Cormack Jolly-Seber model (CJS)
CJS model is a powerful tool to estimate the survival rate of marked individuals using live encounter data (Lebreton, Burnham, Clobert, & Anderson, 1992). The model accounts for imperfect detections, gives estimates of the survival and resighting probabilities, and tests how the latter are determined by intrinsic factors such as age and body size and extrinsic factors such as the weather (Kéry & Schaub, 2011). In odonates, many studies have used CJS to estimate recapture and survival rates (Cordero-Rivera & Stoks, 2008).
We implemented the CJS model using the individual state-space formulation as described by Gimenez et al. (2007). The parameters involved in the likelihood areΦi,t which is the probability that the individuali survives to time occasion t +1 given that it is alive at time occasion t (t=1, 2, …, T-1), andpi,t which is the probability of recapturing (resighting) individual i at time occasion t (t=1, 2, …, T). The initial occasion where individual i is observed is denoted ei . The general state-space formulation of the CJS model includes the observation equation (1) and the state equation (2) where t ≥ ei and\(p_{{i,e}_{i}}\) = 1.
\(Y_{i,t}|X_{i,t}\ \sim\ Bernoulli(X_{i,t}p_{i,t})\) (1)
\(X_{i,t+1}|X_{i,t}\ \sim\ Bernoulli(X_{i,t}\Phi_{i,t})\) (2)
This approach disentangles between the actual demographic process and its observation in the field. The model works such that when individuali is alive at time t , it has probabilitypi,t of being recorded and probability 1-pi,t of not being recorded, which translates into Yi,t following Bernoulli (pi,t ) given Xi,t = 1. When individual i is dead at time occasion t, it cannot be recorded, which translates into Yi,t following Bernoulli (0) given Xi,t = 0. The implementation of the model was carried out using MCMC technique (Brooks, Catchpole, & Morgan, 2000; Gimenez et al., 2009).