Conditions for Eltonian Pyramids in Lotka-Volterra Food Chains

In ecological communities consumers (excluding parasites and parasitoids) are in general larger and less numerous than their resource. This results in a well-known observation known as 'Eltonian pyramids' or the 'pyramid of numbers', and metabolic arguments suggest that this pattern is independent of the number of trophic levels in a system. At the same time, Lotka-Volterra (LV) consumer-resource models are a frequently used tool to study many questions in community ecology, but their capacity to produce Eltonian pyramids has not been formally analysed. Here, I address this knowledge gap by investigating if and when LV food chain models give rise to Eltonian pyramids. I show that Eltonian pyramids are difficult to reproduce without density-dependent mortality in the consumers, unless biologically plausible relationships between mortality rate and interaction strength are taken into account.