Predator-prey Cycles Research Articles

Adaptive foraging by predators as a cause of predator-prey cycles

When foraging has costs, it is generally adaptive for foragers to adjust their foraging effort in response to changes in the population density of their food. If effort decreases in response to increased food density, this can result in a ‘type-2’ functional response; intake rate increases in a negatively accelerated manner as prey density increases. Unlike other mechanisms for type-2 responses, adaptive foraging usually involves a timelag, because foraging behaviours do not often change instantaneously with changes in food density or risks. This paper investigates predator-prey models in which there are explicit dynamics for the rate of adaptive change. Models appropriate to both behavioural and evolutionary change are considered. Both types of change can produce cycles under similar circumstances, but under some evolutionary models there is not sufficient genetic variability for evolutionary change to produce cycles. If there is sufficient variability, the remaining conditions required for cycles are surprisingly insensitive to the nature of the adaptive process. A predator population that approaches the optimum foraging strategy very slowly usually produces cycles under similar conditions as does a very rapidly adapting population.

Patterns of Grouse Shooting in Finland

In Finland, there is a "cyclic" relationship between numbers of birds shot and the abundance of the grouse population. This cyclic pattern rotates clockwise, i.e. opposite to the classical predator-prey cycles predicted by the Lotka-Volterra equations. This means that man kills relatively more grouse during the increasing phase of the grouse cycle than in the decreasing phase. This is a sign of prudent predation. In the late 1970s, however, there may have been some overharvesting of grouse in northern Finland, partly owing to a change in the functional response (increased annual kill per hunter). The shape of the functional response curve in grouse shooting is very often concave, which is not familiar to accepted predator-prey concepts, but which is a logical consequence of the searching image concept. The functional response curve might be concave if the prey species is not particularly important to the predator. In general, not even the relatively high shooting yields in Finland seem to be correlated with population trends of different grouse species.

Stabilization or regulation: what it all means!

Wolda (1989), in the title of his commentary on the concepts of equilibrium and density-dependence, asks "What does it all mean?" This note attempts to answer his question. In his paper, Wolda concludes that, because the concept of density-dependent population regulation rests on the a priori assumption that "populations fluctuate in size around an equilibrium value," and because "the equilibrium cannot be measured," the concept is "devoid of any practical ecological content" and "tests for population regulation cannot be expected to produce the expected results, making them next to useless. " Wolda then goes on to recommend the concept of stabilization (Reddingius and Den Boer 1989), though he does not explain why it is better. I will not belabor the semantic arguments surrounding the meaning of regulation, stabilization and densitydependence which have burdened the ecological literature for decades, and which I have addressed in another paper (Berryman 1989), but instead concentrate on several misconceptions in Wolda's commentary. 1. Wolda claims that "regulationist" arguments rest on the a priori assumption that a stable equilibrium (i.e., a point attractor1) exists. This implies the logic that stable equilibria are a necessary condition for densitydependence, or that equilibria give rise to density-dependence. Regulationists may have made this statement, but it is nevertheless illogical. As I have noted previously (Berryman 1987), equilibria are properties that may emerge from the operation of a dynamic system but they are not the causes of the dynamics. For example, models of predator-prey interactions may or may not exhibit a two-species community equilibrium, depending on the values of their parameters (e.g., see Arditi and Berryman 1991). Although Wolda cites my paper (1987) as a "mere dismissal" of the equilibrium concept, he entirely misses this point, or chooses to ignore it. Thus, the presence of an equilibrium is not a prerequisite to a theory of population dynamics nor to the analysis of population data. Regression, time-series, and key-factor analyses do not require that equilibria exist, but equilibrium structures may emerge as a result of these analyses. For example, attractors emerge from the analyses shown in figure 1 because the parameters have particular values; other values can produce no equilibria or unstable (repelling) equilibria. 2. Wolda implies that, because populations are observed to fluctuate with considerable amplitude, an equilibrium, if it exists at all, must also be changing with time and therefore cannot be estimated empirically. This misconception is due to a narrow perception of equilibrium as a stable node or point attractor. The modern theory of non-linear dynamics, which has been greatly influenced by population ecology, makes it clear that very diverse dynamic behaviors are possible from non-linear feedback systems, including periodic, quasiperiodic and pseudoperiodic cycles (cyclical attractors) and aperiodic chaos (strange attractors) (May 1974; Schaffer and Kot 1986; Berryman and Millstein 1989). Indeed, it may not be possible to determine if the observed fluctuations are due to random buffeting or to deterministic mutually causal (feedback) relationships between variables (e.g., inter-species interactions) (Ellner 1991). If this is not enough, we now know that populations can be influenced by more than one domain of attraction, giving rise to very complicated metastable behavior in varying environments (Ludwig etal. 1978; Berryman etal. 1984). Thus, wide fluctuations in population dynamics can be caused by many things including, but not necessarily limited to, endogenous periodicity and chaos, multiple domains of attraction, time-varying equilibria, stochastic buffeting, or any combination of the above. In addition, the fact that equilibrium structures can be influenced by time-varying forces may make their estimation difficult but it does not invalidate the concept of 1 The term attractor, meaning a region that attracts nearby trajectories of a dynamic variable, is introduced to help clarify the concepts of regulation and stability : Point attractor is a stable equilibrium that attracts trajectories to a fixed point. Cyclical attractor brings trajectories into a stable periodic, quasiperiodic or pseudoperiodic orbit; e.g., a predator-prey cycle. Strange attractor is a stable aperiodic orbit that may have a multiple equilibrium structure; i.e., a complex basin of attraction

Prolonged prey suppression by carnivores - predator-removal experiments.

The hypothesis that carnivores can significantly suppress prey populations after they collapse during drought was tested by predator-removal experiments. Low populations of rabbits (Oryctolagus cuniculus) responded with significantly accelerated growth where foxes (Vulpes vulpes) and feral cats (Felis catus) were continually shot. Experiments in years of good pasture and poor were confirmatory. After only 14 months, the rabbits were well on their way to another eruption whereas untreated populations had remained low for 2.5 yrs until a second drought. These studies confirm the impact of carnivores found for low populations of cyclical prey but there was no measurable effect of predator-removal on the population declines in our studies. They were due to aridity and poor pastures. The concept of Environmentally Modulated Predation is presented. Only after the intervention of a widespread environmental event is such limiting predation possible. Drought is also the cause in arid Australia for dingoes (Canis familiaris dingo) preying seqenntially on rodents, rabbits and red kangaroos, while wildfire was the cause in temperate forests. Such environmental intervention may be more widespread than usually considered, triggering some apparent predator-prey cycles. The major factors limiting rabbits in inland Australia are: adequacy of green herbage during breeding, food scarcity during average summers, critical shortages of food and its low quality (including moisture content) during 'crashes' in drought, followed by limiting predation. Contrasting life-histories are one cause for the ultimate escape of rabbit populations from limiting predation as rabbits can breed continuously but carnivores seasonally only. Patchy predation and alternate prey may also play a part.

What they didn't tell you about limit cycles.

The paper examines the numerous assumptions involved in theories of predator-prey limit cycles. Predatorprey theories should incorporate the environmental fluctuations appropriate to each specific case.

Effects of Host Plant on the Predator-Prey Cycle of Zetzellia mali (Acari: Stigmaeidae) and Its Prey

Population counts of Zetzellia mali (Ewing) and its prey, Aculus schlechtendali (Nalepa), Panonychus ulmi (Koch), and Tetranychus urticae Koch on ‘Delicious’ apple trees were studied to determine what factor(s) regulates predator-prey oscillations. Four interrelated factors were considered: leaf nutrients, soil moisture, leaf conditioning, and growth of the apple leaves. It was observed that prey populations initially increased when the trees added new leaves. Soon thereafter, the predator, Z. mali , increased its numerical response. The combined effect of predation and leaf conditioning caused a decline in the prey populations. With fewer prey available, the numerical response of Z. mali decreased. Leaf nutrients, soil moisture, and leaf conditioning affected the number of phytophagous mites on the trees. The overall predator-prey cycle, however, was not affected.

Effects of freeze-thaw stress on bacterial populations in soil microcosms

To test the effect of freezing on soil biota, isolated from the shortgrass prairie of northeastern Colorado, a series of experiments were performed using gnotobiotic soil microcosms.Pseudomonas paucimobilis was used to examine the effects of freezing on bacteria of different growth stages. Secondly, the effect of multiple freeze-thaw cycles was tested on an assemblage of bacterial species. Lastly, the effect of freezing on predator-prey interactions was studied usingP. paucimobilis and an amoebal predator,Acanthamoeba polyphaga. A temperature of -9°C was not detrimental toP. paucimobilis at any growth stage. A single severe freeze-thaw cycle (-27°C to 23°C) resulted in 40-60% mortality ofP. paucimobilis and the mixed bacteria, although additional freezing events did not reduce the populations further. Multiple freeze-thaw cycles (-9°C to 23°C) gave 40-60% mortality ofP. paucimobilis and the mixed bacteria. Predator-prey population cycles were possibly desynchronized by freeze-thaw events.

Satiable egg eating predators

A model is constructed of a satiable, egg eating predator and a self-limiting, egg-laying prey. As the level of predator satiability and efficiency increases, the response changes from predator extinction and prey survival to the stable coexistence of both species, then to a stable predator-prey cycle through a Hopf bifurcation, and finally to a distorted cycle of extreme predator variation. All calculations have been carried out by computer routines, and the portraits of the population orbits have been done by computer graphics.

Forest fires and the snowshoe hare-Canada lynx cycle.

This paper shows that there is a reasonable coincidence between the Canada lynx cycle and the occurrence of forest and brush fires. Fires set in motion plant succession, potentially leading to an increase in snowshoe hares (Grange, 1965). Snowfall is also correlated with the lynx cycle and tends to account for the variation not accounted for by fires. I conclude that Grange's (1949, 1965) hypothesis that fire and plant succession drive the snowshoe hare cycle deserves serious consideration, as do Butler's (1962) and Watt's (1968, 1973) suggestions that precipitation may drive or decisively modify furbearer 'cycles'. On this evidence, the snowshoe hare-Canada lynx cycle seems likely to be a forced oscillation rather than a predator-prey, parasitehost, or herbivore-vegetation limit cycle, as proposed by several authors. Fire clearly appear to be a periodic phenomenon, not-withstanding the difficulty of showing periodicity in simple weather time series. Fire is itself a meteorological phenomenon, although complexly related to simple weather variables.

The ecology of Sminthurus viridis (L.) (Collembola). I. Processes influencing numbers in pastures in Western Australia

The changes in numbers of Sminthurus viridis (Collembola: Sminthuridae) in pastures in Western Australia were studied for 9 years on one site and for shorter periods on other sites. Five factors affecting numbers are described: (1) weather, (2) soil type (3) botanical composition of the pasture, (4) predation by Bdellodes lapidaria (Acarina: Bdellidae), and (5) eating of dead bodies by newly hatched nymphs. Weather is generally favourable for the active stages during autumn, winter, and spring. In the summer, the species is maintained by aestivating eggs. Dry periods during the winter months sometimes cause high mortalities. Soils containing a high silt-plus-clay content support higher numbers due mainly to increased oviposition. Flea densities increase more rapidly where there is a high proportion of broad-leaved plants, such as clover and capeweed in the pasture. Grassy areas are not favoured. Predation by B. lapidaria effectively reduces numbers. The presence of more than 20 B. lapidaria per square metre early in the winter prevents any outbreak of fleas later in the season. Bdellodes lapidaria numbers increase in response to an increase in flea numbers. An irregular predator-prey cycle is set up in this way. Density-induced mortality, resulting from the newly hatched nymphs eating the bodies of recently dead fleas, plays a dominant role at high densities. This process operates continuously though at decreased intensity at lower densities. When newly hatched nymphs feed upon dead nymphs and adults they ingest materials which cause early death. Sometimes this may lead to a dramatic collapse of the population. Fleas from high-density populations usually contain large quantities of uric acid in their "fat-bodies". It is suggested that death of the mature fleas at high densities is hastened through the storage of excessive amounts of waste material. Death of the young nymphs feeding upon the dead bodies may be brought about by the ingestion of these waste materials, although this has yet to be proven.

On the Volterra-Lotka principle

The supplantation of one of two closely similar competing species by the other (Volterra-Lotka principle) is studied as an example, according to Volterra's general theory of population dynamics, of the decay of a biological association of an odd number 2n+1 of species into one with an even number 2n. The three-species association (n=1) is worked out in detail, with a demonstration of how a Volterra predator-prey cycle gets gradually deformed—when a slightly superior predator is introduced—into another new-predator-prey cycle, spelling a steady eclipse of the original predator. Whenn is made large, the close competitors being embedded in an association of many other species, a statistical treatment of the supplantation process can be given through the author's statistical-mechanical theory of Volterra's dynamics. The result is a probability law, changing systematically as time goes on, for the chance that the successful competitor's population has any given amplitude; explicitly time-dependent measures of mean amplitude and mean frequency of oscillation of all populations can then be worked out. Throughout, the simplifying assumption is made that the competitors differ only as regards intrinsic rate of self-growth. Two things are accomplished by viewing the competition as a decay of 2n+1 into 2n: the competitors are not abstracted from the rest of the biological world, and their population variations are always oscillatory (with long-term rises and falls of amplitude); this is in contrast to the original Volterra-Lotka analysis in which purely static, and therefore ecologically unrealistic, population levels of but two species eventuate.