= Mating-limited macroparasite transmission
{title2=$\Pr(\text{both worm sexes})=(1-e^{-m/2})^2$}
For sexually reproducing worms, an infected <host> need not contain both sexes. Independent random sexes split a Poisson total burden of <mean> $m$ into independent male and female <Poisson distributions> of <mean> $m/2$, giving the displayed <probability> of a fertile mixed-sex burden. For an arbitrary burden <probability generating function> $G$, this <probability> is $1-2G(1/2)+G(0)$. Its low-burden behaviour can introduce an <Allee effect> in transmission, so an asexual mean-burden invasion calculation is not automatically valid.
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