Numerical model of the spatio-temporal dynamics in a water strider group

Abstract

The water strider group demonstrates a very complex dynamics consisting of competition for the food items, territoriality and aggression to the conspecific individuals, escaping from the predators, etc. The situation is even more complex due to the presence of different instars, which in most water strider species live in the same habitat and occupy the same niche. The presented swarm model of water striders demonstrates the realistic population dynamics. For the swarm formation in the model, attraction and repulsion forces were used. Animal motion in the model takes into account inertia and kinetic energy dissipation effects. The model includes three different rates related to the growth of individuals: food appearance rate, food assimilation rate, and stored energy loss rate. The results of our modeling show that the size distribution of individuals seems to be an adequate measure for population status, and it has a characteristic shape for different model parameter combinations. Distribution of the distances between nearest neighbors is other important measure of the population density and its dynamics. Parameters of the model can be tuned in such a way, that the shape of both distributions in a steady phase coincides with that shape observed in a natural population, which helps to understand the factors leading to particular momentary distribution of both parameters (size and distance) in the population. From this point of view, the model can predict how both distributions can further develop from certain state depending on particular combination of factors.

Numerical Modeling of the Collective Behavior of Scarab Beetles Transporting Dung Balls and Competing for Them on Complex Terrain

“…The coefficients μ and ν determine different weights of the corresponding substructures in the total surface $$Z(x,y;{q_0})$$. Below according to the previous studies, [ 21 ] we apply: $$\Delta q = 3{q_{\min }}$$, $$\mu = 0.2$$, and $$\nu = 1$$.…”

“…Previously, we studied an idealized case of one beetle, which tries to move in a randomly chosen, but fixed direction. [ 6,21 ] The numerical procedure in this idealized case is regular, because one can associate one of the axes of coordinates with the preferable direction of motion: $$f_x^{{\rm{ext}}} = {\rm{const}} \ne 0$$; $$f_y^{{\rm{ext}}} = 0$$. However, a randomness and corresponding statistics still exists here, because each time the procedure specified in Equations (1)–(4) randomly generates a new realization of the potential $$U(x,y;{q_0};{U_0})$$.…”

“…Generally speaking, the food can fall into random position $${\overrightarrow r _n}$$ inside the area. In our previous studies of qualitatively close problems, [ 21 ] the food was supposed to be randomly deposed inside populated area. The attraction to the portion of food was simulated by the following term in the attraction force $$\begin{equation}f_{_{jn}}^{{\rm{food}}}({\overrightarrow r _j},{\overrightarrow r _n}) = B_{jn}^{{\rm{food}}}({\overrightarrow r _j} - {\overrightarrow r _n})\exp \left[ { - {{\left( {\frac{{{{\overrightarrow r }_j} - {{\overrightarrow r }_n}}}{{R_{_j}^{{\rm{food}}}}}} \right)}^2}} \right]\end{equation}$$…”

“…The coefficients 𝜇 and 𝜈 determine different weights of the corresponding substructures in the total surface Z(x, y; q 0 ). Below according to the previous studies, [21] we apply: Δq = 3q min , 𝜇 = 0.2, and 𝜈 = 1. At every fixed value of q 0 , the numerical procedure generates a new function Z(x, y; q 0 ) distributed between the particular global minimum Z min and maximum Z max .…”

“…Generally speaking, the food can fall into random position ⃗ r n inside the area. In our previous studies of qualitatively close problems, [21] the food was supposed to be randomly deposed in-side populated area. The attraction to the portion of food was simulated by the following term in the attraction force…”