Probability of permanence and colonization
Using the AS control, we estimated the basal values of the parameters for the permanence and colonization probability for each genus of aquatic insect. The model used in this step was the following modification of the standard model:
\begin{equation} {O_{i,t}\sim Bern\left(P_{i,t}\right)\backslash n}{P_{i,t}=\theta_{g}+O_{i,t-1}\bullet\psi_{g}\backslash n}{\theta_{g}\sim Beta\left(\alpha_{1,g},\beta_{1,g}\right)\backslash n}{\psi_{g}\sim Beta\left(\alpha_{2,g},\beta_{2,g}\right)\backslash n}{\alpha_{1,g}\sim Gamma\left(0.001,0.001\right)\backslash n}{\beta_{1,g}\sim Gamma\left(0.001,0.001\right)\backslash n}{\alpha_{2,g}\sim Gamma\left(0.001,0.001\right)\backslash n}{\beta_{1,g}\sim Gamma\left(0.001,0.001\right)}\nonumber \\ \end{equation}
(model 2)
where Oi,t was the occurrence of genus iat time t , Pi,t was the probability of the occurrence of genus i at time t given its occurrence at time t –1. The parameters \(\alpha\) and \(\beta\) in model 2 were the priori distribution of the probabilities of permanence (\(\psi\)) and colonization (\(\theta\)) of group g to which genus i belongs.