The current rate of species extinction is ∼1,000 times the background rate of extinction and is attributable to human impact, ecological and demographic fluctuations, and inbreeding due to small population sizes. The rate and the initiation date of rapid population decline (RPD) can provide important clues about the driving forces of population decline in threatened species, but they are generally unknown. We analyzed the genetic diversity data in 2,764 vertebrate species. Our population genetics modeling suggests that in many threatened vertebrate species the RPD on average began in the late 19th century, and the mean current size of threatened vertebrates is only 5% of their ancestral size. We estimated a ∼25% population decline every 10 y in threatened vertebrate species.

Accelerated losses of biodiversity are a hallmark of the current era. Large declines of population size have been widely observed and currently 22,176 species are threatened by extinction. The time at which a threatened species began rapid population decline (RPD) and the rate of RPD provide important clues about the driving forces of population decline and anticipated extinction time. However, these parameters remain unknown for the vast majority of threatened species. Here we analyzed the genetic diversity data of nuclear and mitochondrial loci of 2,764 vertebrate species and found that the mean genetic diversity is lower in threatened species than in related nonthreatened species. Our coalescence-based modeling suggests that in many threatened species the RPD began ∼123 y ago (a 95% confidence interval of 20–260 y). This estimated date coincides with widespread industrialization and a profound change in global living ecosystems over the past two centuries. On average the population size declined by ∼25% every 10 y in a threatened species, and the population size was reduced to ∼5% of its ancestral size. Moreover, the ancestral size of threatened species was, on average, ∼22% smaller than that of nonthreatened species. Because the time period of RPD is short, the cumulative effect of RPD on genetic diversity is still not strong, so that the smaller ancestral size of threatened species may be the major cause of their reduced genetic diversity; RPD explains 24.1–37.5% of the difference in genetic diversity between threatened and nonthreatened species.

Although preservation of biodiversity is vital to a sustainable human society, rapid population decline (RPD) continues to be widespread across taxa (1⇓–3). When RPD occurs, it is accompanied by a loss of genetic diversity. Genetic diversity is reflected in the genetic differences among individuals and is essential for populations to adapt to changing environments (4). The start date and the rate of RPD provide useful information for effective conservation of threatened species and are important for promotion of public awareness of the threat. However, these two key parameters are difficult to estimate because there are virtually no time-series data on population size over hundreds of years. For most species, the population size may only be traced back to 40 y (2). Therefore, an alternative approach is to estimate the start date and the rate of RPD, using mathematical modeling.

Changes in population size over thousands of years could be inferred for a species from genome-wide DNA polymorphism data (5⇓–7). However, it remains a formidable technical challenge to infer the event of RPD because the signal of such an event is weak in the typical time scale of observable polymorphisms (8). To overcome the limited resolution power of the genetic data from a single species, we propose an approach that draws conclusions based on the collective support from many species. The central premise of our approach is that the threat of extinction of thousands of species was primarily due to a common cause in the past that led to a significant depletion of available habitats and resources. Consequently, we were able to draw conclusions based on present-day polymorphism data from a large number of threatened species and their nonthreatened relatives. Our method is depicted in Fig. 1. Here we studied RPD in vertebrates, because vertebrates have been more extensively investigated in the past. However, our conclusions should have some generality because vertebrate species live in a wide range of ecosystems. Moreover, the proposed method is also suitable for studying nonvertebrate species.

Schematic inference on the start date and the rate of RPD under one particular demographic model. The coalescence simulations were conducted conditional on the sample sizes, the numbers of loci, the pattern of missing data, the generation times, the census sizes, the species distributions, and the years of sampling. The data were summarized as the relative difference in four genetic diversity measurements between two species groups. The species categorized as near threatened (NT) and least concern (LC) are treated as the nonthreatened species. The threatened species include those listed as critically endangered (CR), endangered (EN), and vulnerable (VU) ( 6 ). The uncategorized species include those that are listed as data deficient and have not been evaluated by the IUCN.

Results and Discussion

Data Collected. We reviewed more than 10,000 peer-reviewed papers published in the last two and half decades, among which ∼2,500 papers in 164 scientific journals were found to have surveyed the genetic diversity of at least one vertebrate species. The level of genetic diversity was measured with one of the following summary statistics (9): the expected and observed heterozygosity ( H e and H o ), the number of alleles per locus ( α ) at the microsatellite loci, Watterson’s θ w (10), and the mean number of nucleotide differences per nucleotide site between two mitochondrial sequences ( π ). The collected dataset includes 2,764 vertebrate species belonging to 1,466 genera and 465 families (Fig. 2). Then, we used the International Union for Conservation of Nature (IUCN) Red List categories (3) to determine the level of extinction risk for each species, and the species were categorized into three groups: nonthreatened species (NS), threatened species (TS), and uncategorized species (Fig. 2B). The uncategorized species include (i) those that are listed as data deficient and (ii) those that have not been evaluated by the IUCN. A taxon is listed as data-deficient when there is inadequate information to make an assessment of its risk of extinction (3). The uncategorized species were excluded from our analyses (Fig. 1), unless noted otherwise. Fig. 2. Categories of the 2,764 vertebrate species used in this study. (A) The number and relative proportion of the species in each taxon category. (B) IUCN Red List categories of the examined species and their relative proportions. CR, critically endangered; DD, data deficient; EN, endangered; LC, least concern; NE, not evaluated; NT, near threatened; VU, vulnerable. The threatened species include the species of critically endangered, endangered, and vulnerable, and the nonthreatened species include the near-threatened and least-concern species.

Comparison of Genetic Diversity Between Nonthreatened and Threatened Species. Following a previous study (11), we compared the genetic diversity between nonthreatened and threatened vertebrate species using the permutation test (12). The establishment of those IUCN categories does not rely on the information of genetic diversity. Although the distributions of genetic diversity of nonthreatened and threatened species overlap (Fig. 3 A and B and SI Appendix, Fig. S1), the mean genetic diversity of nonthreatened species is significantly higher than that of related threatened species in all 16 comparisons (Fig. 3 C–E and SI Appendix, Table S1), generally agreeing with the previous finding (11). The results remain the same when we recompiled the data with different numbers of microsatellite loci ( < or ≥ 10 loci) or different sequenced lengths of the D-loop ( < or ≥ 500 bp) (SI Appendix, Fig. S2). Fig. 3. Comparisons of genetic diversity between nonthreatened and threatened vertebrate species. (A) Empirical distributions of H e on microsatellite loci. (B) Empirical distributions of Watterson’s θ w calculated from sequence variation in the D-loop (control region) of mitochondrial DNA. (C) Results of the permutation test on H e of microsatellite loci between nonthreatened and threatened species. (D) Results of the permutation test on the number of alleles per microsatellite locus ( α ) between nonthreatened and threatened species. (E) Results of the permutation test on Watterson’s θ w and the mean pairwise nucleotide differences ( π ) in the D-loop and coding regions in the mitochondrial genome. The null hypothesis of the permutation test is that the mean genetic diversity of nonthreatened species is equal to that of threatened species. The numbers of species examined are shown on the columns, and the one-tailed P values of the test are shown above the columns. The SEM is presented as an error bar. To ensure a reliable estimation of genetic diversity for a species, we required a sample size of n ≥ 20 individuals. *P < 0.05, ***P < 0.01. To examine whether differences in population structure can explain the reduction in genetic diversity of threatened species, we first compared the Fst values (an indicator of recent population structure estimated from microsatellite loci) between two species groups and found no significant difference (P = 0.25) (SI Appendix, Table S2). Next, we calculated the one-tailed P values of Tajima’s D (13) for the mitochondrial DNA polymorphism data, which is sensitive to ancient but not recent population structure (14). There was also no significant difference between the two species groups (P = 0.67) (SI Appendix, Table S2). Thus, population structure differences are unlikely the principle cause of the difference in genetic diversity between nonthreatened and threatened species. To assess the impact of recent demographic change on genetic diversity of threatened species, we considered pairs of nonthreatened and threatened species from the same family. For each pair we calculated the ratio of the long-term effective population size ( N e ) and the ratio of the effective population size at present N ( 0 ) . The observed genetic diversity provides an estimate of N e = θ / 4 μ for autosomes (15) or N e = θ / μ for mitochondrial DNA (10), where μ is the mutation rate per generation. Therefore, the ratio of N e between two species groups was estimated as θ ^ N S / θ ^ T S for either autosomal or mitochondrial loci, where the subscripts NS and TS stand for nonthreatened and threatened species, respectively. Also, the ratio of N ( 0 ) was approximated by the ratio of the current census size N ′ . This is based on the finding that the ratio of effective to actual population size ( f = N ( 0 ) / N ′ ) has a mean value of 0.1 (16) and is largely independent of N ′ . We found that N e , N S / N e , T S (median 1.89, the 5th and 95th percentiles 0.16 and 15.32, respectively) is remarkably smaller than N N S ( 0 ) / N T S ( 0 ) (median 36.95, the 5th and 95th percentiles 1.9 and 3,282.9, respectively) ( P < 10 − 5 ) (Fig. 4 and SI Appendix, Tables S3 and S4). This may indicate a much larger ancestral size and a RPD across all or most of the threatened taxa. Fig. 4. Ratios of long-term effective population size (circles, measured as θ ^ N S / θ ^ T S ) and ratios of effective population size at present (crosses, measured as N ′ N S / N ′ T S ) between nonthreatened and threatened species for five vertebrate classes. Species group pairs are from the same family. θ ^ was calculated using the D-loop of mitochondrial DNA (10) and allelic variation at microsatellite loci (15). We suggest that the recent impacts on population size could be measured by N N S ( 0 ) / N T S ( 0 ) and normalized by θ ^ N S / θ ^ T S . Then we examined which families of species were affected the most or the least (SI Appendix, Table S5). A larger impact index indicates that one or a few threatened species in the family experienced a more severe population decline.

Demographic Models. We used a model-based approach to quantify the RPD. One model is illustrated in Fig. 5A. The essential premise is that many threatened species began the RPD at similar times due to the increased impact of human activities and habitat losses. Specifically, the model assumes that each threatened species began an exponential decrease in size t years ago, which follows a distribution with the mean equal to τ , whereas nonthreatened species have maintained a constant population size (the case of nonthreatened species with nonconstant size is examined below). Naturally, the time t splits the population history into two phases (Fig. 5A). We define R = E ( θ w , N S ( t ) ) / E ( θ w , T S ( t ) ) ≈ E ( N ′ N S ( t ) ) / E ( N ′ T S ( t ) ) , which is the ratio of the ancestral genetic diversity of nonthreatened species to that of threatened species at time t and represents the difference in census size between the two species groups before RPD. Fig. 5. Coalescence-based modeling and analysis. (A) The two-phase model of exponential population decline for threatened species with a constant effective population size of nonthreatened species during both phases. (B) The likelihood surface obtained from the analysis. (C) The estimates based on the data from all studied species and subgroups of species. The estimates ( R ^ , τ ^ ) are shown by open circles, the estimates of τ conditional on R are shown in solid lines, and their 95% confidence intervals are given in dashed lines. The estimates for the case of 40% species were averaged over five random replicates. (D) The estimates based on the microsatellite data from five taxa. (E) The estimates based on the data from species with different generation times. (F) Results from species categorized as temperate and tropical zones. To estimate the two parameters ( R and τ ), a numerical approximation of their likelihood L ( R , τ ) was obtained using the principle of rejection sampling (5, 17, 18) after representing the data as the relative differences in the mean genetic diversity between the two species groups (Methods). Then we explored each of the scenarios with the start date of RPD that follows the normal, the exponential, and the one-point (i.e., constant) distribution with the mean τ . The SD of the normal distribution was estimated as the SD of t ^ among 18 well-documented mammal and bird species (SI Appendix, Table S6). The estimated τ ^ is 111, 154, and 123 y, respectively. Judging from the amount of uncertainty associated with these estimates, it seems that τ ^ is robust with regard to the assumption of the distribution of t . However, assuming a nonconstant t will lead to a substantial increase in computation/simulation time in subsequent analyses. Therefore, only the one-point distribution of t was implemented in the subsequent analyses. The surface of the likelihood L ( R , τ ) is shown in Fig. 5B. The estimate R ^ is 1.22 (Fig. 5C) with a 95% confidence interval between 1.11 and 1.35, implying that the ancestral size of threatened vertebrate species was, on average, 22% smaller than that of nonthreatened vertebrate species. As expected, R is more precise than N e , N S / N e , T S estimated above because the latter was estimated from the small number of species and had a very large variance. The corresponding τ ^ is 123 y with a 95% confidence interval of 20–260 y, and the rate of RPD ( λ ^ ) implies a 24.5% population decline every 10 y. The results suggest that the difference in genetic diversity between the two species groups (Fig. 3) was due to the joint effect of the smaller ancestral size of threatened species and the RPD that began on average in the late 19th century. Then, the effect of RPD was quantified by comparing the simulated genetic diversity between the cases of RPD and no RPD. We found that RPD explains 24.1–37.5% of the difference in genetic diversity between the two species groups (SI Appendix, Table S7). The effect varies with different measurements of genetic diversity because the number of alleles per locus ( α ) and Watterson’s θ w are more sensitive to RPD than the expected heterozygosity ( H e ) and π (19, 20). The effect of RPD on the reduction in genetic diversity is relatively weak because the time period of RPD is short and because the observed differences in genetic diversity between the two species groups were small. For example, the initial simulated heterozygosity of threatened species was 0.572, and the reduced heterozygosity after RPD was 0.558. That is, only 2.4% of the heterozygosity was lost due to RPD because the time period of RPD was only 123 y.