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Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1997 May 27;94(11):5713–5715. doi: 10.1073/pnas.94.11.5713

Safety in numbers: Sophisticated vigilance by Allenby’s gerbil

Michael L Rosenzweig *,, Zvika Abramsky , Aziz Subach
PMCID: PMC20844  PMID: 9159138

Abstract

Since 1963, nonlinear predation theory has predicted that, at low population densities, victim species may well be mutualistic rather than competitive. Theory identifies this mutualism as a principal source of dynamic instability in the interaction. Using gerbils and trained barn owls, we conducted the first (to our knowledge) field tests of the theory’s prediction of mutualism. The behavior of the gerbils confirms its existence.


The dynamical theory of nonlinear population interactions, particularly predation theory, has long predicted that potential victims, when they are uncommon, may well be mutualistic rather than competitive (14). We use the word mutualism in its population dynamic sense, i.e., if V is the population density of victims, they are mutualistic if and only if ∂(d ln V/dt)/∂V > 0. Low densities of potential victims should be mutualists because they should reduce each other’s burden of predation more than each other’s supply of resources, not because they herd or school or engage in other group defense strategies (5). Investigators soon found evidence of this mutualism in their laboratory work (5, §), but it has not before been confirmed in the field, to our knowledge.

This paper shows that a small (26 g), predominantly granivorous, nocturnal desert rodent (Gerbillus allenbyi) behaves in the field as if natural selection has molded it to take advantage of this indirect and sophisticated consequence of nonlinear predation theory. Its individuals compete strongly with each other for the resources of their sand dune habitat (79), but, when uncommon and faced with an increased danger of predation, the gerbils coalesce while foraging. No evidence suggests that gerbils actively cooperate with each other in their own defense. Their coalescence merely spreads the predation risk passively among more individuals. Although they engage in no other behavior except relocation, that behavior permits them—in a sense—to be somewhat vigilant while foraging (10).

Theory

The qualitative theory of predation dynamics explores the properties of predation equations and their solutions without ever specifying the equations in detail (14). This recommends it for work with vertebrates whose population dynamics often has strong qualitative features but varies enough through time so as to frustrate any attempt to specify the equations themselves. The theory relies on isocline analysis.

An isocline is a line in a state space. The state space (or phase plane) has one axis for the population of each species, e.g., V for victim density and P for predator density. (It has no axes for any other variable—none even for time itself). By definition, at every point on an isocline, the time derivative of one state variable (or a fixed transformation of it such as its logarithm) has a fixed value. Fig. 1 shows an example of a zero isocline for victims (d ln V/dt = 0).

Figure 1.

Figure 1

An example of a theoretical victim zero isocline (the unimodal curve). Below it, victim population increases (dashed area); above, it declines. The block arrow depicts a thought experiment in which victims alone are increased in the vicinity of the positively sloped portion of the isocline. Here victims are dynamically mutualistic: the experiment moves them from negative to positive rates of change.

Some predators can become satiated. They may also take considerable time to process their victims. These characteristics—satiety and significant processing times—certainly predominate among vertebrates that are predators, like the owls we use in our work. Because of satiety and significant processing time, qualitative predation theory predicts that the zero isocline of the victims of such predators should have a positive slope over lower victim densities and a negative slope over higher ones (5). In the vicinity of the positively sloped portion of this isocline, the victims are mutualistic by definition (Fig. 1). This mutualism is a primary source of instability in predatory dynamics (14).

Method

Despite the widespread use of isoclines in developing ecological theory, no one has measured predator or victim isoclines for any organism in the field. One obstacle has been that measuring the population dynamics of larger organisms requires large areas and a long time to observe. To address this problem, we developed a relatively quick field method to measure negatively sloped isoclines, or at least the perception of these isoclines by foraging animals (11). But this method will not work for positively sloped isoclines (12). In this paper, we have modified it so that it can.

Imagine a world consisting of a pair of matched patches. Suppose average fitness, W, is defined to be the per capita rate of increase in a population, and Wi is “fitness in patch i.” Now assume that the function Wi = f(Vi) has a positive slope over low values of Vi. Such positive slopes indicate intraspecific mutualism (by definition).

Now let Vim be a value of Vi which falls on the mutualistic side of the function f. Imagine that both patches have Vim victims. That is, the number of victims is the same in the two patches. Individuals facing only competition should remain equally numerous in the two matched patches (12). However, this system contains predation too, and that has converted the victim interaction (in the region of Vim) from competition to mutualism. Because ∂(d ln V/dt)/∂V > 0, natural selection will reward any individual that moves from one patch to the other. Whichever patch—by chance—first receives an extra victim will become superior to its mate. A second victim that moves to it will therefore enjoy higher fitness. Having moved, it will have further reduced the now depleted patch. This gives a third victim even more cause to move to the denser patch, and so on. Thus, in the presence of mutualism, individuals faced with the choice of a pair of equal patches should coalesce in one of them. They show their vigilance while foraging (10) not by engaging in any special behavior that interferes with their foraging but simply by foraging at higher population densities.

These considerations suggest a test for mutualism: set up two matched subplots with the same densities of predators and victims. Victims facing competition should remain equally divided between the subplots. But when mutualism rules, victims should drift toward one or the other subplot.

We used this method on Allenby’s gerbils in a pair of 2-ha field enclosures (each 200 m × 100 m). We set the enclosures in the Negev Desert at Holot Mashabim Nature Reserve (31°01′N × 34°45′E) 50 km south of Beer Sheva, Israel. Allenby’s gerbil shares this reserve with many other species, including barn owls (Tyto alba), which are among the major natural predators of gerbils in the preserve. Moreover, Allenby’s gerbil does respond to barn owls as if they pose a threat. Gerbils do not respond to owl calls or investigator noises, only to owl overflights (13). So we trained some barn owls to fly at our command and used them to impose experimental threats of predation at a level under our control (13). We varied the number of barn owl flights between four and seven flights per 2 hr per ha. But in each experimental trial, we kept the rate of barn owl flights equal in the following two subplots.

A 100-m fence subdivides each of the two enclosures into a matched pair of square 1-ha subplots. Large holes perforating this fence allow gerbils to pass freely from one subplot to its mate. Thus, the gerbils can adjust their densities in the two subplots until they perceive no advantage from further change. We measure these densities as activities, AGA, in sample quadrats distributed regularly in each plot.

After experimental adjustment of the gerbil population size in a pair of patches, we allowed the gerbils to habituate to their surroundings for at least two nights. Then we flew the owls every other night from 2100 to 2300 at the predetermined predation level for each subplot. We measured AGA at 2300. We also conducted control trials in which no owls were flown. We performed our experiments during the late summers of 1994 and 1995. Because the activity of gerbils decreases significantly during nights with considerable moonlight, we restricted our experiments to the 2–3 weeks per month in which the moon was less than half full.

Results

Fig. 2 displays the data of both controls and experimentals as g, a positive, standardized function of the difference between the foraging activity in an a subplot compared with its matched b subplot:

graphic file with name M1.gif

where Inline graphic = (AGAa + AGAb)/2. Standardization to g eliminates the artifact of a correlation between the difference and the mean.

Figure 2.

Figure 2

The standardized difference in activity densities of G. allenbyi (AGA) in subplots a and b as a function of the average activity density. Flights by trained barn owls in 29 trials provided a predation threat. In the absence of owls in flight (56 trials), activity densities were always similar in the two subplots, revealing the intraspecific competition among the gerbils. (Noninteracting individuals should drift aimlessly between the subplots.) In the presence of a threat, the behavior of the gerbils depended on their density: at moderate and high densities (Inline graphic > 12), gerbils used the subplots equally; intraspecific competition prevailed. At low densities (Inline graphic< 12), one of the plots had much more activity than the other, showing that the gerbils had tended to coalesce; mutualism prevailed.

In Fig. 2, we show 56 control trials (i.e., those with no owl flights). Of these, 12 come from 1994 or 1995. The remainder come from identical trials in the same subplots during previous years (8, 9). In control trials, AGAaAGAb at all values of Inline graphic (thus g ≈ 0). This confirms the sensitivity of these gerbils to intraspecific competition even at low densities.

But experimentals (n = 29) show intraspecific competition only at higher Inline graphic values. Here again, AGAaAGAb. Trials at these moderate to high gerbil abundances (i.e., Inline graphic > 12) reflect the greater importance of intraspecific competition compared with mutualism. These trials agree completely with companion results obtained to study that competition by using unequal owl flight pressures in the subplots (14). Those companion studies also showed that gerbil responses depend on a redistribution of their foraging effort, not on its curtailment.

On the other hand, as predicted by qualitative predation theory, experimental trials at low AGA tend to have disparate values of AGAa and AGAb. Fourteen of the 20 experimental trials at Inline graphic < 12 have differences that exceed the largest difference recorded from the controls. Over the years, we have repeatedly tested G. allenbyi in these enclosures to see if they divided their activities nearly equally between two subplots when conditions were the same on each side of the fence (8, 9, 14). This is the only time they have not, and they did not do so in either of the 2 years we ran the experiments.

Our study strongly suggests that at very low population densities (Inline graphic < 12), the G. allenbyi zero isocline has positive slope. In the present paper and elsewhere (14), we have also measured it at higher densities (Inline graphic > 12). There, its slope is negative; so it must have a peak not far from Inline graphic ≈ 12.

Many theoretical variations in predatory interactions could eliminate the humped shape of the victim isocline, and so its presence in a single system does not mean it is always present. Yet, for the first time to our knowledge, the salient features of a victim isocline have been measured in the field. And it did prove to be humped shape as predicted over 30 years ago.

In summary, foraging Allenby’s gerbils usually disperse as if they were competing with each other. The exception to this behavior occurs at low gerbil densities in the presence of a predation threat. Then they coalesce as if they were mutualists. That behavioral shift agrees with the joint prediction of natural selection and the nonlinear theory of predatory population dynamics. Thus, the behavior of these gerbils reflects a sophisticated adaptation to dynamical interactions within their own species and with other species. Although we do not know how they do it, Allenby’s gerbil seems able simultaneously to assess both its risk of predation and its own densities. Rodents of other species, specifically voles, also forage together to reduce their risk of predation (15, 16), but they are not known to coalesce or disperse depending on their own density and the current threat of predation.

Acknowledgments

Yoni Witztum and Ido Zurim helped feed and train the owls and helped run the experiments. Dr. Beni Perelman helped care for the owls and maintain their health. The U.S.–Israel Binational Science Foundation (Grant 93-00059) supported the research. Gordon Orians and two anonymous reviewers suggested improvements in the manuscript.

Footnotes

Moving to the denser patch will continue only until competition among the victims in the denser patch outweighs the mutualism in the sparser patch. So, it is possible that movement will cease before the sparser plot is entirely empty of victims.

AGA is the foraging activity density of G. allenbyi. AGA is linearly proportional to gerbil population density and is a more sensitive measure of population pressure than simple density. (A gerbil in an enclosure may or may not be active aboveground during a specific period. If it is not active, it may as well be absent.) To measure AGA, we observed gerbil tracks left in 0.4 m × 0.4 m sand-tracking plots (smoothed at 2045 and read at 2300). Each hectare had 40 sand-tracking plots.

§

The first conscious confirmation is ref. 6. See ref. 5 for a few of the many others, including even earlier ones that went unnoticed by their discoverers.

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