Extinction threshold is a term used in conservation biology to explain the point at which a

species In biology, a species is the basic unit of classification and a taxonomic rank of an organism, as well as a unit of biodiversity. A species is often defined as the largest group of organisms in which any two individuals of the appropriate s ...

population Population typically refers to the number of people in a single area, whether it be a city or town, region, country, continent, or the world. Governments typically quantify the size of the resident population within their jurisdiction using a ...

or metapopulation, 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,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 In ecology, extinction debt is the future extinction of species due to events in the past. The phrases dead clade walking and survival without recovery express the same idea. Extinction debt occurs because of time delays between impacts on a speci ...

. 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 and habitat reduction) is the process by which a natural habitat becomes incapable of supporting its native species. The organisms that previously inhabited the site are displaced or dead, thereby ...

and habitat fragmentation.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 "Dick" Levins (June 1, 1930 – January 19, 2016) was an ex-tropical farmer turned ecologist, a population geneticist, biomathematician, mathematical ecologist, and philosopher of science who researched diversity in human populations. U ...

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 Roy ...

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 In Finnish mythology, Otso (also known as Karhu, Ohto, Kontio, Metsän kuningas, and Mesikämmen) is a bear, the sacred king of animals and leader of the forest. It was deeply feared and respected by old Finnish tribes. Otso appears in the Finnis ...

and

Ilkka Hanski Ilkka Aulis Hanski (14 February 1953 – 10 May 2016) was a Finnish ecologist at the University of Helsinki, Finland. The Metapopulation Research Center led by Hanski, until his death, has been nominated as a Center of Excellence by the Academy ...

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 (often measured as ''per capita'' population growth rate) of a population or species. History and backgro ...

Rescue effect The rescue effect is a phenomenon which was first described by Brown and Kodric-Brown,Brown JH, Kodric-Brown A. 1977 Turnover rates in insular biogeography: effect of immigration on extinction. Ecology 58, 445– 449. (doi:10.2307/ 1935620) and is ...

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