A unimodal curve for primate group size along a gradient of population density

Abstract

When plotted along a gradient of population density, the mean group size in populations of several primate species has a unimodal distribution, i.e., mean group size is greater at intermediate population densities than at higher or lower population densities. In this study I present a mathematical model to clarify the cause of this relationship. Population density is assumed to affect group size by enhancing between- or within-group competition and by changing the number of neighboring groups around each group. The mean group size is predicted to decline as population density increases above a critical value, owing to the increasing number of neighboring groups.

Appendix

Equation ${\text{F}}_{{n^{*} + 1}} > {\text{F}}_{{n^{*} }}$ can be transformed into

$$ \left( {\frac{1} {2} + \gamma } \right)b - w\left( {1 + \delta } \right) > \left\{ {\frac{{m - 1}} {m}\frac{1} {2} + \frac{1} {m}\left( {\frac{1} {2} - \gamma } \right)} \right\}b - w, $$

which is equivalent to Eq. 6. Equation ${\text{F}}_{{n^{*} - 1}} > {\text{F}}_{{n^{*} }}$ can also be transformed into Eq. 7.