Population dynamics model of the hard clam, Mercenaria mercenaria:: Development of the age- and length-frequency structure of the population

An individual-based model was developed to simulate growth of the hard clam, Mercenaria mercenaria, in response to temperature, salinity and food supply conditions. Unique characteristics of the model are that: (1) length and tissue weight are related only by condition index, so that weight, up to a point, can vary independently of length, and (2) age is decoupled from length. Tissue weight changes result from the difference in assimilation and respiration. Changes in hard clam condition are determined from a standard length-weight relationship for average hard clam growth. Changes in hard clam length (growth) occur only when condition index is greater than zero, which happens when excess weight for a given length is attained. No change in length occurs if condition index is zero (mean case) or negative (less weight than expected at a given length). This model structure resolves limitations that accompany models used to simulate the growth and development of shellfish populations. The length-frequency distribution for a cohort was developed from the individual-based model through simulation of a suite of genotypes with varying physiological capabilities. Hard clam populations were then formed by the yearly concatenation of cohorts with partially independent trajectories that are produced by cohort- and population-based processes. Development and verification of the hard clam model was done using long-term data sets from Great South Bay, New York that have been collected by the Town of Islip, New York. The ability to separately track length and age in the simulations allowed derivation of a general mathematical relationship for describing age-length relationships in hard clam populations. The mathematical relationship, which is based on a twisted bivariate Gaussian distribution, reproduces the features of age-length distributions observed for hard clam populations. The parameters obtained from fitting the twisted bivariate Gaussian to simulated hard clam length-frequency distributions obtained for varying conditions yield insight into the growth and mortality processes and population-dependent processes, compensatory and otherwise, that structured the population. This in turn provides a basis for development of theoretical models of population age-length compositions. The twisted bivariate Gaussian also offers the possibility of rapidly and inexpensively developing age-length keys, used to convert length-based data to age-based data, by permitting a relatively few known age-length pairs to be expanded into the full age- and length-frequency structure of the population.