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Part 1
Background
This exercise uses the Lotka-Volterra model to explore the sustainability of an ecosystem with rabbits, foxes
and hunting. We start by exploring the eect of hunting rates rates in a deterministic model.
A stochastic extension further allow us to explore the sustainability of the ecosystem using a combination
of Gillespie and Montecarlo simulations.
Questions Part 1A [2 marks]
The system tracks the number of rabbits x, and foxes y, and the dynamics are given by:

_ x = g(x; y)
_ y = h(x; y)
In the absence of foxes and hunting, rabbits grow exponentially with a growth rate b and a death rate
d (b > d); the number of rabbits eaten by foxes is proportional to the product of the number of rabbits
present and the number of foxes present by a factor . Foxes decline exponentially in isolation, with a
birth and death rate b0 and d0