Starvation Driven Diffusion as a Survival Strategy of Biological Organisms

Abstract

The purpose of this article is to introduce a diffusion model for biological organisms that increase their motility when food or other resource is insufficient. It is shown in this paper that Fick's diffusion law does not explain such a starvation driven diffusion correctly. The diffusion model for nonuniform Brownian motion in Kim (Einstein's random walk and thermal diffusion, preprint http://amath.kaist.ac.kr/papers/Kim/31.pdf , 2013) is employed in this paper and a Fokker-Planck type diffusion law is obtained. Lotka-Volterra type competition systems with spatial heterogeneity are tested, where one species follows the starvation driven diffusion and the other follows the linear diffusion. In heterogeneous environments, the starvation driven diffusion turns out to be a better survival strategy than the linear one. Various issues such as the global asymptotic stability, convergence to an ideal free distribution, the extinction and coexistence of competing species are discussed.

Evolution of Dispersal with Starvation Measure and Coexistence

“…Then, the uniform parabolicity of the problem gives the positivity to the solution and hence the satisfaction measure is well defined for all t > 0. If the motility function γ is taken as a decreasing function of the satisfaction measure, one may obtain the same theory (see Cho and Kim 2013;Kim et al 2013Kim et al , 2014. The first competition model of this paper is…”

“…This is the model introduced in Cho and Kim (2013). An analysis for the competition between the first and the third phenotypes is in Kim et al (2013).…”

“…The starvation-driven diffusion (SDD for brevity) has recently been introduced by Cho and Kim (2013) to mathematically model dispersal increase in the event of starvation. One of our main interests is in the correct timing of dispersal increase in the event of starvation.…”

Spatially Resolved Measurement of the Stress Tensor in Thin Membranes Using Bending Waves

“…On the one hand, methods to measure the concentration [23] or the temperature [24] in particle or heatdiffusion systems as a function of space and time are known. On the other hand, inhomogeneous diffusion is a topic of continuing theoretical interest, which has been discussed for several decades [25][26][27][28][29][30][31]. In order to know the diffusion law, the microscopic nature of the system has to be examined [27].…”

Perception-based foraging for competing resources: Assessing pest population dynamics at the landscape scale from heterogeneous resource distribution

“…Accounting for resource availability as a determinant of mobility in population models is a question recently explored from a 'placebased' angle (Cho and Kim, 2013) where mobility was defined from local density-dependent resource availability (an issue generally associated with the theoretical concept of Ideal Free Distribution, Fretwell and Lucas, 1969). Here we put density-dependence aside, which seems relevant regarding our biological model, thus focusing on resource perception.…”