ecology - References concerning the relative population sizes of predator and prey

In an ecosystem, say there are two species in a predator-prey relationship. What is the most typical ratio of these species' population densities? For instance, it could be that for every fox, there are ten rabbits. Actually, the precise ratios are somewhat irrelevant; mostly I would like to know if we can say that the number of prey is generally larger than the number of predators.

I would like references to articles, textbooks, etc. that contain information about such ratios.

Note that this is aimed at the number of species within a single ecosystem. However, if this information is hard to quantify (perhaps because it is hard to define where an ecosystem ends), global populations could be used as an estimate.

Forgive me if this is ill-defined or trivial, I'm a physicist by training.

Thanks.

Answer

You are indeed correct that the prey of predators are usually more common than their predators, especially if you focus on "true" predation (i.e. remove parasitism and parasitoidism). As a rule of thumb, the energy conversion between trophic stages is 10% (first proposed in Lindeman, 1942), which sets one sort of bound on the density relationship between predators and prey. The relationship is extremely variable though, which is easily understood if you consider the density relationships of hares and foxes vs. whales and krill.

For a general reference, Hatton et al (2015, "The predator-prey power law: Biomass scaling across terrestrial and aquatic biomes") might work, even though it is mainly framed in terms of biomass. However, the paper clearly states that biomass and density usually go hand in hand. The main result of the paper is that the biomass relationships between predators and prey collapse to very regular power laws (exponent 3/4) across ecosystems.

As mentioned above, and depending on who you ask, parasitism and parasitoidism are sometimes seen as types of predation. There, the density relationships between "predator" (parasitoid) and "prey" can be very different, especially at certain points in time or at certain lifestages. For instance, in insects it is not uncommon for one "prey" (host) to give rise to a large number of newly hatched "predators". This means that the number of parasitoids can probably outnumber the number of hosts, at least at smaller spatial scales, at some time periods (e.g. late summer, before the parasitoid is hit by high winter mortality).