Assessing the impact of discretisation assumptions in a length-structured population growth model

Most of the traditional assessment models are age-structured. However, many biological and exploitation processes are more length-dependent than age-dependent, and the required length–age conversion of available data is often not reliable. Consequently, length-structured or age–length structured models have undergone considerable development in recent years. The growth transition matrix used to model the mean growth and growth variability of the population, is of primary importance in a length-structured matrix model. Building this growth transition matrix is not trivial and it is necessary to assess the impact that various assumptions may have to identify robust model structures. In this study, we assess the effects of (1) time and length discretisation, (2) the distribution of individuals within length classes and (3) the statistical distribution used to describe growth variability, by fitting a growth matrix model to individual quasi-continuous simulated growth data. The study quantitatively demonstrates that the choice of the time step and of length class width is the key point when building a length-structured population growth model. The use of a gamma distribution for the growth increments and/or a uniform distribution of individuals within length classes were found to make the model more robust.