Models for Eco-evolutionary Extinction Vortices and their Detection

The smaller a population is, the faster it looses genetic variation due to genetic drift. Loss of genetic variation can reduce population growth rate, making populations even smaller and more vulnerable to loss of genetic variation, and so on. Ultimately, the population can be driven to extinction by this “eco-evolutionary extinction vortex”. So far, extinction vortices due to loss of genetic variation have been mainly described verbally. However, quantitative models are needed to better understand when such vortices arise and to develop methods for detecting them. Here we propose quantitative eco-evolutionary models, both individual-based simulations and analytic approximations, that link loss of genetic variation and population decline. Our models assume stochastic population dynamics and multi-locus genetics with different forms of balancing selection. Using mathematical analysis and simulations, we identify parameter combinations that exhibit strong interactions between population size and genetic variation as populations decline to extinction and match our definition of an eco-evolutionary vortex, i.e. the per-capita population decline rates and per-locus fixation rates increase with decreasing population size and number of polymorphic loci. We further highlight cues and early warning signals that may be useful in identifying populations undergoing an eco-evolutionary extinction vortex.

Interactions between demography, genetics, and landscape connectivity increase extinction probability for a small population of large carnivores in a major metropolitan area

The extinction vortex is a theoretical model describing the process by which extinction risk is elevated in small, isolated populations owing to interactions between environmental, demographic, and genetic factors. However, empirical demonstrations of these interactions have been elusive. We modelled the dynamics of a small mountain lion population isolated by anthropogenic barriers in greater Los Angeles, California, to evaluate the influence of demographic, genetic, and landscape factors on extinction probability. The population exhibited strong survival and reproduction, and the model predicted stable median population growth and a 15% probability of extinction over 50 years in the absence of inbreeding depression. However, our model also predicted the population will lose 40–57% of its heterozygosity in 50 years. When we reduced demographic parameters proportional to reductions documented in another wild population of mountain lions that experienced inbreeding depression, extinction probability rose to 99.7%. Simulating greater landscape connectivity by increasing immigration to greater than or equal to one migrant per generation appears sufficient to largely maintain genetic diversity and reduce extinction probability. We provide empirical support for the central tenet of the extinction vortex as interactions between genetics and demography greatly increased extinction probability relative to the risk from demographic and environmental stochasticity alone. Our modelling approach realistically integrates demographic and genetic data to provide a comprehensive assessment of factors threatening small populations.

Stochastic Modeling of Density-Dependent Diploid Populations and the Extinction Vortex

We model and study the genetic evolution and conservation of a population of diploid hermaphroditic organisms, evolving continuously in time and subject to resource competition. In the absence of mutations, the population follows a three-type, nonlinear birth-and-death process, in which birth rates are designed to integrate Mendelian reproduction. We are interested in the long-term genetic behavior of the population (adaptive dynamics), and in particular we compute the fixation probability of a slightly nonneutral allele in the absence of mutations, which involves finding the unique subpolynomial solution of a nonlinear three-dimensional recurrence relationship. This equation is simplified to a one-dimensional relationship which is proved to admit exactly one bounded solution. Adding rare mutations and rescaling time, we study the successive mutation fixations in the population, which are given by the jumps of a limiting Markov process on the genotypes space. At this time scale, we prove that the fixation rate of deleterious mutations increases with the number of already fixed mutations, which creates a vicious circle called the extinction vortex.

Stochastic Modeling of Density-Dependent Diploid Populations and the Extinction Vortex

We model and study the genetic evolution and conservation of a population of diploid hermaphroditic organisms, evolving continuously in time and subject to resource competition. In the absence of mutations, the population follows a three-type, nonlinear birth-and-death process, in which birth rates are designed to integrate Mendelian reproduction. We are interested in the long-term genetic behavior of the population (adaptive dynamics), and in particular we compute the fixation probability of a slightly nonneutral allele in the absence of mutations, which involves finding the unique subpolynomial solution of a nonlinear three-dimensional recurrence relationship. This equation is simplified to a one-dimensional relationship which is proved to admit exactly one bounded solution. Adding rare mutations and rescaling time, we study the successive mutation fixations in the population, which are given by the jumps of a limiting Markov process on the genotypes space. At this time scale, we prove that the fixation rate of deleterious mutations increases with the number of already fixed mutations, which creates a vicious circle called the extinction vortex.

Can the grey literature help us understand the decline and extinction of the Near Threatened Eurasian otter Lutra lutra in Latium, central Italy?

To trace the local extinction of the Eurasian otter Lutra lutra in Latium, central Italy, and examine the causes of the species’ disappearance, we reviewed and classified information from both the scientific and grey literature according to the reliability and geographical accuracy of the records. The temporal and spatial patterns of 160 records from 23 geographical subunits from 1832 to 2006 suggest that the species collapsed between 1960 and 1975; two different extinction patterns were revealed by a set of multivariate analyses. In northern Latium the species collapsed because of several independent local threats. In central and southern Latium the species collapsed because of catastrophic habitat alteration (land reclamation during the 1930s) that negatively affected the source population. After this event the species went extinct in hilly and mountainous areas, where several population sinks occurred. We presume that this latter process drove the remnant otter subpopulations to extinction in central Italy, emphasizing the role of an extinction vortex in causing the collapse of this metapopulation rather than the classical threats recognized for this species. The value of the grey literature for a posteriori historical analysis of local extinction dynamics is highlighted by this research.