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.