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).