supplementary.md

\pagenumbering{gobble}

Figure S1. Parameters can be estimated by Maximum Likelihood

While the full posterior distribution can be sampled using various bayesian machinery, this is not necessary for obtaining point estimates of $\mu$ and $\phi$. A maximum likelihood estimate of each can be calculated by rearranging eq. 4 and fitting a Beta distribution to the result:

{#fig:penciltrick}

We include this result because ecologists may wish to apply our methods for estimating $L$, $Co$ or $L/S$ without fitting a Bayesian posterior of their own. This approach loses information about the sample size of webs, but nevertheless provides a close match to both the empirical data and the bayesian posterior.

parameter	MLE estimate	MAP estimate
$\mu$	0.087	0.086 ± 0.0037
$\phi$	21.0	24.3 ± 2.4