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