Ecological Archives E093-057-A3

Benedikt R. Schmidt, Walter Hödl, and Michael Schaub. 2012. From metamorphosis to maturity in complex life cycles: equal performance of different juvenile life history pathways. Ecology 93:657–667.

Appendix C. Description of the multi-state mark-recapture model in matrix notation.

To estimate age-specific survival probabilities, age-specific probabilities to start reproduction and recapture probabilities a multi-state model with the two states “metamorph” and “breeder” was used. From one occasion to the next, individuals may move between these two states, they may survive and the may be recaptured. These events can be described by a matrix of state transition probabilities, by a vector of state-specific survival probabilities and a vector of state-specific recapture probabilities, respectively. In the following, the states at time t are in rows and the states at time t + 1 in columns. Because the parameters change with age, we show the model for each age class:

From age 0 to 1 year:  
 
 
 
 
 
 
1 - α1   α1 φ1y 0
0   1 φad p
     
From age 1 to x - 1 years:   
 
 
 
 
 
 
1 - αz   αz φad 0
0   1 φad p
     

where αz is the probability to start to reproduce at age z, and where z {2, …, x - 1}

From age x - 1 to x years (full reproduction is assumed at age x [in fact ax = 1]):   
 
 
 
 
 
 
0   1 φad 0
0   1 φad p
     
From age x onwards:   
 
 
 
 
 
 
1   0 φad 0
0   1 φad p
     

The parameters in this model are:

αz: probability to start to reproduce at age z
φ1y: survival probability in the first year
φad: survival probability after the first year
p: recapture probability

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