where U is another normalized variable and Σ is the component of the environmental variance that cannot be explained by fluctuations in the covariates. This leads to the relation:
σ e2 = var(∑ai yi,t ) + σ2, eqn 5
so that the covariates together explain a fraction:
p = var(∑ ai yi,t )/[var(∑ ai yi,t ) + σ2], eqn 6
of the total environmental variance.
Estimating population parameters
A problem in estimating the population parameters is that individuals were killed by humans. We therefore made two analyses. In the first analysis we used the total population counts (excluding individuals that had emigrated out of the area). In the second analysis we removed the individuals that had been killed by various kinds of human activities.