*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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