Genetic algorithm evaluation of parameters of a density-dependent matrix population model

Background/Question/Methods Data were collected in 5 20 x 100 m plots in mono-dominant Mauritia flexuosa stands located in the Ecuadorian Amazon to parameterize a size-based matrix population model. The population was assumed to be stable and at the approximate carrying capacity for the site. The model consisted of seven size classes, and seedling growth rate and survival was assumed to decrease with density using a Ricker function. It is likely that palm size was generally estimated more accurately than size-specific mortality and growth rates during the two-year sampling period due to the limited numbers of observations. In order to evaluate whether the set of 13 growth and survival parameters within the range of observed variation among plots were consistent with the observed size class distribution, a Genetic Algorithm (GA) was used. The GA was based on selecting 1,750 sets of parameter values from within the observed ranges, applying the constraint that total survival + mortality for each size class must be equal to 1.0 (rescaling, if necessary), running each set of parameters and determining relative fitness by the distance from the observed size class distribution. The best sets of parameters have higher representation in the next generation of the GA, with recombination and mutation adding new parameter combinations.

Results/Conclusions

The nominal set of pooled parameters for the population projects an equilibrium population that differs from the observed size class distribution by 67.03 (Σ(absolute value(observed -simulated) over all non-seedling size classes) in a observed population of 336 non-seedling palms. Running the GA over 75 generations led to a best score of 4.98, representing a close fit to the observed size class range. The scores from 15 GA runs ranged from 4.98 to 15.09. Although the pooled parameter estimates were not consistent with the observed size class distribution, consistent values were found within the parameter space using the GA.