm{alpha }}}}}}}_{i-1}{{sin }}{phi }_{{s}_{{{mathrm {ref}}}},i}}{{{cos }}{phi }_{i-1}}+left({{{{{{rm{lambda }}}}}}}_{i}-{{{{{{rm{lambda }}}}}}}_{{c}_{{{mathrm {ref}}}},i}right){{sin }}{alpha }_{i-1}{{cos }}{phi }_{i}right], & {{{{{rm{proximate}}}}}} ; left(15{{{{{rm{b}}}}}}right).end{array}right.$$The first square-bracketed terms in Eqs. (15a, b) are identical to the fixed sun compass (Eq. (14)), reflecting seasonal and latitudinal dependence in sun-azimuth. For headings with a Southward component (α0  1) and nonexistent for North–South headings (G = 1, reflecting no longitude bands being crossed). We expected this factor to affect compass courses differentially according to their error-accumulating or self-correcting nature.We further modified the effective goal-area breadth to account for a (geographically) circular goal area on the sphere, i.e., effectively modulating the longitudinal component of the goal-area breadth at the arrival latitude, ∅A:$${beta }_{{mathrm {A}}}=beta sqrt{{{{{sin }}}^{2}bar{alpha }+left({{cos }}bar{alpha }/{{cos }}{{{phi }}}_{{mathrm {A}}}right)}^{2}}.$$
(19)
To account for differential sensitivity among compass-courses, we generalized the normal many-wrongs relation between performance and number of steps, (1/{hat{N}}^{eta }), from η = 0.5 (Eqs. (3) and (16)) to$$eta left({sigma }_{{step}}|s,bright)=left(0.5+bright){e}^{-s{{sigma }_{{step}}}^{2}},$$
(20)
where b  0 self-correction, and s represents a modulating exponential damping factor, consistent with the limiting circular-uniform case (as κ → 0, i.e., ({sigma }_{{{mathrm {step}}}}to infty)), where no (timely) convergence of heading is expected with an increasing number of steps.In assessing performance, we also accounted for seasonal migration constraints via a population-specific maximum number of steps, Nmax (Table 2; this became significant for the longest-distance simulations with large expected errors, i.e., small ({{{{{{rm{kappa }}}}}}}_{{{mathrm {step}}}}=1/{sigma }_{{{mathrm {step}}}}^{2})). The probability of having arrived at the goal latitude can be estimated using the Central Limit Theorem:$${p}_{{{phi }},{N}_{{max }}}cong frac{1}{2}left[1-{erf}left(left(frac{{N}_{0}}{{N}_{{max }}}-frac{{I}_{1}left({{{{{{rm{kappa }}}}}}}_{{{mathrm {step}}}}right)}{{I}_{0}left({{{{{{rm{kappa }}}}}}}_{{{mathrm {step}}}}right)}right)cdot frac{{{cos }}bar{alpha }}{{sigma }_{{mathrm {C}}}sqrt{2}}right)right],$$
(21)
where Ij is the modified Bessel function of the first kind and order j53, and σC (the standard deviation in the latitudinal component of flight-step distance) can be calculated using Bessel functions together with known properties of sums of cosines53,77 (Supplementary Note 2).Regression-estimated performanceWe fit the parameters in the spherical-geometry factor (Eq. (18)) and many-wrongs effect (Eq. (20)) according to expected performance, estimated as the product of sufficiently timely migration (Eq. (21)) and sufficiently precise migration, now generalized from Eq. (16), i.e.$${p}_{beta ,hat{N}}cong {erf}left(frac{{beta }_{{mathrm {A}}}}{{G}^{{g}}sqrt{2left({{sigma }_{{{mathrm {ind}}}}}^{2}+{sigma }_{{{mathrm {step}}}}/{hat{N}}^{n}right)}}right),$$
(22)
This resulted in up to four fitted parameters for each compass course

i.

an exponent, g, to the spherical-geometry factor (Eq. (19)), i.e., Gg, reflecting how growth or self-correction in errors between steps further augments or reduces this factor,

ii.

a baseline offset, b0, to the “normal” exponent η = 0.5, which mediates the relation between the number of steps and performance (Eq. (20)),

iii.

an exponent s reflecting how decreasing precision among flight-steps dampens the many-wrongs convergence (Eq. (20)),

iv.

for TCSC courses, a modulation, ρ, to the offset, b0, quantifying the extent to which self-correction increases with increased flight-step distance Rstep, i.e., ({{b={b}_{0}R}_{{{mathrm {step}}}}^{{prime} }}^{rho }) in Eq. (20), where ({R}_{{{mathrm {step}}}}^{{prime} })is the flight-step distance scaled by its median value among species.

Parameters were fit using MATLAB routine fitnlm based on compass course performance among species and seven error scenarios (5°, 10°, 20°, 30°, 40°, 50°, and 60° directional precision among flight-steps), for all combinations (including or excluding the four parameters). The most parsimonious combination of parameters was selected using MATLAB routine aicbic, based on the AICc, the Akaike information criterion corrected for small sample size57. Null values for the spherical-geometry parameter were set to g = 1, and for the parameters governing convergence of route-mean headings b0 = 0, s = 0, and, for TCSC courses, ρ = 0 (for loxodrome courses, ρ = 0 by default, i.e., was not fitted).Statistics and reproducibilityOur simulation results, regression fitting and AICc-model selection are reproducible using the MATLAB scripts (see the section “Code availability”).Reporting summaryFurther information on research design is available in the Nature Research Reporting Summary linked to this article. More