Extinction threshold is a term used in

conservation biology Conservation biology is the study of the conservation of nature and of Earth's biodiversity with the aim of protecting species, their habitats, and ecosystems from excessive rates of extinction and the erosion of biotic interactions. It is an i ...

to explain the point at which a

species A species () is often defined as the largest group of organisms in which any two individuals of the appropriate sexes or mating types can produce fertile offspring, typically by sexual reproduction. It is the basic unit of Taxonomy (biology), ...

population Population is a set of humans or other organisms in a given region or area. Governments conduct a census to quantify the resident population size within a given jurisdiction. The term is also applied to non-human animals, microorganisms, and pl ...

metapopulation A metapopulation consists of a group of spatially separated populations of the same species which interact at some level. The term metapopulation was coined by Richard Levins in 1969 to describe a model of population dynamics of insect pests in a ...

, experiences an abrupt change in density or number because of an important parameter, such as habitat loss. It is at this critical value below which a species, population, or metapopulation, will go

extinct Extinction is the termination of an organism by the death of its Endling, last member. A taxon may become Functional extinction, functionally extinct before the death of its last member if it loses the capacity to Reproduction, reproduce and ...

,Ovaskainen, O. and Hanski, I. 2003:Extinction Threshold in Metapopulation Models, Ann.Zool.Fennic.40:81-97. though this may take a long time for species just below the critical value, a phenomenon known as extinction debt. Extinction thresholds are important to conservation biologists when studying a species in a population or metapopulation context because the colonization rate must be larger than the extinction rate, otherwise the entire entity will go extinct once it reaches the threshold.Groom, M., Meffe, G. K., and Carroll, C.R. 2000:Principles of Conservation Biology, 3rd Ed, Sinauer Associates. Extinction thresholds are realized under a number of circumstances and the point in modeling them is to define the conditions that lead a population to extinction.With, K.A. and King, A.W. 1999:Extinction Thresholds For Species in Fractal Landscapes, Conservation Biology: Vol 13, No.2, pp.314-326. Modeling extinction thresholds can explain the relationship between extinction threshold and

habitat loss Habitat destruction (also termed habitat loss or habitat reduction) occurs when a natural habitat is no longer able to support its native species. The organisms once living there have either moved elsewhere, or are dead, leading to a decrease ...

and

habitat fragmentation Habitat fragmentation describes the emergence of discontinuities (fragmentation) in an organism's preferred environment (habitat), causing population fragmentation and ecosystem decay. Causes of habitat fragmentation include geological proces ...

.Fahrig, Lenore. 2002:Effect of Habitat Fragmentation on the Extinction Threshold: A Synthesis, Ecological Applications: Vol.12, No.2, pp.346-353.

Mathematical models

Metapopulation-type models are used to predict extinction thresholds. The classic metapopulation model is the Levins Model, which is the model of metapopulation dynamics established by

Richard Levins Richard Levins (June 1, 1930 – January 19, 2016) was a Marxist biologist, a population geneticist, biomathematician, mathematical ecologist, and philosopher of science who researched genetic diversity, diversity in human populations. Until his ...

in the 1960s. It was used to evaluate patch occupancy in a large network of patches. This model was extended in the 1980s by

Russell Lande Russell Scott Lande (born 1951) is an American evolutionary biologist and ecologist, and an International Chair Professor at Centre for Biodiversity Dynamics at the Norwegian University of Science and Technology (NTNU). He is a fellow of the Ro ...

to include habitat occupancy. This mathematical model is used to infer the extinction values and important population densities. These mathematical models are primarily used to study extinction thresholds because of the difficulty in understanding extinction processes through empirical methods and the current lack of research on this subject.Deredec, A. and Courchamp, F, 2003:Extinction Thresholds in Host-Parasite Dynamics, Ann. Zool. Fennic. 40:115-130. When determining an extinction threshold there are two types of models that can be used: deterministic and stochastic metapopulation models.

Deterministic

Deterministic metapopulation models assume that there are an infinite number of habitat patches available and predict that the metapopulation will go extinct only if the threshold is not met. ''dp/dt = chp (1-p)-ep'' Where p= occupied patches, e= extinction rate, c= colonization rate, and h= amount of habitat. A species will persist only if ''h> δ'' where ''δ=e/c'' δ= species parameter, or how successful a species is in colonizing a patch.

Stochastic

Stochastic metapopulation models take into account stochasticity, which is the non-deterministic or random processes in nature. With this approach a metapopulation may be above the threshold if determined that it is unlikely it will go extinct within a certain time period. The complex nature of these models can result in a small metapopulation that is considered to be above the deterministic extinction threshold, but in reality has a high risk of extinction.

Other factors

When using metapopulation-type models to predict extinction thresholds there are a number of factors that can affect the results of a model. First, including more complicated models, rather than relying solely on the Levins model produces different dynamics. For example, in an article published in 2004, Otso Ovaskainen and Ilkka Hanski explained with an empirical example that when factors such as

Allee effect The Allee effect is a phenomenon in biology characterized by a correlation between population size or density and the mean individual fitness (biology), fitness (often measured as ''per capita'' population growth rate) of a population or species. ...

or Rescue effect were included in modeling the extinction threshold, there were unexpected extinctions in a high number of species. A more complex model came up with different results, and in practicing conservation biology this can add more confusion to efforts to save a species from the extinction threshold. Transient dynamics, which are effects on the extinction threshold because of instability in either the metapopulation or environmental conditions, is also a large player in modeling results. Landscapes that have recently endured habitat loss and fragmentation may be less able to sustain a metapopulation than previously understood without considering transient dynamics. Finally, environmental stochasticity, which may be spatially correlated, can lead to amplified regional stochastic fluctuations and therefore greatly affect the extinction risk.

Notes

External links

Anne Deredec & Franck Courchamp, "Extinction thresholds in host–parasite dynamics"

"Extinction Thresholds and Metapopulation Persistence in Dynamic Landscapes"
{{Conservation of species Threshold Conservation biology