Goodness of Fit of Probability Distributions for Sightings as Species Approach Extinction

Estimating the probability that a species is extinct and the timing of extinctions is useful in biological fields ranging from paleoecology to conservation biology. Various statistical methods have been introduced to infer the time of extinction and extinction probability from a series of individual sightings. There is little evidence, however, as to which of these models provide adequate fit to actual sighting records. We use L-moment diagrams and probability plot correlation coefficient (PPCC) hypothesis tests to evaluate the goodness of fit of various probabilistic models to sighting data collected for a set of North American and Hawaiian bird populations that have either gone extinct, or are suspected of having gone extinct, during the past 150 years. For our data, the uniform, truncated exponential, and generalized Pareto models performed moderately well, but the Weibull model performed poorly. Of the acceptable models, the uniform distribution performed best based on PPCC goodness of fit comparisons and sequential Bonferroni-type tests. Further analyses using field significance tests suggest that although the uniform distribution is the best of those considered, additional work remains to evaluate the truncated exponential model more fully. The methods we present here provide a framework for evaluating subsequent models.     

Quantifying Extinction Probabilities from Sighting Records: Inference and Uncertainties

Methods are needed to estimate the probability that a population is extinct, whether to underpin decisions regarding the continuation of a invasive species eradication program, or to decide whether further searches for a rare and endangered species could be warranted. Current models for inferring extinction probability based on sighting data typically assume a constant or declining sighting rate. We develop methods to analyse these models in a Bayesian framework to estimate detection and survival probabilities of a population conditional on sighting data. We note, however, that the assumption of a constant or declining sighting rate may be hard to justify, especially for incursions of invasive species with potentially positive population growth rates. We therefore explored introducing additional process complexity via density-dependent survival and detection probabilities, with population density no longer constrained to be constant or decreasing. These models were applied to sparse carcass discoveries associated with the recent incursion of the European red fox (Vulpes vulpes) into Tasmania, Australia. While a simple model provided apparently precise estimates of parameters and extinction probability, estimates arising from the more complex model were much more uncertain, with the sparse data unable to clearly resolve the underlying population processes. The outcome of this analysis was a much higher possibility of population persistence. We conclude that if it is safe to assume detection and survival parameters are constant, then existing models can be readily applied to sighting data to estimate extinction probability. If not, methods reliant on these simple assumptions are likely overstating their accuracy, and their use to underpin decision-making potentially fraught. Instead, researchers will need to more carefully specify priors about possible population processes.     

Correlates of rediscovery and the detectability of extinction in mammals

Extinction is difficult to detect, even in well-known taxa such as mammals. Species with long gaps in their sighting records, which might be considered possibly extinct, are often rediscovered. We used data on rediscovery rates of missing mammals to test whether extinction from different causes is equally detectable and to find which traits affect the probability of rediscovery. We find that species affected by habitat loss were much more likely to be misclassified as extinct or to remain missing than those affected by introduced predators and diseases, or overkill, unless they had very restricted distributions. We conclude that extinctions owing to habitat loss are most difficult to detect; hence, impacts of habitat loss on extinction have probably been overestimated, especially relative to introduced species. It is most likely that the highest rates of rediscovery will come from searching for species that have gone missing during the 20th century and have relatively large ranges threatened by habitat loss, rather than from additional effort focused on charismatic missing species.     

Extinct or still out there? Disentangling influences on extinction and rediscovery helps to clarify the fate of species on the edge

Each year, two or three species that had been considered to be extinct are rediscovered. Uncertainty about whether or not a species is extinct is common, because rare and highly threatened species are difficult to detect. Biological traits such as body size and range size are expected to be associated with extinction. However, these traits, together with the intensity of search effort, might influence the probability of detection and extinction differently. This makes statistical analysis of extinction and rediscovery challenging. Here, we use a variant of survival analysis known as cure rate modelling to differentiate factors that influence rediscovery from those that influence extinction. We analyse a global data set of 99 mammals that have been categorized as extinct or possibly extinct. We estimate the probability that each of these mammals is still extant and thus estimate the proportion of missing (presumed extinct) mammals that are incorrectly assigned extinction. We find that body mass and population density are predictors of extinction, and body mass and search effort predict rediscovery. In mammals, extinction rate increases with body mass and population density, and these traits act synergistically to greatly elevate extinction rate in large species that also occurred in formerly dense populations. However, when they remain extant, larger‐bodied missing species are rediscovered sooner than smaller species. Greater search effort increases the probability of rediscovery in larger species of missing mammals, but has a minimal effect on small species, which take longer to be rediscovered, if extant. By separating the effects of species characteristics on extinction and detection, and using models with the assumption that a proportion of missing species will never be rediscovered, our new approach provides estimates of extinction probability in species with few observation records and scant ecological information.     

Effects of environmental variation on extinction and establishment

Theoretical models predict that increasing environmental variation increases the probability of extinction, decreases the probability of establishment, and influences the distribution of times to extinction or establishment. We conducted an experiment with 281 independent populations of Daphnia magna under controlled laboratory conditions to test these predictions. Consistent with the theory, the fraction of populations going extinct increased and the fraction of populations establishing self‐sustaining populations decreased under higher levels of environmental variation compared with controls. Time to extinction decreased under higher levels of environmental variation, but we found no effect on time to establishment. These results are consistent with theoretical predictions from models of extinction. They therefore support the use of stochastic population models to predict the fates of introductions of non‐indigenous species or native endangered species based on historic fluctuations and/or expected future conditions.     

Herbarium records do not predict rediscovery of presumed nationally extinct species

Rediscoveries of species previously thought to be extinct present a dilemma to conservation biology. On one hand, such instances offer the chance to change the course of events away from one that would have led to extinctions. On the other hand, public support for conservation may wane if scientists are frequently seen to overstate and prematurely declare extinctions. Recent studies have adopted a probabilistic approach to infer extinction, using sightings or collections and statistical models to calculate the chance that a species may still be extant. We conduct the first broad-scale test of such models using a recently compiled national red list and national herbarium collection records, including collections of presumed nationally extinct species made after the red list publication, which constitute “rediscoveries”. There was little evidence that the probabilities calculated by these models were associated with rediscoveries over a 3.5-year period. Current probabilistic models of extinction using sighting records could hence be inadequate for use with most natural history collection data.     

When Did Carcharocles megalodon Become Extinct? A New Analysis of the Fossil Record

Carcharocles megalodon (“Megalodon”) is the largest shark that ever lived. Based on its distribution, dental morphology, and associated fauna, it has been suggested that this species was a cosmopolitan apex predator that fed on marine mammals from the middle Miocene to the Pliocene (15.9–2.6 Ma). Prevailing theory suggests that the extinction of apex predators affects ecosystem dynamics. Accordingly, knowing the time of extinction of C. megalodon is a fundamental step towards understanding the effects of such an event in ancient communities. However, the time of extinction of this important species has never been quantitatively assessed. Here, we synthesize the most recent records of C. megalodon from the literature and scientific collections and infer the date of its extinction by making a novel use of the Optimal Linear Estimation (OLE) model. Our results suggest that C. megalodon went extinct around 2.6 Ma. Furthermore, when contrasting our results with known ecological and macroevolutionary trends in marine mammals, it became evident that the modern composition and function of modern gigantic filter-feeding whales was established after the extinction of C. megalodon. Consequently, the study of the time of extinction of C. megalodon provides the basis to improve our understanding of the responses of marine species to the removal of apex predators, presenting a deep-time perspective for the conservation of modern ecosystems.     

Spatial and temporal extinction dynamics in a freshwater cetacean

Geographical range contraction is a fundamental ecological characteristic of species population decline, but relatively little investigation has been conducted into general trends in the dynamic properties of range collapse. The Yangtze River dolphin or baiji (Lipotes vexillifer), probably the first large mammal species to have become extinct in over 50 years, was believed to have experienced major range collapse during its decline through progressive large-scale range contraction and fragmentation. This range-collapse model is challenged by a new dataset of 406 baiji last-sighting records collected from across the baiji''s historical range during an interview survey of Yangtze fishing communities. Although baiji regional abundance may have varied across its range, analyses of the extensive new sighting series provide comprehensive evidence that baiji population decline was not associated with any major contraction in geographical range across the middle–lower Yangtze drainage, even in the decade immediately before probable global extinction of the species. Extinction risk in baiji was therefore seemingly not related to evidence of range collapse. Baiji apparently underwent large-scale periodic and seasonal movements across their range, and we propose that range contraction and fragmentation may not be general biogeographic characteristics for declining populations of mobile species in connected landscapes.     

‘Tales of Symphonia’: extinction dynamics in response to past climate change in Madagascan rainforests

Madagascar''s rainforests are among the most biodiverse in the world. Understanding the population dynamics of important species within these forests in response to past climatic variability provides valuable insight into current and future species composition. Here, we use a population-level approach to analyse palaeoecological records over the last 5300 years to understand how populations of Symphonia cf. verrucosa became locally extinct in some rainforest fragments along the southeast coast of Madagascar in response to rapid climate change, yet persisted in others. Our results indicate that regional (climate) variability contributed to synchronous decline of S. cf. verrucosa populations in these forests. Superimposed on regional fluctuations were local processes that could have contributed or mitigated extinction. Specifically, in the forest with low soil nutrients, population model predictions indicated that there was coexistence between S. cf. verrucosa and Erica spp., but in the nutrient-rich forest, interspecific effects between Symphonia and Erica spp. may have pushed Symphonia to extinction at the peak of climatic change. We also demonstrate that Symphonia is a good indicator of a threshold event, exhibiting erratic fluctuations prior to and long after the critical climatic point has passed.     

Responses of Metapopulation Dynamics to Two Different Kinds of Habitat Destruction Caused by Human Activities

Habitat destruction can be classified into instantaneous destruction and continuous destruction by the different ways of human destroying habitat. Previous studies, however, always focused on instantaneous destruction. In this study, we develop a universal model, Multi-time scale N-species model, to study and compare the responses of metapopulation dynamics to both kinds of habitat destruction. The model explores that: (1) under instantaneous habitat destruction, species extinction is determined by the proportion of habitat destruction (D) and the structure of metapopulation (q). When D>q, species will go extinct ranked from the best competitor to the worst. When D≤ q, no species will go extinct, but the equilibrium abundances of odd-ranked competitors will decrease, and the equilibrium abundances of even-ranked competitors will increase; (2) under continuous destruction, species extinction is dependent on the speed of habitat destruction and the metapopulation structure. The higher the speed of habitat destruction and the bigger q are, the earlier species go extinct. Usually, there are two possible mechanisms of species extinction: one is that all species go extinct collectively following complete destruction, and the other is that species go extinct in ranked competitive order from best to worst, and the survivals, if they exist, will go extinct collectively following complete destruction. The oscillation amplitudes of inferior competitors are so large as to increase the probability of stochastic extinction under instantaneous destruction. Therefore, it is relatively propitious for the persistence of rare species under slow and continuous destruction, especially when continuous destruction stops.     

Life-history characters and phylogeny are correlated with extinction risk in the Australian angiosperms

Aim To determine whether life‐history characters that affect population persistence (e.g. habit and life span) and those that influence reproductive success (e.g. sexual system and fruit type) are non‐randomly correlated with extinction risk (i.e. threat category) in the Australian flora (c. 19,000 species, of which c. 14% is threatened). To identify patterns that present useful conservation directions. To understand patterns of extinction risk in the Australian flora at a broad scale. Location Continental Australia. Methods A country‐wide exploration of four life‐history characters in the Australian flora (n = 18,822 species) was undertaken using reference texts, expert opinion, herbarium records and field work. For each character and threat‐category combination, a G‐test (using a log‐linear model) was performed to test the null hypothesis that the two factors were independent in their effects on count. A generalized linear model (GLM) with a logit link and binomial error distribution was constructed with the proportion of taxa in each extinction risk category as the response variable and the habit, sex and fruit‐type characters as explanatory terms. In a separate approach, we investigated patterns across the threat categories of non‐endangered extant, endangered, and extinct using a multinomial model. We examined whether or not species‐poor genera were more likely to contain threatened or extinct species than species‐rich genera. A GLM with a binomial error distribution and logit link function was constructed to obtain a weighted regression on the proportion of species listed as extinct or endangered within a genus versus the log of the size of the genus. We also used a supertree analysis and character tracing to investigate the role of phylogeny on extinction risk. Results We found that the Australian flora is primarily composed of bisexual shrubs with dry‐dehiscent fruits. Dioecious breeding systems (separate female and male flowers on separate plants) in many floras are the predominant unisexual system, but in Australia there are unexpectedly high levels of monoecy (separate female and male flowers on the same plant). Within the extinct data set of 31 species we detected a significant departure from that expected for habit but not for life span, sexual system or fruit type. There are significantly fewer trees on the extinct list than expected. This may reflect the greater resilience of trees than of other growth habits to extinction processes as well as the observation time‐frame. Within the endangered data set of 450 species we found significant differences in the representation of the observed characters from that expected within sex systems and fruit types. We show that, depending on the life form, unisexual breeding systems can be significantly and positively associated with endangered species compared with non‐threatened species. For example, there are more monoecious species than expected by chance among the tree species listed as endangered but fewer among the herbaceous life forms. Threat category was found to be non‐randomly clustered in some clades. Main conclusions Life‐history characters in certain combinations are predictive of extinction risk. Phylogeny is also an important component of extinction risk. We suggest that specific life‐history characters could be used for conservation planning and as an early warning sign for detecting vulnerability in lists of species.     

The shrinking ark: patterns of large mammal extinctions in India

Mammal extinctions are widespread globally, with South Asian species being most threatened. We examine local extinctions of 25 mammals in India. We use historical records to obtain a set of locations at which each species was known to have been present at some time in the last 200 years. We then use occupancy estimation models to draw inferences about current presence at these same locations based on field observations of local experts. We examine predictions about the influence of key factors such as protected areas, forest cover, elevation, human population density and cultural tolerance on species extinction. For all 25 species, estimated local extinction probabilities (referenced to a 100 year time frame) range between 0.14 and 0.96. Time elapsed since the historical occurrence record was an important determinant of extinction probability for 14 species. Protected areas are positively associated with lower extinction of 18 species, although many species occur outside them. We find evidence that higher proportion of forest cover is associated with lower extinction probabilities for seven species. However, for species that prefer open habitats (which have experienced intensive land-use change), forest cover alone appears insufficient to ensure persistence (the complement of extinction). We find that higher altitude is positively associated with lower extinction for eight species. Human population density is positively associated with extinction of 13 species. We find that ‘culturally tolerated’ species do exhibit higher persistence. Overall, large-bodied, rare and habitat specialist mammals tend to have higher extinction probabilities.     

Acipenser sturio and Acipenser nudiventris in the Danube – extant or extinct?

The presence of Atlantic sturgeon ( Acipenser sturio) and ship sturgeon ( Acipenser nudiventris ) in the Danube has been known through only occasional, chance sightings; significant uncertainty remains as to whether these species are already extinct or still present in the Danube River basin. In this study, five different statistical methods were applied for assessment of their extinction probability. All methods provided a significant probability that the Atlantic sturgeon is extinct, with extinction having occurred somewhere between 1966 and 1970. Although the applied methods provided different results, all indicated that the ship sturgeon is probably still present, but that extinction may occur within a few decades. Sensitivity analyses of these statistical methods projected that new sightings of ship sturgeon in the coming years would not extend the length of extinction by more than a few years. The best management approach for these two species, given the lack of knowledge on their presence in the Danube River basin, could be to apply all feasible protection measures for the other four Danube sturgeon species. These measures could at the same time provide protection for these two species, presuming they are not already extinct or beyond recovery.     

DNA from a 100-year-old holotype confirms the validity of a potentially extinct hummingbird species

We used mtDNA sequence data to confirm that the controversial 100-year-old holotype of the Bogotá sunangel (Heliangelus zusii) represents a valid species. We demonstrate that H. zusii is genetically well differentiated from taxa previously hypothesized to have given rise to the specimen via hybridization. Phylogenetic analyses place H. zusii as sister to a clade of mid- to high-elevation Andean species currently placed in the genera Taphrolesbia and Aglaiocercus. Heliangelus zusii, presumed extinct, has never been observed in nature by biologists. We infer that the species occupied a restricted distribution between the upper tropical and temperate zones of the northern Andes and that it was most probably driven to extinction by deforestation that accompanied human population growth during the nineteenth and early twentieth centuries. We demonstrate the feasibility of obtaining DNA from nearly microscopic tissue samples from old hummingbird specimens and suggest that these methods could be used to resolve the taxonomy of dozens of avian taxa known only from type specimens.     

The effect of selection history on extinction risk during severe environmental change

Environments rarely remain the same over time, and populations are therefore frequently at risk of going extinct when changes are significant enough to reduce fitness. Although many studies have investigated what attributes of the new environments and of the populations experiencing these changes will affect their probability of going extinct, limited work has been directed towards determining the role of population history on the probability of going extinct during severe environmental change. Here, we compare the extinction risk of populations with a history of selection in a benign environment, to populations with a history of selection in one or two stressful environments. We exposed spores and lines of the green alga Chlamydomonas reinhardtii from these three different histories to a range of severe environmental changes. We found that the extinction risk was higher for populations with a history of selection in stressful environments compared to populations with a history of selection in a benign environment. This effect was not due to differences in initial population sizes. Finally, the rates of extinction were highly repeatable within histories, indicating strong historical contingency of extinction risk. Hence, information on the selection history of a population can be used to predict their probability of going extinct during environmental change.     

Assessing the role of off‐take and source–sink dynamics in the extinction of the amphidromous New Zealand grayling (Prototroctes oxyrhynchus)

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Stochastic models for the Trojan Y-Chromosome eradication strategy of an invasive species

The Trojan Y-Chromosome (TYC) strategy, an autocidal genetic biocontrol method, has been proposed to eliminate invasive alien species. In this work, we develop a Markov jump process model for this strategy, and we verify that there is a positive probability for wild-type females going extinct within a finite time. Moreover, when sex-reversed Trojan females are introduced at a constant population size, we formulate a stochastic differential equation (SDE) model as an approximation to the proposed Markov jump process model. Using the SDE model, we investigate the probability distribution and expectation of the extinction time of wild-type females by solving Kolmogorov equations associated with these statistics. The results indicate how the probability distribution and expectation of the extinction time are shaped by the initial conditions and the model parameters.     

Integration of palaeontological, historical, and geographical data on the extinction of koa-finches

Identifying the root causes of extinction or endangerment requires long chronological records that begin before a population started to decline and extend until its extinction or functional extinction. We present a case study of the koa‐finches, genus Rhodacanthis, an extinct group of Hawaiian honeycreepers that was specialized to feed on green pods and seeds of the koa tree or other leguminous plants. Six island populations of koa‐finches are known; four in the Holocene fossil record and two that survived until the 1890s. We document the palaeoecological context of the fossils and identify constraints on the age span of the specimen record for each population using stratigraphic contexts, associated radiometric determinations, and museum specimen data. We estimate the potential geographical range of koa‐finches at the time of human arrival using two methods: assessment of their historical and palaeo‐habitats, and geographical information system mapping of the pre‐human distribution of the koa plant (Acacia koa) and its sister species, the koai‘a plant (Acacia koaia). After integrating the foregoing data with chronological records and distributional maps of the potential forcing agents of extinction, we conclude that at least two extinctions of island populations were due to ecological change in the lowlands in the prehistorical and perhaps the early historical periods. In the same time frame, the koa‐finch populations on Hawai‘i Island became rare and restricted to upland refugia, making them vulnerable to the upland forest harvesting and degradation that was accelerating in the 1890s. Neither climatic variation nor mosquito‐vectored diseases are likely to have caused the observed extinctions. This study illustrates an approach that can be applied to many other extinct and endangered island species to better understand the causes of high extinction rates in the human era.     

Ecological correlates of local extinction and colonisation in the British ladybird beetles (Coleoptera: Coccinellidae)

Five main drivers of population declines have been identified: climate change, habitat degradation, invasive alien species (IAS), overexploitation and pollution. Each of these drivers interacts with the others, and also with the intrinsic traits of individual species, to determine species’ distribution and range dynamics. We explored the relative importance of life-history and resource-use traits, climate, habitat, and the IAS Harmonia axyridis in driving local extinction and colonisation dynamics across 25 ladybird species (Coleoptera: Coccinellidae).Species were classified as continually present, continually absent, extinct, or colonising in each of 4,642 1-km² grid squares. The spatial distribution of local extinction and colonisation events (in the grid squares) across all species’ ranges were related to ecological traits, overlap with H. axyridis, climate, and habitat factors within generalised linear models (GLMs). GLMs were also used to relate species’ traits, range characteristics, and niche overlap with H. axyridis to extinction and colonisation rates summarised at the species level. Bayesian model averaging was used to account for model uncertainty, and produce reduced sets of models which were well-supported by data. Species with a high degree of niche overlap with H. axyridis suffered higher extinction rates in both analyses, while at the spatial scale extinctions were more likely and colonisations less likely in areas with a high proportion of urban land cover. In the spatial analysis, polymorphic species with large range sizes were more likely to colonise and less likely to go extinct, and sunny grid squares were more likely to be colonised. Large, multivoltine species and rainy grid squares were less likely to colonise or be colonised. In conclusion for ladybirds, extinction and colonisation dynamics are influenced by several factors. The only factor that both increased the local extinction likelihood and reduced colonisation likelihood was urban land cover, while ecological overlap with H. axyridis greatly increased extinction rates. Continued spread of H. axyridis is likely to adversely affect native species and urban areas may be particularly vulnerable.     

Estimating population trends using population viability analyses for the conservation ofCapra pyrenaica

Large herbivore populations can suffer important oscillations with considerable effects on ecosystem functions and services, yet our capacity to predict population fate is limited and conditional upon the availability of data. This study investigated the interannual variation in the growth rate of populations ofCapra pyrenaica Schinz, 1838, and its extinction risk by comparing the dynamics of populations that were stable for more than two decades (Gredos and Tortosa-Beceite), populations that had increased recently (Tejeda-Almijara), and populations that were in decline (Cazorla-Segura) or extinct (the Pyrenees population; hereafter, bucardo). To estimate quasi-extinction threshold assessments (50% of population extinct in this study), which have implications for the conservation of the species, we used empirical data and the predictions derived from several theoretical models. The results indicate that when variance of log population growth rate reaches a specific threshold, the probability of quasi-extinction increased drastically. ForC. pyrenaica, we recommend keeping population variance < 0.05, which will reduce the likelihood that the irruptive oscillations caused by environmental and demographic stochasticity will put the population at risk. Models to predict the dynamics ofC. pyrenaica populations should incorporate temporal stochasticity because, in this study, it strongly increased the likelihood that a population declined.