Dear, Rk Naresh!

I think that You should see Lotka–Volterra equations, which determine predator–prey model (https://en.wikipedia.org/wiki/Lotka–Volterra_equations).

The model of predator–prey isn't simple (linear).

Best regards, Vladislav.

Dr Vladislav N. Nikitin thank you for your contribution to the discussion

Predator and prey populations cycle through time, as predators decrease numbers of prey. Lack of food resources in turn decrease predator abundance, and the lack of predation pressure allow prey populations to rebound.When preys are high, predators increase and reduce the number of prey by predation. When predators are low, prey decrease and thus reduce the number of predators by starvation. These predator/prey relationships thereby promote stability in ecosystems and enable them to maintain large numbers of species. Population curves for predator prey are often sinusoidal. As the population of prey increases, predators have more food, are healthier and can give birth to and sustain more offspring. As the predator population increases, the prey population decreases. Without enough food, the predator population also declines. The relationship controls the population size of both species. The predators keep the prey population under control and the size of the population of prey limits the amount of predators an ecosystem can support. Predator-prey cycles are based on a feeding relationship between two species: if the prey species rapidly multiplies, the number of predators increases until the predators eventually eat so many prey that the prey population dwindles again. Soon afterwards, predator numbers likewise decrease due to starvation. Predators help control the populations of prey species, which in turn affects the quantity of plants and animals further along the food web. Sharks, as often prey upon old or sick fish, leaving healthier animals to flourish. The relationships between predators and prey play an important role in structuring ecological communities, with predators influencing the dynamics of their prey in ways that cascade through ecosystems to affect processes such as productivity, biodiversity, nutrient cycling, disease dynamics, carbon storage, and more.More predators kill more prey, which, along with food scarcity, decreases the population. When prey becomes scarcer, the predator population declines until prey is again more abundant. Therefore, the two balance each other.

Dr Rana Hamza Shakil thank you for your contribution to the discussion

As the prey population increases, there is more food for predators. So, after a slight lag, the predator population increases as well. As the number of predators’ increases, more prey is captured. As a result, the prey population starts to decrease. More predators kill more prey, which, along with food scarcity, decreases the population. When prey becomes scarcer, the predator population declines until prey is again more abundant. Therefore, the two balance each other. Predator and prey populations cycle through time, as predators decrease numbers of prey. Lack of food resources in turn decrease predator abundance, and the lack of predation pressure allow prey populations to rebound. Predators help control the populations of prey species, which in turn affects the quantity of plants and animals further along the food web. Sharks, for example, often prey upon old or sick fish, leaving healthier animals to flourish. There is a balance between parasites and their host and predators and prey," he says. "They keep each other from destroying the ecosystem. Animals help plants reproduce by carrying pollen from plant-to-plant and by spreading seeds. Animals that eat insects and small mammals help reduce damage by caterpillars, rabbits, and other plant-eaters. When preys are high, predators increase and reduce the number of prey by predation. When predators are low, prey decrease and thus reduce the number of predators by starvation. These predator/prey relationships thereby promote stability in ecosystems and enable them to maintain large numbers of species. The relationship controls the population size of both species. The predators keep the prey population under control and the size of the population of prey limits the amount of predators an ecosystem can support.