Experimental design and estimation of growth rate distributions in size-structured shrimp populations

Abstract

We discuss inverse problem results for problems involving the estimation of probability distributions using aggregate data for growth in populations. We begin with a mathematical model describing variability in the early growth process of size-structured shrimp populations and discuss a computational methodology for the design of experiments to validate the model and estimate growth rate distributions in shrimp populations. Parameter estimation findings using experimental data from experiments so designed for shrimp populations cultivated at Advanced BioNutrition Corporation are presented illustrating the usefulness of mathematical and statistical modeling in understanding the uncertainty in the growth dynamics of such populations.

A Computational Comparison of Alternatives to Including Uncertainty in Structured Population Models,

“…However, the analysis in [7] reveals that in some cases the size distribution (the probability density function of X(t)) obtained from the stochastic growth model is exactly the same as that obtained from the probabilistic growth model. For example, if we consider the two models 8) and assume their initial size distributions are the same, then we obtain at each time t the same size distribution from these two distinct formulations. Here b 0 , σ 0 and c 0 are positive constants (for application purposes), and B is a normal random variable with b a realization of B.…”

“…Applications are diverse and include populations ranging from cells to whole organisms in animal, plant and marine species [1,3,5,7,8,9,12,14,17,18,19,20,21,22,24]. One of the intrinsic assumptions in standard size-structured population models is that all individuals of the same size have the same size-dependent growth rate.…”

Asymptotic Properties of Probability Measure Estimators in a Nonparametric Model

“…Equation (1.1) is often referred to as a nonparametric model (a model with all the unknown parameters being in an infinite-dimensional parameter space) in the statistics literature. Such models are motivated by a number of applications arising in biology and physics, for example, in modeling mosquitofish populations [9] and shrimp populations [6], in wave propagation in biotissue [15], in modeling of a complex nonmagnetic dielectric materials [4,10], and in HIV cellular models [3]. Here we only elaborate one of the motivating examples, a recent project investigated by our group.…”

Propagation of Uncertainty in Dynamical Systems

“…This model, referred to as growth rate distributed size-structured (GRDSS) population model, was first formulated in [1,6] in 1986, and has been successfully used to model mosquitofish population in the rice fields, where the data exhibits both bimodality and dispersion in size as time increases (e.g., see [1]). In addition, this model was also used to model the early growth of shrimp populations, which exhibits a great deal of variability in size as time evolves even though the shrimp begin with approximately similar size [3,4]. Based on the above discussions, we see that the GRDSS model can be associated with some stochastic process, which is obtained due to the variability in the individual's growth rate and also the variability in the initial size of individuals in the population.…”