Sooperation of Biology and Mathematics: Game Theory

Abstract

Game Theory is a groundbreaking theory which has explained various analyses in different domains of Science and Commerce. In here, strategies of Evolutionary Biology are explained in the light of Game Theory.

Introduction

Mathematics and Biology are both important domains of Science and their union in some applications had drawn the attention of many eminent personalities in solving various problems. Game Theory is one such application. The backdrop of Game Theory came with a famous quote of Prof. John Nash Jr.”The best result would come from everyone in the group doing what is best for himself and the group.” Well, this quote also contains the fundamentals of Evolutionary Biology and Gene Flow across the generations to come. That’s where John Maynard Smith took the initiative to explore the uncharted territories of Biology especially Evolutionary Biology and Ecology with the help of Game Theory.

Aim: In the minds of Biologists, Evolution is an interesting topic which can’t be seen in real-time but its result with gradualism is changing the world right from the beginning of the genesis of life. When the first cell is formed from macromolecules, an unexpected but wonderful turn happened in the heart of the Earth resulting in a complex system originating from simple molecules and then controlling the Earth’s environment on their own. But as fate it is, those species saw their end with the hands of their own nature and they gradually fade away from the face of the Earth. Palaeontologists have long worked tirelessly describing a species with respect to their body patterns and their habitant. After that nothing more could be learnt about them or why they have gone extinct. This is where Game Theory filled the loopholes and helped Scientists in describing the glorious species of the past.

Experimental Analysis and Discussions

Well the behavioural study is strictly an observation study and proper documentation. In this case, Ecology plays a vital role in joining the puzzles of observation and helping to bring out the real picture of the species' habitat. Scientists have now begun considering the process of gene flow between species of past and the current species in the world. The starting point developed on the survival strategies of the species.” Survival of the Fittest” a term Darwin once told the world and now this term formed the very backbone of observation of species behaviour with the application of Game Theory. Before taking into consideration of the quotation of John Nash, a species coming into the Earth must decide the alliance of survival, it must choose its own pack, become a pack hunter, ready to be hunted or hunted in groups. What makes it so keen to forge an alliance with other species, it is nothing but Group Selection. Well in this case individual species within the group prevent itself to commit any selfish act that would jeopardise the entire clan and helps everyone within the group to survive. Well, one can obviously say that this may cause some disadvantages to the individual. Well, it is true sometimes but with the progress of time, the red card faced by the individual helps to survive itself by preventing any loss of resources and also helping the genes to transmit between generations. Obviously, this is a trump card for the existence of the species which soon outcasts every nearby species. A payoff strategy is another way of gaining a foothold in the survivor list. This strategy helps a species to know its probability of encounter with another species which may turn into an intra or inter-competition. Hence, mathematics plays an important role in describing the cost of such encounters. Well in many clans, it is seen that an individual can sacrifice its own life for the benefit of the group. Who has told them to do so? The answer is no one. They knew from the very beginning that their destiny is something else, they are not those saviours which protect a clan by giving birth to offspring, but they are those who act alone to save the entire gene pool of its community. By this way, the genes are transmitted to the next generation and in every generation, there are individuals acting as silent guardians protecting the group. Well, then what happens to selfish individuals with selfish genes? Obviously, they all meet their ends but at different levels. A species not cooperating with groups will act as a lone one and in time makes it vulnerable to any passing challenges. In some cases, though an exception of course, the species may live through but still, its spectrum of action becomes broadly diminished and the success of genes passing through generations gets low. In co-evolution, a species constantly threatened by predation ultimately develops its own adaptive features which if becomes favourable attains evolutionary shape and with this, the predator will also adopt new strategies to prevent the diminishing of its food resources, it is just like the game of stone, paper, scissors where no strategies are good for long-lasting impact. In Handicap Principle, an observer may find it very difficult for the fitness of the species but actually it is decreasing the cost of investing in something vital for its life, examples can be seen in peacock. Gradually over a period of time when these strategies attain a particular form, they stabilise to a way that no other strategies can gain any advantages over them and thus these strategies are known as Evolutionary Stable Strategies.

Conclusion

Still, a lot of work has to be done to uncover a large number of loopholes in Evolutionary Biology, for example, the mutation concept with the help of game theory.New mathematical models are currently being made for more precise analysis and it may give us hopeful results.