The motivations of movement through space for herbivores are different from carnivores, for example. As an outcome, the reasons behind an animal spread are numerous. Several biological factors that influence the movement include the preference towards a resource, the presence of home range or the escape from preying.

There is an extensive amount of work in mathematical biology about the effects of distinct behaviours on animal dispersal. How spatial memory influences the redistribution or the impact of the resource depletion in the population search for food and even the living circumstances for example. The existence of different behaviours influences on how a population

*…show more content…*

Thus, the interrelation amidst the predator and prey consider the following dynamics: the preying species don't have any other predatory animals, which don't consume another resource of food than its target. Both species have population dynamics based on their fitness. When the prey spots a potential attacker, it alarms the others with a chance of survival that depends on the rate of the sentinels.

A way to analyze this proposed dynamic is by constructing a model of a partial differential equation system considering the existence of altruistic vigilance. In which I would like to understand the pattern formation for the two species given the presence of guards and its influences on the population dynamics for preys and predators.

Furthermore, it's clear that the number of preying individuals who are at the time sentinels is dependent on the absolute size of the prey population. Nevertheless, this sentinel rate affects the fitness of the altruistic species since if there are too many individuals surveying for predators the number of animals foraging decays, thus the population would be extinct over time. Subsequently, the changes in the prey's health impair the predator fitness and growth, consequently its movement towards a

*…show more content…*

According to the obtained information, the intention is to demonstrate whether or not the altruism is beneficial to a prey population.

Thus, the research focuses its analytical approach on the partial differential equations studies, and the numerical on numeric solutions and the influence of different parameters have on these distinct outcomes. The use of the mathematical tools and the computational analysis improve the obtained results, such biological details and if available field data.

In conclusion, this project pretends to comprehend the altruistic behaviour of the vigilance that a few species have and how the mechanism affects the predator-prey dynamics. As well the creation of patterns as a result of the interaction between a predator and its prey and the aftermath of this relationship on the populations over