Analysis of a Schnute postulate-based unified growth model for model selection in evolutionary computations

Abstract

In order to evaluate the feasibility of a combined evolutionary algorithm-information theoretic approach to select the best model from a set of candidate invasive species models in ecology, and/ or to evolve the most parsimonious model from a suite of competing models by comparing their relative performance, it is prudent to use a unified model that covers a myriad of situations. Using Schnute's postulates as a starting point, we present a single, unified model for growth that can be successfully utilized for model selection in evolutionary computations. Depending on the parameter settings, the unified equation can describe several growth mechanisms. Such a generalized model mechanism, which encompasses a suite of competing models, can be successfully implemented in evolutionary computational algorithms to evolve the most parsimonious model that best fits ground truth data. We have done exactly this by testing the effectiveness of our reaction-diffusion-advection (RDA) model in an evolutionary computation model selection algorithm. The algorithm was validated (with success) against field data sets of the Zebra mussel invasion of Lake Champlain in the United States.

On the Approximation of the Cut and Step Functions by Logistic and Gompertz Functions

“…Gompertz models prove to be useful in animal and agro-sciences as well [8], [21], [27], [48]. The Gompertz model has been applied in modelling aggregation processes [25], [26]; it is a subject of numerous theoretical modelling studies as well [6], [7], [9], [20], [37], [40].…”

Modeling invasive species spread in Lake Champlain via evolutionary computations

“…1a, b) which includes the following biological attributes: dispersal (diffusion), advection (both in the x and y directions), and growth terms (both linear and non-linear density dependence see, for example, Bentil et al (2007)) for this work. The community of models describing this phenomenon is given by …”

“…D is the diffusion coefficient, w x and w y are advection in the x and y directions, respectively, K is the carrying capacity, a is growth rate, b is a dimensionless shape parameter, and q mimics Allee effect, a threshold population size below which the population declines (see Bentil et al (2007) for more details on the reaction component, f(n)). Table 1 illustrates the matrix of complexities that is included in the RD model equation.…”

“…This goal is accomplished by using ecological field data and in this case Zebra mussel Table 1 A matrix of the complexities of biological invasions which includes linear and non-linear density dependence, isotropic and anisotropic spread data from Lake Champlain in Vermont. The generalized model, whose reaction component was first proposed by Bentil et al (2007) accounts for the complexities of the spread of invasive species such as linear and non-linear density-dependent growth, Allee effect, and both isotropic and anisotropic spread (diffusion and advection). The generalized model is very useful for model selection because it leads to a nested set of RD equations through which a competition for the best model that describes field data can be evolved.…”

“…We motivate our modeling procedure in ''Materials and methods'' section by first giving a brief exposition of a simple reaction diffusion equation model with a generalized reaction term, such as described in Bentil et al (2007). We estimate the wave speed and incorporate the reaction diffusion model in an evolutionary algorithm.…”