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First Look: When an increase in predator numbers can lead to an increase in prey

When numbers of predators and their prey rise and fall over time, one would expect peaks in prey abundance to precede spikes in predator abundance. Now scientists find the opposite, counter-intuitively, also can happen. Predator numbers can rise before prey numbers do, report findings detailed in the Proceedings of the National Academy of Sciences.

Mathematical theory regarding the interactions between predators and prey typically assume that when cycles in their numbers occur, high points in prey abundance occur before peaks in predator abundance. When predators are scarce, prey rises in numbers. As their source of food increases, predators rise in abundance. When there are enough predators, prey numbers decline. With a scarcity of food, the number of predators crashes and the cycle repeats.

“Thus, if you have data on the numbers of individuals over time, the ordering of the peaks can give you insight into who is eating whom,” says mathematical biologist Michael Cortez at the Georgia Institute of Technology in Atlanta. “This viewpoint was proposed over 90 years ago by the eminent mathematical biologists Vito Volterra and Alfred Lotka.”

These models of predator-prey interactions generally assume traits of these species stay relatively constant on time scales observable in the field and lab. However, Cortez and theoretical ecologist Joshua Weitz at the Georgia Institute of Technology in Atlanta noted that predator and prey may coevolve on time scales that researchers can actually see, with changes in the defensive traits of prey spurring changes in the efficiency of its predator.

The researchers discovered that co-evolution between predators and prey can reverse the ordering usually seen in fluctuations of their abundances, yielding cycles where peaks in prey abundance follow peaks in predator abundance. “From the traditional viewpoint, these reversed or ‘clockwise’ cycles would suggest that the prey are eating the predators!” Cortez says.

To understand how these reversed cycles arise, imagine a small population of prey and a large population of predators. The prey are high-defense, meaning their defenses are very effective versus predators. The predators are inefficient, meaning they have traits are not very effective at capturing prey.

The high-defense prey drive numbers of inefficient predators to low abundance. As a result, prey numbers rise.

This rise in high-defense prey spurs the development of effective predators, whose traits are effective at capturing even high-defense prey. As a result, predator numbers rise, and prey numbers start to fall.

The researchers assumed efficient predation traits are costly for predators to develop. This means the numbers of efficient predators remains low. Since there is no longer any advantage for prey to possess costly high-defense traits, low-defense prey emerge, whose defensive traits are not very effective at protecting prey but are also not very costly.

Since efficient predators are good at capturing both high-defense and low-defense prey, predator numbers continue to rise while prey levels continue to fall. When relatively few prey are present, natural selection that favors inefficient predators, who are not very effective at capturing prey but also are have an energetic advantage over the more effective predators. The inefficient predators replace the effective predators, and one sees a rise in predator numbers and a further decrease in prey numbers.

Since many ineffective predators are present, natural selection favors low-defense prey. The cycle then repeats.

The researchers detected three cases of reversed cycles in data from bacteria-killing bacteriophage viruses and cholera bacteria; from mink and muskrats; and from gyrfalcons and rock ptarmigans.

The investigators suggest that detecting such reversed cycles might reveal that co-evolution of predator and prey is driving these systems.

“In public discourse, evolution is often associated with events taking place over historical or geological time scales. However, this is not necessarily the case. Evolution, and indeed co-evolution, is ongoing,” Cortez says. “Our work shows that changes in population sizes over short time periods can be, in part, driven by changes in the genetic makeup of those populations. Hence, in moving forward our study helps to reveal how co-evolution, like evolution, may need to be taken into account when considering how populations respond both to each other and to a changing environment.”

Although this work suggests that co-evolution can influence the fluctuations of predators and prey in simple communities with one predator species and one prey species, in actuality, “species live in very complex and diverse communities,” Cortez says. One important direction to go from here “is understanding how predator-prey co-evolution alters the dynamics of large biological communities with several different species of predators and prey.”

Categories: Applied Mathematics | Population Biology
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