Neglecting uncertainty behind Allee effect estimation may generate false predictions of population extinction risk

Authors

  • Luděk Berec,

    1. Dept of Biosystematics and Ecology, Inst. of Entomology, Biology Centre ASCR, Branišovská 31, CZ-37005 České Budějovice, Czech Republic, and: Inst. of Mathematics and Biomathematics, Faculty of Science, Univ. of South Bohemia, Branišovská 31, CZ-37005 České Budějovice, Czech Republic.
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  • Tomáš Mrkvička

    1. Dept of Biosystematics and Ecology, Inst. of Entomology, Biology Centre ASCR, Branišovská 31, CZ-37005 České Budějovice, Czech Republic, and: Inst. of Mathematics and Biomathematics, Faculty of Science, Univ. of South Bohemia, Branišovská 31, CZ-37005 České Budějovice, Czech Republic.
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L. Berec, Dept of Biosystematics and Ecology, Inst. of Entomology, Biology Centre ASCR, Branišovská 31, CZ-37005 České Budějovice, Czech Republic, and: Inst. of Mathematics and Biomathematics, Faculty of Science, Univ. of South Bohemia, Branišovská 31, CZ-37005 České Budějovice, Czech Republic. E-mail: berec@entu.cas.cz

Abstract

Estimation of extinction thresholds arising from Allee effects (Allee thresholds) and related probabilities of population extinction is notoriously difficult. One way is to analyze adequately parameterized population models. Traditionally, a point estimate is substituted for the Allee effect strength in such models. However, each point estimate entails an underlying uncertainty. We explore how accounting for this uncertainty affects the probability of population extinction, and show that this probability decreases sigmoidally with increasing population density, even in the absence of any stochasticity. Deviations from when only a point estimate of the Allee effect strength is used can be significant, unless stochasticity is added and the stochastic noise intensity is high. Significant deviations from when only a point estimate is used also occur when the Allee threshold and the environmental carrying capacity of the species are close enough one to another. We also show that the impact of the uncertainty in the Allee effect strength estimate increases as the Allee effect strength itself increases and decreases as the species recovery potential increases. This is not a good news, since we would like to preferentially and efficiently manage slowly recovering populations prone to strong Allee effects. Still, there is a way to come up with relatively good Allee threshold estimates. Besides an obvious option of collecting as many data as possible, the impact of the uncertainty can be mitigated by diversifying Allee effect experiments such that we put more emphasis on larger size groups. This is somewhat surprising, given that frequent complaints on the (im)possibility of detecting Allee effects concern difficulties in locating, observing and experimenting on rare populations. Our results extend current theory surrounding Allee effects and have broad ramifications for applied ecology.

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