where s = r − 1/2 σe2 is the stochastic growth rate. The sum is taken over values of t for which xt+1 as well as xt are recorded.
Equation 7 is maximized numerically with respect to the unknown parameters s and σe2. The uncertainties were found by parametric bootstrapping, simulating the process a large number of times using the estimated population parameters (Sæther et al. 2000).
We then repeated the analyses, subtracting the number of animals killed by humans from the mean of ENt (eqn 1). Similarly, –ln(1 − kt) must be subtracted in the expression for EXt (eqn 2), where kt is the proportion of animals killed.