Hassell model

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The Hassell model (or Hassell equation) is a classic discrete-time population model which gives the estimates for a single species the number of individuals in the population in a given discrete time step as a function of the number of individuals in the preceding time step. It is a generalization of the Beverton-Holt model and historically descends from the Ricker model.

${\displaystyle N_{t+1}={\frac {R_{0}N_{t}}{(1+aN_{t})^{b}}}.}$

The equation was written by Michael Hassell in 1975. Here ${\displaystyle R_{0}}$ is to be understood as the competition-free growth rate, ${\displaystyle b}$ as a value that parameterizes the kind of competition ranging from scramble competition to contest competition, and while ${\displaystyle a}$ lacks a clear and distinct biological meaning, simple algebra reveals that if ${\displaystyle b=1}$, then ${\displaystyle a=1/K}$, where ${\displaystyle K}$ denotes the long-run carrying capacity.

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