- To understand the concept of social behavior in predator-prey dynamics.
- Understanding the effects of spatial distribution of prey population on predator foraging using a mathematical simulator.
- To understand, how the cooperation among the predators would increase the foraging efficiency.
To understand the biological concept of "Predator-prey dynamics: effects of social behavior":
Social behavior characterizes the interactions that occur among individuals. These interactions can be aggressive, mutualistic, cooperative, altruistic and parental. When individuals interact repeatedly, social relationships develop and these can form among strangers, relatives, members of the same or opposite sex, and member of the same or different generations. Sets of consistent social relationships produce social systems or social organizations that can be variations on monogamous or polygamous themes and involve various types of helpers. The nature of any social system is ultimately determined by ecological and social circumstances, demography, and kinship.
Altruistic: Unselfish concern for the welfare of others or selflessness.
Demography: Statistical study of human populations.
Affiliative: To become closely connected or associated.
Agonistic: Competitive interaction.
Social interactions, both affiliative and agonistic, occur sometimes with relatives, sometimes with strangers, sometimes with members of the same sex, sometimes with members of other sex; and sometimes with members of the same generation while at other times with members of other generations. The interactions themselves can be aggressive, cooperative or even altruistic and develop into strong relationships among particular individuals. Depending on the nature of these relationships and with whom they form a variety of social systems can develop. Some may be made up mostly of kin or mostly of non-kin, some may be based on territorial separation or on the aggregation of competitors, some will exhibit monogamous as opposed to polygamous relationships between the sexes, and some will rely on the help of non-mates in the rearing of offspring. This seemingly bewildering pattern of social diversity is shaped ultimately by ecological circumstances and patterns of demography. But the very nature of a population's social structure itself will in turn affect the population's demography and its place in the biological community.
Social animals form groups. While some are temporary, others are more permanent. Given that animals in groups incur automatic costs of increased disease and parasite transmission as well as intensified competition, groups will only form when there are sufficiently large benefits to offset these costs. Benefits largely come in three forms. First, animals can develop forms of social behavior specific to stable groups that compensate them for the costs of group living. One such example is forming mutual grooming partnerships as do olive baboons (Papio Anubis) to lower disease and parasite transmission. Second, by forming groups, animals can enhance foraging by being better able to find, acquire, or defend food. Examples include colonial cliff swallows (Hirundo Pyrrhonota) that transfer information about the locations of rich but ephemeral feeding sites or troops of monkeys who drive smaller troops away from feeding trees. And third, animals in groups can reduce their risk of being preyed upon by either increasing the likelihood of detecting predators, diluting their personal risks, or by decreasing the likelihood that predators can make a kill; confusion and cooperative defence are mechanisms that provide such anti-predator benefits. Examples include the scattering of fish in schools, or the gathering of young inside a ring of adult musk oxen (Ovibos Moschatus) facing outwards toward approaching predators with upturned horns.
Depending on the nature of the social relationships that develop, groups take on particular organizational forms. These relationships are shaped by the features of an individual's physical and social environment. Particular distributions of food, water (bottom-up factors) and predators (top-down factors), in conjunction with the physiological demands of individuals differing in body sizes or reproductive states, will determine the frequency and magnitude of competitive and cooperative interactions that occur. In the case of exceptionally large animals, when they hunt, they were to cause risk to more individuals. This becomes especially important when sickness or injury may be debilitating enough to prevent hunting and the individual becomes dependent on the group for support during such times. Predators must also be wary of competition from other predators that are inclined to steal their kill. The larger the animal is, the less likely it will be subject to such opportunistic conflicts.
Therefore we find that this same result parallels the size of the social group with corresponding successes against such predations. However, the problem is more difficult with predators since they have to deal with a specific finite resource for food. The more predators are involved, the larger the prey animal must be to nourish them after a kill. Once again, we have an equilibrium point that needs to be considered so that the size of a social group must compliment the availability of prey animals. Too few prey animals will result in the group dying out, or having to separate into smaller groups to survive.
It is also clear that the social environment becomes the training ground for new members, which is especially important for predators since they must be taught the intricacies of prey detection, tracking, and killing. In groups like the wolf, the task of raising the young is essentially a group activity, despite the fact that only the alpha male and female reproduce. This is another compelling case of where belonging to a cooperative group with its attendant rules is clearly a more beneficial arrangement which supersedes the "selfishness" of simply passing on ones' genes.
It should be understood that not all animals interact in social groups and some may only have limited contact with such groups (either as predators or prey). However, it should also be noted that while these animals certainly behave in a self-interested manner, there is none that could be said to exhibit any trait remotely resembling "selfishness". In general, cooperative behavior serves several purposes in ensuring that predators are able to hunt prey that might normally be beyond their ability to kill. This ensures that a singular effort can result in enough food for many and thereby mitigate the risks inherent in having to provide multiple kills. A cooperative group also provides a means by which future mates may be selected and the group organization ensures that the young are protected from external predation. In all likelihood it is these conditions that probably gave rise to group cooperation in the first place, since these animals would've shared a geographic proximity and frequent encounters as contrasted with the largest predators that typically have more far-ranging territories.
In having examined these various aspects of biology, I hope that it has become clear that simplistic ideas of "survival of the fittest" or "selfishness" don't even begin to describe the intricacies of animal adaptations. While there are many animals that operate as individuals, there are numerous examples indicating adaptations from simple "part-time" social groups (schools of fish, and seasonal flocks of birds) to highly complex social groups (wolves, horses, and humans). In all cases, the degree of socialization is also a determining factor in the direction selection pressures have worked to "create" the modern day animals. In many cases, the social aspects of an animal group are inseparable from the individual, since there is no survival capability for the individual outside the group. Therefore, we have to recognize that while these social groups consist of individuals, each capable of acting in their own self-interest, the results will be colored by the group requirements and create a form of "super-organism" that is now representative of the species.
Understanding the effects of spatial distribution of prey population on predator foraging by setting up different theta values using mathematical simulator:
Having given a brief description on social behavior, here we try to explore the predator-prey dynamics with respect to the spatial distribution of the prey population. Consider prey populations exist in patches with different densities; in this case consider the example of lemur species. The densities of lemur species vary from habitat to habitat which is denoted with the term 'theta' in these simulations. Below equations denote the predator and prey dynamics with the first equation concerning the predator dynamics and the second to the prey dynamics. By assigning different theta values, we try to understand how the predator fossa (Cryptoprocta ferox) tries to exploit its prey depending on their spatial distribution.
Where N1 is the number of predators,
r is the rate of growth,
k is the carrying capacity,
theta refers to the crowding effect,
N2 is the prey population,
b is the consumption rate,
a refers to the number of encounters result in kill,
d refers to the death rate.
In the mathematical simulator, the user is expected to set different theta values which are provided as a slider bar and observe the plots, in which prey population is plotted against predator population.
To understand, how the cooperation among the predators would increase the foraging efficiency with the help of a mathematical simulator.
Here, we attempt to understand the foraging efficiency of the predator by considering that they cooperate with each other. The efficiency of the predator is calculated with the below equation. The term 'c' in the equation describes the efficiency of the predator. The user is expected to simulate this equation with the developed mathematical simulator by changing the efficiency of the equation. Predator efficiency increases with the cooperation among other predators, i.e., forming a social group. Without the cooperation, the efficiency of the predator and the chance of hunting down its prey considerably decreased.
Where c refers to the advantage to the predators of cooperating in the hunt,
n2 refers to the number of predators.