Bias in estimating the Malthusian parameter for Leslie matrices

For Leslie matrices of order 3 × 3 or larger, conditions for concavity or convexity of the Malthusian parameter in each of the entries in the matrix are given. Both cases are possible so it follows that the expected population growth rate computed from a Leslie matrix whose entries are random variables can be either smaller or larger than the growth rate computed from the expected value of the matrix. Boyce [(1977) Theor. Pop. Biol.12] showed that in the 2 × 2 case this bias is always positive; we give a numerical example illustrating the magnitude of the bias in this case, and compare it with the sampling error of the parameter for the same example.