Basic model of purposeful kinesis

Abstract

The notions of taxis and kinesis are introduced and used to describe two types of behaviour of an organism in non-uniform conditions: (i) Taxis means the guided movement to more favorable conditions; (ii) Kinesis is the non-directional change in space motion in response to the change of conditions. Migration and dispersal of animals has evolved under control of natural selection. In a simple formalisation, the strategy of dispersal should increase Darwinian fitness. We introduce new models of purposeful kinesis with diffusion coefficient dependent on fitness. The local and instant evaluation of Darwinian fitness is used, the reproduction coefficient. New models include one additional parameter, intensity of kinesis, and may be considered as the minimal models of purposeful kinesis. The properties of models are explored by a series of numerical experiments. It is demonstrated how kinesis could be beneficial for assimilation of patches of food or of periodic fluctuations. Kinesis based on local and instant estimations of fitness is not always beneficial: for species with the Allee effect it can delay invasion and spreading. It is proven that kinesis cannot modify stability of positive homogeneous steady states.

Mobility cost and degenerated diffusion in kinesis models

“…In our previous model ( 1), ( 2) the trade-off between the cost of mobility and the possible benefits from mobility was not accounted (Gorban and C ¸abukoǧlu, 2018). Let us introduce here the cost of mobility as a negative linear feedback of the mobility µ on the reproduction coefficient r:…”

“…The kinesis strategy controlled by the locally and instantly evaluated well-being can be described in simple words: Animals stay longer in good conditions and leave more quickly bad conditions. If the well-being is measured by the instant and local reproduction coefficient then the diffusion model of kinesis gives for mobility µ i of ith species (Gorban and C ¸abukoǧlu, 2018):…”

“…This model aimed to describe the 'purposeful' kinesis (Gorban and C ¸abukoǧlu, 2018) that helps animals to increase there fitness when the conditions are bad (for low reproduction coefficient mobility increases and the possibility to find better conditions may increase) and not to decrease fitness when conditions are good enough (for high values of reproduction coefficient mobility decreases). The instant quality of conditions is measured by the local and instant reproduction coefficient.…”

“…The instant quality of conditions is measured by the local and instant reproduction coefficient. Gorban and C ¸abukoǧlu (2018) demonstrated on a series of benchmarks for models (2) with mobilities (1) that:…”

Adaptive movement strategy in rock-paper-scissors models

“…Interacting with the environment makes individuals respond appropriately, adapting either their movement speed (kinesis behaviour) or direction (taxis movement) [13]. In both cases, instead of an aimless motion, individuals are guided by local cues they instinctively interpret or learn to decipher, i.e., the motion pattern is a result of an innate or conditioned behaviour, respectively [14]. Understanding the organisms' adaptive movement strategy has also helped the development of engineering tools with sophisticated mechanisms of artificial intelligence that allow animats to change strategies to survive in hostile scenarios [15].…”