= Aggregation of macroparasite burdens
{title2=$\operatorname{Var}(j)=m+m^2/k$}
If host-specific <equilibrium> <mean> burden has a <gamma distribution>, conditional <Poisson distributions> produce a <Poisson-gamma mixture>, hence a <negative binomial distribution>. With <mean> $m$ and shape $k$, its zero-burden <probability> is $(1+m/k)^{-k}$. Decreasing $k$ increases aggregation: a smaller infected-host <prevalence> can accompany the same <mean> burden and more heavily infected individuals.
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