Stochasticity in the Parasite-Driven Trait Evolution of Competing Species Masks the Distinctive Consequences of Distance Metrics

Christian Buhat,Dylan Talabis,Jomar Rabajante,Genaro Cuaresma,Maica Gavina,Ariel Babierra,Anthony Cueno

doi:10.3390/pr5040074

Christian Buhat, Dylan Talabis + Show 5 more

Open Access

https://doi.org/10.3390/pr5040074

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Abstract

Various distance metrics and their induced norms are employed in the quantitative modeling of evolutionary dynamics. Minimization of these distance metrics, when applied to evolutionary optimization, are hypothesized to result in different outcomes. Here, we apply the different distance metrics to the evolutionary trait dynamics brought about by the interaction between two competing species infected by parasites (exploiters). We present deterministic cases showing the distinctive selection outcomes under the Manhattan, Euclidean, and Chebyshev norms. Specifically, we show how they differ in the time of convergence to the desired optima (e.g., no disease), and in the egalitarian sharing of carrying capacity between the competing species. However, when randomness is introduced to the population dynamics of parasites and to the trait dynamics of the competing species, the distinctive characteristics of the outcomes under the three norms become indistinguishable. Our results provide theoretical cases of when evolutionary dynamics using different distance metrics exhibit similar outcomes.

Highlights

Parasitism-induced coevolution is an interesting topic of evolutionary biology, as parasites can drive biodiversity and balance in communities [1,2,3,4]
We identify the distinctive characteristics of the resulting trait dynamics under the Manhattan, Euclidean, and Chebyshev norms
To understand the extent of the regularity of the trait dynamics convergence, we investigate the pattern of convergence under different parameter values of ε and γ (Figure 2)

Summary

Introduction

Parasitism-induced coevolution is an interesting topic of evolutionary biology, as parasites can drive biodiversity and balance in communities [1,2,3,4]. One of which is the selection gradient in differential equation form [12,13,14,15,16,17] In this model, if the selection gradient results in a positive change in fitness value, the trait becomes more favored and further improved. We investigate the differences in the effect of the three metrics to the resulting trait dynamics of competing populations. The distance metric used in obtaining the desired evolutionary outcome is hypothesized to have a significant effect on the trait and population dynamics of species [28,29,30]. Predicting the population dynamics of species could be subject to the metric used in data analysis and simulations This has crucial implications on formulating ecological conclusions. Introductory background and discussion on advances in the fields evolutionary parasitology and evolution of exploitation are available in literature [40,41,42,43,44]

The Mathematical Model

Simulation Results and Discussion

Effect

Conclusions