Ecological Archives A024-087-A1

Annie J. Yau, Hunter S. Lenihan, Bruce E. Kendall. 2014. Fishery management priorities vary with self-recruitment in sedentary marine populations. Ecological Applications 24:1490–1504. http://dx.doi.org/10.1890/13-1201.1

Appendix A. Fitting survival models in an integral projection model for giant clams, Tridacna maxima.

To fit a function describing survival, s(x), to the next time step as a function of size, we first fit linear, second-order, and third-order logistic regression models to the survival data. We selected the most parsimonious model using second order Akaike information criterion (AICc) scores (Burnham and Anderson 2002). Of these models, the third-order logistic regression model had the lowest AICc score, with the other models differing from the lowest AICc score by >7.1. However, this third-order logistic regression resulted in an artificial increase in survival for the largest clams >140 mm (Fig. A1(A)), which was likely a result of the small sample size for those sizes instead of an actual increase in survival of large clams.

The limitation of linear logistic regression is that it cannot asymptote to a value less than one; the fitted third-order model suggests that an intermediate asymptote would be appropriate. We developed a nonlinear logistic regression model:

logit(s(x)) = as + bs/(x + cs),                       (A.1)

where logit-1(as) is the asymptotic survival, cs is a half-saturation constant controlling the rate of approach to the asymptote, and logit-1(as + bs/cs) is the intercept. This functional form allows survival to increase as recruits grow into juveniles, then asymptote as clams reach the largest sizes. We used nonlinear minimization to estimate the parameters of the model; the fitted model is shown in Fig. A1(B). The AICc score of this nonlinear logistic regression was slightly higher but only differed from the AICc score of the third-order logistic regression by Δi = 2.33, giving the nonlinear model substantial support. We chose the nonlinear logistic model of survival because of its fit to the empirical data, and the resulting realistic asymptotic survival of the largest clams. All analyses were conducted using R version 2.10.1 or higher (R Development Core Team 2009).

Literature cited

Burnham, K. P., and D. R. Anderson. 2002. Model selection and multimodel inference: a practical information-theoretic approach. Springer Verlag.

R Development Core Team. 2009. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.


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