In this paper we developed mathematical model of prey and predator wild life population of finite size. We consider a prey population can be divided into two age groups. One part of prey species are adults and other part of prey species are juveniles or infants. A mathematical framework has been generated in terms of a system of nonlinear difference equations including all the significant parameters. The solutions are worked out in terms of finite polynomial. Numerical computations have been made for the change of populations in successive generations and different values of the parameters. Graphs have been plotted to depict the comparative variations.

Migration, Juveniles, nth generation, mathematical

1. Our model tries to describe the population of prey and predators for different generations based on the birth rate, death rate and interaction between these two species. The model can be utilized to predict the population growth of such interacting species in a confined environment. 2. The food availability for prey population has been considered to be significantly high which shows that there is no competition among prey population for primary food sources. However, this assumption may not match with actual realities and competition for food might be a crucial factor which future research studies might like to take in to account. The future research study should focus on realistic food availability for prey population which will have a moderating effect on their growth rate of prey population as competition increases. It will subsequently result in stagnant growth rate of predator population with time. 3. Interestingly our mathematical formalism depicts strong dependence of growth of predators upon the food availability (i.e. prey population) not only for current generation but also all for previous generations. The increasing prey population across the generations creates a huge increase in the population of predators. Hence the growth of predator varies slowly in the beginning and growth rate increases across the generation. 4. The population growth rate of prey as well as predator increases slowly in the beginning but subsequently picks up. It is primarily because of the fact that food availability for the predator grows with time which results in faster effective growth rate in subsequent generation. 5. The generation dependant migration and its consequence on the evolution of single wild life species as depicted in Saxena (2011) are interestingly applicable in the Prey-Predator dynamics as well. However, the generation dependant migration is replaced by some other generation dependant terms with altogether different physical significance [14]. Our study has ignored the external factors which might affect the population dynamics of any ecosystem. Such effects have been studied in some other contexts [15]. It would be interesting to include the effect of pollution in the evolution of Prey and Predators Models. Future research studies may like to include this interesting possibility. Further the stability analysis of the prey predator dynamics which has been extensively studied in several other contexts can be included in our mathematical formalism [16].

V.P. Saxena and Lalita Dhurve (2022). Mathematical Modelling of Prey and Predator Species with Two Age Group of Prey Population. International Journal on Emerging Technologies, 13(2): 06–11.