Normal versus gamma: stochastic models of copepod molting rate
Additional Document Info
Molting rate is a key life history parameter in copepods. Since copepod population growth is an inherently exponential process, accurate formulation of molting rate is of critical importance. Many experiments have been conducted to culture different copepod species under varying temperatures and food concentrations. Probability density functions (PDFs) then were used to estimate the median development time (MDT) of different copepod stages from the experimental data. These MDTs are used in copepod population models. Asymmetrical PDFs are widely used to model molting rate, because the shapes of these curves are similar to laboratory data on cohort development. In this paper, we developed an individual stochastic model (ISM) to simulate the molting rate with different PDFs. We showed that there was no connection between the asymmetry of cohorts and the asymmetry of the molting PDF. Although age-within-stage models have been widely used to simulate copepod population dynamics, we found that none had used the correct formulation of molting rate. The population model requires the probability of molting at each time step, whereas the laboratory-derived PDF is the frequency distribution of stage duration. Therefore, the PDF cannot be applied directly to the population model. We present here a corrected formula based on the PDF for use in copepod population models, termed the probability of molting for remaining individuals (PMR). Despite emphasis on use of the gamma function for copepod molting, we found simpler functions work equally well, but that prior use of incorrect molting rate functions in copepod models can seriously overestimate generation time.