AboutZoos, Since 2008


New math­e­mat­i­cal model can help save endan­gered species

pub­lished 27 Jan­u­ary 2019 | mod­i­fied 27 Jan­u­ary 2019

One of the great­est chal­lenges in sav­ing endan­gered species is to pre­dict if an ani­mal pop­u­la­tion will die out. Accu­rate and reli­able mod­els are cru­cial for conservationists.

What does the blue whale have in com­mon with the Ben­gal tiger and the green tur­tle? They share the risk of extinc­tion and are clas­si­fied as endan­gered species. There are mul­ti­ple rea­sons for species to die out, and cli­mate changes are among the main reasons.

demographic ratesDemo­graphic rates of sev­eral species as mod­elled by Colchero and col­leagues.
Image: Uni­ver­sity of South­ern Den­mark, Fac­ulty of Science.

The risk of extinc­tion varies from species to species depend­ing on how indi­vid­u­als in its pop­u­la­tions repro­duce and how long each ani­mal sur­vives. Under­stand­ing the dynam­ics of sur­vival and repro­duc­tion can sup­port man­age­ment actions to improve a species’ chance of surviving.

Math­e­mat­i­cal and sta­tis­ti­cal mod­els have become pow­er­ful tools to help explain these dynam­ics. How­ever, the qual­ity of the infor­ma­tion we use to con­struct such mod­els is cru­cial to improve our chances of accu­rately pre­dict­ing the fate of pop­u­la­tions in nature. A new study led by pro­fes­sor Colchero of the Uni­ver­sity of South­ern Den­mark (SDU) show­ing the results of improved pop­u­la­tion dynam­ics mod­el­ling is pub­lished on 9 Decem­ber 2018 in the jour­nal Ecol­ogy Let­ters.

A model that over-​simplifies sur­vival and repro­duc­tion can give the illu­sion that a pop­u­la­tion is thriv­ing when in real­ity it will go extinct.

Fer­nando Colchero, lead author, asso­ciate Pro­fes­sor Inter­dis­ci­pli­nary Cen­ter on Pop­u­la­tion Dynam­ics and Depart­ment of Math­e­mat­ics and Com­puter Sci­ence, Uni­ver­sity of South­ern Den­mark, Odense.

Colchero’s research focuses on math­e­mat­i­cally recre­at­ing the pop­u­la­tion dynam­ics by bet­ter under­stand­ing the species’ demog­ra­phy. He works on con­struct­ing and explor­ing sto­chas­tic pop­u­la­tion mod­els that pre­dict how a cer­tain pop­u­la­tion (for exam­ple an endan­gered species) will change over time.

These mod­els include math­e­mat­i­cal fac­tors to describe how the species’ envi­ron­ment, sur­vival rates and repro­duc­tion deter­mine to the population’s size and growth. For prac­ti­cal rea­sons some assump­tions are necessary.

Two com­monly accepted assump­tions are that sur­vival and repro­duc­tion are con­stant with age, and that high sur­vival in the species goes hand in hand with repro­duc­tion across all age groups within a species. Colchero chal­lenged these assump­tions by account­ing for age-​specific sur­vival and repro­duc­tion, and for trade-​offs between sur­vival and repro­duc­tion. This is, that some­times con­di­tions that favour sur­vival will be unfavourable for repro­duc­tion, and vice versa.

For his work Colchero used sta­tis­tics, math­e­mat­i­cal deriva­tions, and com­puter sim­u­la­tions with data from wild pop­u­la­tions of 24 species of ver­te­brates. The out­come was a sig­nif­i­cantly improved model that had more accu­rate pre­dic­tions for a species’ pop­u­la­tion growth.

Despite the tech­ni­cal nature of Fernando’s work, this type of model can have very prac­ti­cal impli­ca­tions as they pro­vide qual­i­fied expla­na­tions for the under­ly­ing rea­sons for the extinc­tion. This can be used to take man­age­ment actions and may help pre­vent extinc­tion of endan­gered species.

(Source: SDU Fac­ulty of Sci­ence news release, 11.01.2019)

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Tiger range countries map

Tiger map” (CC BY 2.5) by Sander­son et al., 2006.

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