Ecological Archives E087-008-A2

Subhash R. Lele. 2006. Sampling variability and estimates of density dependence: a composite-likelihood approach. Ecology 87:189–202.

Appendix B. Mathematical details of the computation of the means, variances, and covariance of the nonstationary Gompertz process.

In the following I give full details of the calculations of the means, variances, and covariance of the nonstationary Gompertz process.

 Let  and . With this notation, we can rewrite the Nonstationary Gompertz model as follows:. Hence we can write . Substituting this expression in the first expression, we can rewrite the first expression as:. Simplifying and repeating similar substitutions, we obtain:

.

Using this and the fact that environmental noise has mean 0, variance etc., it follows that:

,

 where .

Last expression is simple algebraic simplification by noting the following results:

and .



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