An extensive history of 163 years of fruitful research on evolutionary science made our sense of consciousness to another level. We know that the occurrence of natural selection is continuous and deeply connected with the concept of survival of the fittest. Whether it may be for living beings on the earth or in the socio-economic world. In this article, I have tried to explain the science behind the intensity of species interaction from a game theoretic perspective that makes a noticeable difference in fitness level.
The fitness of any species is an overall average measurement determined by each individual of that species population. To gain fitness, every species needs a certain amount of food, water, shelter, etc. But these resources are not so plenty that species can continue a limitless growth in their population. So, interaction for resources is an inevitable reality that happening constantly in our world. Different kinds of interaction flawlessly shaped the ever-changing nature of species fitness. Now the question is, how does the interaction intention come into this picture? Although the word 'intention' has a social interaction background, it is now a distinguished part of ecological psychology. When organisms interact with others, they are performing the action or making decisions under this 'intention' state knowingly or maybe unknowingly. Broadly speaking, these decisions were usually considered as 'strategies' in the context of game theory. But 'strategies' are defined on the basis of genetically encoded characteristics of an organism which are achieved as an inheritance. Whereas the interaction intention can be defined as the effects of the adaptive force which has to be faced externally. Therefore, there is a subtle difference between interaction strategy and interaction intention which has been observed in many socio-ecological phenomena.
As an example, we consider the competition between two people who are fighting for some resources. One of them has a very tall and heavy body and the other has a relatively short and thin body. Then strength-wise, the taller and heavier man should win this contest, and it often does. So, the output of this strategy-wise game or interaction is that taller and heavier people would get more pay-off rather than shorter and thin people. Due to his/her small body insecurity, if the shorter person is well trained for self-defense and for attacking a bigger opponent, then he will reflect his skill during this competition. Even so, the shorter person can defeat the taller person with his instant reflexes and constant hitting of the opponent's weak spots. That means, in this case, the result of the game can be different, although the strategies are the same as in the previous one. Here the adaptation of self-defense training is not an inheritance characteristic though it makes a difference in the result of the interaction. Precisely this fact is what we consider as the 'intention' of interaction, and it has a more important, larger role in the modern mutated world of organisms.
After this observation, I think that if it is possible for human interaction, it can also happen in other organisms, and the thing training for humans can seem similar to adaptation for survival in nature for other organisms. Because to get better fitness, organisms are always trying to reshape their traits for the ever-changing environment. But the adaption process for existence flows from generation to generation, and slowly, it is upgraded genetically by many phases of variation, which is called a mutation. That is, on evolutionary time scales, adaptation also transformed over time into genetically encoded traits. So how can we distinguish the interaction intention from the general concept of adaptation? This can be thought of as a bit of a reflex action to adapt to an adverse circumstance, such as a potential threat or greed to get more resources. Its purpose of execution is only for the security of resources and to rescue own from threats by others. For each different interaction, there are two possibilities that interaction intensity is either it is constant or maybe changeable. However, for simplicity, we treat the interaction intensity as a constant parameter in our study.
Our research begins with the quest for a mathematical approach to explain the evolutionary trajectory of traits of any organism. Primarily our aim was to portray the behavioral characteristics as a different deterministic entity. For this, the game theoretic setup is best among the best and was introduced by John Maynard Smith in 1973 as the ‘Evolutionary game theory.’ Then after a long period of literature survey, I noticed that despite a huge collection of studies, there are no such attempts available that should focus on our thinking concept. So, we redefined the mathematical model based on the game theoretic formation (Replicator dynamics: a frequency-dependent approach) with the noble inclusion of interaction intensity in the fitness level. Our entire approach is based on the manifestation of the Darwinian theory of natural selection, where the best-fitted are able to compete, survive and reproduce. The basic ecological ingredients, such as intrinsic growth rate, population density, and sigmoidal growth pattern, are mixed up in the evolutionary context. Analyzing this non-linear dynamical system, we have reached some stationary states where the population density is asymptotically stable with a stable proportion of behaviourally different subpopulations. A point to be noted is that the possibility of mutation has been very modestly avoided here because the interaction intention does not cause any genetic variation in the organism.