# Contents

## Idea

the Wikipedia article:

The Allee effect - or underpopulation effect - is a phenomenon in biology characterized by a positive correlation between population density and the per capita population growth rate in very small populations.

## Details

### Mathematical formulation

Here it is seen in the form of an extra term in the logistics equation: ${d x \over d t} = {r\over K} (K-x) x (a-x)$ where $a$ is the Allee extinction threshold.

## References

ABSTRACT: Conservation programs often focus on studying extinction risks encountered by small populations and determining minimum population sizes below which they cannot recover. In certain cases, per capita rates of population growth become negative at low population density. This ‘Allee effect’ (or ‘depensation’) is rarely considered in marine systems. We conducted surveys of adult density, reproductive behavior, and spawning in natural populations of Caribbean queen conch Strombus gigas at 2 locations in the Exuma Cays, Bahamas, to test for Allee effects.

Mating never occurred when density was $\lt 56 conch ha^-11$, and spawning never occurred at $\lt 48 conch ha^-1$, clearly demonstrating theoperation of depensatory mechanisms. Reproductive behavior then increased rapidly to asymptotes at densities near 200 conch ha–1. Heavily exploited populations of queen conch in the Caribbean have been slow to recover despite fishery closures. Failure to recover could result from spawning stockdensities that are reduced to the point at which Allee effects begin to operate on reproductive behavior.

category: ecology