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.

• A way to reword your question is Typically, how many individuals are there at each trophic level?. Keywords, you should be looking for are "food chain", "trophic level", "trophic dynamic", "cascade effect" and "trophic pyramid". – Remi.b Jun 11 '17 at 16:49
• @Remi.b Ah, that makes sense, thanks! Do I even need a reference to say that there are more individuals at lower levels? Isn't it necessarily so, considering that not all the energy (some is lost) from one level can be transferred to the level above it? – Bobson Dugnutt Jun 11 '17 at 16:52
• @Remi.b Hmm, but then what if the ecosystem is not very clearly trophically stacked/separated (so it is more appropriately called a food web)? – Bobson Dugnutt Jun 11 '17 at 16:53
• No ecosystems are. But I would have thought your question as necessarily implying this simplified categorization. The model you present is an even more extreme simplification of the reality of food webs after all. Don't get me wrong, I think the question is of interest (I up voted it). You don't need reference or anything for your post to be valid. I was just trying to offer you some vocabulary that may help you (or other users) to look for such estimates. – Remi.b Jun 11 '17 at 16:57
• @Remi.b Sorry, I should have been more clear: I didn't mean that I needed the reference in order to ask my question, here on the site, but rather for the thesis I'm writing (I'm working with population dynamics), where I claim that prey are usually more abundant in number than the species preying on them. After your comment it seemed self-evident that this was the case, so I was wondering whether a reference was even needed in my thesis. – Bobson Dugnutt Jun 11 '17 at 17:11

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).

• "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." This. – Charles Aug 10 '17 at 11:55
• Thank you for the answer! Another example of predator outnumbering the prey would be phages vs. bacteria. – Bobson Dugnutt Aug 16 '17 at 17:15
• @Lovsovs Definitely! If you go small and use a liberal definition of predator this is indeed common. – fileunderwater Aug 16 '17 at 18:47

mostly I would like to know if we can say that the number of prey is generally larger than the number of predators.

If this is actually your real question, the answer is straightforward: the most widely-used classification of trophic strategies that I'm aware of (Lafferty & Kuris 2002; full reference below) includes the requirement that a predator attacks (first dichotomy) and kills (second dichotomy) multiple victims in its lifetime. So your statement is necessarily true; if each predator kills more than one prey, prey must (generally) outnumber predators.

Be aware that this ignores micropredators, parasitoids, parasites etc, though.