The interplay between phenotypic and ontogenetic plasticities can be assessed using reaction-diffusion models : The case of Pseudoplatystoma fishes.

Every morphological, behavioral, or even developmental character expression of living beings is coded in its genotype and is expressed in its phenotype. Nevertheless, the interplay between phenotypic and ontogenetic plasticities, that is, the capability to manifest trait variations, is a current field of research that needs morphometric, numerical, or even mathematical modeling investigations. In the present work, we are searching for a phenotypic index able to identify the underlying correlation among phenotypic, ontogenetic, and geographic distribution of the evolutionary development of species of the same genus. By studying the case of Pseudoplatystoma fishes, we use their skin patterns as an auxiliary trait that can be reproduced by means of a reaction diffusion (RD) model. From this model, we infer the phenotypic index in terms of one of the parameters appearing in the mathematical equations. To achieve this objective, we perform extensive numerical simulations and analysis of the model equations and link the parameter variations with different environmental and physicochemical conditions in which the individuals develop, and which may be regulated by the ontogenetic plasticity of the species. Our numerical study indicates that the patterns predicted by a set of reaction diffusion equations are not uniquely determined by the value of the parameters of the equation, but also depend on how the process is initiated and on the spatial distribution of values of these parameters. These factors are therefore significant, since they show that an individual's growth dynamics and apparent secondary transport processes, like advection, can be determinant for the alignment of motifs in a skin pattern. Our results allow us to discern the correlation between phenotypic, ontogenetic, and geographic distribution of the different species of Pseudoplatystoma fishes, thus indicating that RD models represent a useful taxonomic tool able to quantify evolutionary indexes.