A general relationship between extinction risk and carrying capacity

TL;DR

This study reveals that the probability of population extinction universally follows a modified Gompertz curve relative to carrying capacity, based on extensive simulations and analytical modeling, informing conservation strategies.

Contribution

It demonstrates that a modified Gompertz curve accurately models extinction risk across diverse populations, providing a new mathematical framework for conservation biology.

Findings

Extinction risk follows a modified Gompertz curve across populations.

The pattern holds under various ecological and demographic conditions.

Analytical models confirm the generality of the relationship.

Abstract

Understanding the relationship between a populations probability of extinction and its carrying capacity frames conservation status assessments and guides efforts to understand and mitigate the ongoing biodiversity crisis. Despite this, our understanding of the mathematical form of this relationship remains limited. We conducted ~5 billion population viability assessments that jointly converge on a modified Gompertz curve. This pattern is consistent across >1700 distinct model populations, representing different breeding systems and widely varying rates of population growth, levels of environmental stochasticity, adult survival rate, age at first breeding, and initial population size. Analytical treatment of the underlying dynamics shows that few assumptions suffice to show that the relationship holds for any extant population subject to density-dependent growth. Finally, we discuss the implications of these results and consider the practical use of our findings by conservationists.