Proc. Natl. Acad. Sci. USA Vol. 95, pp. 13052–13055, October 1998 Ecology

Spatial scales of desert locust gregarization

MATTHEW COLLETT,EMMA DESPLAND,STEPHEN J. SIMPSON*, AND DAVID C. KRAKAUER

Department of Zoology, University of , South Parks Road, Oxford OX1 3PS,

Communicated by Richard Southwood, , Oxford, United Kingdom, August 12, 1998 (received for review March 25, 1998)

ABSTRACT Central to swarm formation in migratory process is carried out four times with the origin of the boxes locusts is a crowding-induced change from a ‘‘solitarious’’ to successively shifted diagonally across one grid square. By using a ‘‘gregarious’’ phenotype. This change can occur within the the mean number of nonempty boxes N(r), the fractal dimension lifetime of a single locust and accrues across generations. It is calculated as Ϫ1 times the slope of the linear regression of log represents an extreme example of phenotypic plasticity. We N(r) against log r. Because we were interested in the smallest present computer simulations and a laboratory experiment scales, we used only r ϭ 1, 2, and 4. The box-counting method that show how differences in resource distributions, conspic- measures the fractal dimension of the resource, not the boundary uous only at small spatial scales, can have significant effects of the resource. Thus, the more continuous the resource distri- on phase change at the population level; local spatial concen- bution, the closer the fractal dimension is to 2.0. With only 20 tration of resource induces gregarization. Simulations also points, this box-counting algorithm can result in a maximum show that populations inhabiting a locally concentrated re- dimension of 1.28. source tend to change phase rapidly and synchronously in Laboratory Experiment. Experiments were conducted in a response to altered population densities. Our results show why 70-cm by 70-cm Perspex arena with 20 small pots of wheat shoots information about the structure of resource at small spatial 1 cm in diameter and 2 cm high. The pots were placed on a 64 by scales should become key components in monitoring and 64 grid within the arena according to the random fractal algo- control strategies. rithm. The experiments were performed with isolated-reared (4) mid-second-instar nymphs, whose solitary-reared parents origi- nated from eggs laid by crowd-reared adults. Nymphs were used The desert locust, Schistocerca gregaria, is one of the world’s most only once and were deprived of food for 12 h before testing. Tests notorious insect pests. Most of the time, it exists at low densities lasted 8 h, and at the end of each run, the behavioral-phase state across sub-Saharan Africa and into India. At unpredictable of each locust was assayed. For the assay, locusts were isolated intervals, plagues occur; swarms leave this recession zone and and graded according to rates of 13 types of movement and invade neighboring areas of Africa, Asia, and Europe. The grooming behavior observed over a 10-min period (see ref. 4). We crowding-induced phase transition between the ‘‘solitarious’’ and used five resource distributions for experiments with groups of 10 ‘‘gregarious’’ forms involves a suite of changes in behavior, or 20 nymphs. An additional three distributions were used for morphometry, color, development, fecundity, and endocrine runs with 10 locusts. Each experiment was performed twice, for physiology (1–3). Gregarious individuals become more active and a total of 26 runs. are attracted, instead of repelled, by other locusts. Most phase Computer Simulation. The computer simulation used a con- characters change between instars or accrue across generations tinuous two-dimensional arena with edges identified to form a through maternal inheritance (4–7), but a solitarious individual’s torus. Time was divided into 50,000 iterations; 10,000 iterations behavior becomes gregarious after only4hofcrowding and were allowed for the population to reach equilibrium, and results reverts to solitariousness after only4hofreisolation (4, 5, 8). The were collected over the following 40,000 iterations. As in the detailed time course of behavioral-phase change has been quan- experiment, 20 patches of resource were placed by using the tified only recently and has important implications for selecting random fractal algorithm on a 64 by 64 grid superimposed on the the appropriate temporal and spatial scales required to under- arena. Simulations were run with 10 and 20 initially solitarious stand locust swarming. locusts, placed at random within the arena. An experimental study has shown that locusts confined in an Model locusts are characterized by (i) a behavioral-phase state, experimental arena for 8 h are more gregarious if the arena g, which ranges from 0 (solitarious) to 1 (gregarious), and (ii)a contains a lower density of resource (e.g. food, perches, or Cartesian coordinate. Each locust has periods of movement favorable microclimatic sites; ref. 8). In the present study, we according to rules with parameters derived from earlier experi- examine the effects of resource distribution and locust density on mental studies (4, 5, 10): the probability of going to a resource gregarization, while keeping the overall density of resource patch (P); the probability of leaving a resource patch (Q1); the constant. maximum distance moved in an iteration (R); the rate of increase in movement with gregarization (B); and the phase-dependent MATERIALS AND METHODS probability of leaving an unsuitable patch (Q2). Locusts interact when in the same grid square. A locust experiences a unit of Fractal Dimension of Resource. Fractal surfaces used in the contact whenever another individual starts or finishes movement experiment and simulation were created on a 64 by 64 grid by within its grid square. Locusts that move within an iteration do so using an algorithm with midpoint displacement (9). Food patches synchronously, and contact is calculated at the initiation and end were located on the highest 20 points. The fractal dimension of of movement. The rate of behavioral-phase change of an indi- the resulting distribution is then described by using a box-counting vidual at time t is a saturating function of the cumulative amount algorithm. The arena is divided into boxes of length r grid squares, and the number of boxes containing food patches is counted. This Abbreviations: A, contact-saturation level; B, rate of increase of movement with gregarization; c, cumulative contact experienced; d, The publication costs of this article were defrayed in part by page charge distance; g, behavioral-phase state; P, probability of going to a resource patch; Q , probability of leaving a resource patch; Q , payment. This article must therefore be hereby marked ‘‘advertisement’’ in 1 2 phase-dependent probability of leaving a resource patch; r, length of accordance with 18 U.S.C. §1734 solely to indicate this fact. grid square; R, maximum distance moved in an iteration; t, time. © 1998 by The National Academy of Sciences 0027-8424͞98͞9513052-4$2.00͞0 *To whom reprint requests should be addressed. e-mail: stephen. PNAS is available online at www.pnas.org. [email protected].

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of contact it experiences (ct) over the preceding 500 iterations. were observed for only 8 h; thus, the equilibrium level of The amount of saturation is adjusted with parameter A (the gregarization might not have been reached. contact-saturation level; we let A ϭ 40). The gregarization of a Disentangling Mechanisms in the Simulation. How can we ϭ ϩ ⅐ ͞ Ϫ locust is updated as gtϩ1 gt 0.01 (min(1, ct A) 0.5). If gtϩ1 explain the effect of resource distribution on gregarization? exceeds the limits 0 or 1, it is given the value of that limit. The resource determines the distribution of locusts. In the An individual’s movement increases with its behavioral experimental arena, locusts tend to stay near food patches. In ϭ ϩ ͞ gregarization, modelled by bg 1 Bg. Endogenous move- the simulation, every 1 P movements takes a locust to a ment, which occurs with probability bgQ1, is proportional to its resource patch, whereas subsequent movements take it grad- phase state. Additional contact-induced movement provides ually away. Behavioral gregarization of real locusts is triggered an attractive–repulsive response. The probability of moving in principally by contact (11, 12). In the simulation, the rate of the iteration after contact depends on the presence of other behavioral change is a saturating function of the cumulative locusts; if locusts are present, it decreases with gregarization, number of contacts experienced over the preceding 500 iter- Ϫ bgQ2(1 g). Otherwise, it increases, bgQ2g. Movement is with ations. The simulation identifies three mechanisms by which equal probability to any point within a distance bgR.Ifitis spatial distribution of resource influences the distribution of contact-induced, then the movement is repeated until the the cumulative contact ct. The first two act on the mean individual is no longer in the same grid square. After the initial instantaneous-contact rate, whereas the third acts through the movement, an individual may go directly to food with proba- distribution of the cumulative contact. bility P. The patch is chosen at random with probability The Mean Contact Rate. To make explicit the scale at which decreasing with distance from the individual—the probability individual behavior and resource distribution interact, contact ͞ ͞ 1.5 of moving to patch j is bgP ¥i(dj di) where di is the distance can be divided into two (scale-dependent) classes: contact (on the torus) between the locust and resource patch i. between individuals that have most recently visited the same patch (or are on it) and contact away from a patch between RESULTS individuals that have recently visited different patches (Fig. 2a). Each of the two mechanisms acting on the mean instan- Effect of Resource Distribution. The results of the laboratory taneous contact rate acts on a different class of contact and experiment show that for a fixed number of locusts and resource over a different spatial scale. patches, the mean gregarization of the population increases with There is a relationship between the uniformity of the spatial concentration of the resource (Fig. 1a). Least-squares resource distribution and the rate of contact between individ- linear regression is y ϭ 0.40 ϩ 0.17x, R2 ϭ 0.80, for 10 locusts, and uals on or from the same patch (Fig. 2b). The uniformity of the for 20 locusts y ϭ 0.49 ϩ 0.16x, R2 ϭ 0.95. These lines differ resource distribution is reflected in the distribution of locusts. significantly in elevation, with 20 locusts being more gregarized We measured the latter with the Shannon–Weaver informa- ¥ Ϫ after the 8-h treatment than 10 locusts (analysis of covariance tion measure: i pi log pi, where pi is the relative frequency with fractal dimension as covariable, and locust number as with which patch i is visited. The least-squares linear regression Ͻ ϭ Ͻ ϭ Ϫ 2 ϭ treatment gave P 0.0001 for fractal dimension, F1,10 56.3; P is y 0.21 0.057x, R 0.34. Evenly spaced distributions ϭ 0.0003 for treatment, F1,10 17.8). in either a single clump or evenly scattered have high infor- The results of the simulation show a similar trend to the mation measures. Uneven, intermediate distributions which experimental results; population gregarization increases with are formed of larger clumps with some scattered patches have locust density and the fractal dimension of the habitat (Fig. 1b). lower information measures. In an uneven distribution, there The average population gregarization was not affected by the are outlying patches that are visited less frequently. The locusts initial phase state of the model locusts, suggesting that there is a are therefore effectively concentrated in fewer patches, and single equilibrium level of gregarization possible for any partic- the crowding causes greater gregarization. ular habitat and population density. The second mechanism by which resource distribution af- Although designed to allow for direct comparison, the labo- fects gregarization acts on the second class of contact. Locusts ratory experiment differed from the simulation in two significant originating from different patches meet more often the closer ways. First, the experimental arena had edges by which the locusts together the resource patches (Fig. 2a). This tends to make aggregated. This aggregation increased the basal rate of gre- gregarization increase with fractal dimension. garization so that locusts were partially gregarized after 8 h, even The rate at which individuals from the same patch meet is in an arena with widely dispersed food sites. Second, the locusts high, and the uniformity of distribution affects the rate over a

FIG.1. (a) The average behavioral-phase state of the 10 or 20 experimental locusts at the end of8hinthearena. Each point represents the mean of two experimental runs with the same resource distribution. There is a significant effect of both fractal dimension and number of locusts (see text). (b) The mean gregarization of the 10 or 20 model locusts over the final 40,000 iterations of a simulation. Parameters were chosen such that a solitarious locust would spend, on average, 10 iterations on a patch followed by 100 iterations away (P ϭ 0.1, Q1 ϭ 0.1, and R ϭ 0.5). Gregarized locusts have a 50% increase in the rate and distance of movement (B ϭ 0.5), and the rate of contact-induced movement is Q2 ϭ 0.5. Results from 124 simulations with 102 different resource distributions were pooled according to fractal dimension, and each point shows the mean of no fewer than 10 simulations. Downloaded by guest on October 3, 2021 13054 Ecology: Collett et al. Proc. Natl. Acad. Sci. USA 95 (1998)

FIG.2. (a) The effects of resource distribution on the mean amount of instantaneous contact experienced by simulated locusts. Parameter values were chosen such that a locust’s behavior is not affected by its phase state or the presence of other locusts (B ϭ 0.0, Q2 ϭ 0.0, and other parameters as in Fig. 1a). Each point is the mean of a single simulation run. (b) The effect of the uniformity of the resource distribution on the rate of instantaneous contact between locusts that have most recently visited the same patch—from the same simulation runs as in a (i.e., excluding phase-related behavioral changes). (c) The effects of resource distribution on the distribution of cumulative contact. The mean and standard deviations of the distribution of the effective cumulative amount of contact (min(ct, A)) for all individuals of each simulation are shown—from the same simulation runs as in a (i.e., excluding phase-related behavioral changes). (d) The effects of phase-dependent individual behavior on population gregarization. The figure contrasts the effects of using phase-related behavioral changes with the same parameters as in Fig. 1b with the effects of using no behavioral changes with the same parameters as in a. Results are pooled as in Fig. 1b, and the error bars show the standard deviation of the simulation mean.

large range of spatial scales. However, the effect is small. For deviation. In contrast to the simple instantaneous contact the second mechanism to be significant, individuals must shown in Fig. 2a, the effective cumulative contact rate is frequently leave the resource patches. This only happens if the greater in a clumped resource distribution. patches are the same scale as the range of an individual’s Phase-Related Behavior. The effects of resource distribu- movement over a brief time (minutes). In the simulation, only tion on the extent to which locusts interact and hence gregarize differences in resource distribution at small spatial scales have are apparent even in the absence of phase-related changes in a large effect on the total amount of contact. behavior, as seen in Fig. 2 a–c where such behaviors were The Distribution of Contact. The third mechanism acts excluded. The net result of including phase-related behaviors through the cumulative contact experienced over a physiolog- in simulations is that the contact rate in a population depends ically relevant length of time, rather than simply the mean on the phase states of the individuals, as well as the distribution instantaneous contact rate. Greater movement between of resource. The equilibrium gregarization therefore becomes patches means a more homogeneous mixing of locusts, leading a more critical function of resource distribution (Fig. 2d) and to a smaller variance in the cumulative amount of contact ct population density. within the population. This is important, because the rate of When a locust becomes gregarious, it is attracted by other gregarization is a saturating function of an individual’s cumu- locusts, whereas a solitarious individual is repelled. A gregar- lative contact. Saturation occurs both because there is a ious locust, therefore, comes into contact with other locusts ϭ Ͼ maximal gregarized state (g 1) and because if ct A, then more often than does a solitarious locust. The phase- ϭ the effect on the rate of gregarization is the same as if ct A. dependent attractive–repulsive behavior of a locust acts to If the mean rate of contact is sufficient for gregarization, then push it towards either gregarious or solitarious extremes. A the smaller the variance, the greater the amount of gregariza- change in the phase of an individual has a similar effect on the tion in a population. With lower mean levels of contact, greater contact experienced by the rest of the population—a gregar- aggregation is necessary for gregarization. In the 500 iterations ious locust has a stronger gregarizing influence than a soli- over which a model locust ‘‘remembers’’ its contact, it will on tarious one. Attraction among gregarious insects and repulsion average have left a resource patch at least five times. In a among solitarious ones tend to prevent individuals from concentrated resource, a locust is less likely to visit the same reversing phase. Because of the behavioral changes, a partial patch in succession, and so the cumulative amount of contact phase change in an individual makes further change in that is more evenly distributed. Fig. 2c shows the distribution of the individual easier. It also increases the probability that the effective cumulative amount of contact (min(ct, A)) from phase of other locusts will change in the same direction. Thus, individuals most recently on the same patch. The more there is positive feedback from behavioral change acting at clumped the resource distribution, the smaller the standard both the individual and population level. Downloaded by guest on October 3, 2021 Ecology: Collett et al. Proc. Natl. Acad. Sci. USA 95 (1998) 13055

The second significant behavioral effect of gregarization is a their movement and survival depend on wind systems and the general increase in movement. Gregarious individuals move availability of food. Control at this point is difficult. Instead, a further and more often, increasing the amount of contact be- major aim of desert locust management is to target nascent tween individuals. The effect is strongest in clumped habitat, swarms, before or during the several consecutive generations of where locusts are closer together, and so a moving individual is crowding necessary for the full phase transition. Existing attempts more likely to come into contact with others. Increased move- to predict the emergence of swarms based on time-series analyses ment also means that there is greater mixing. When the mean of outbreaks have been largely unsuccessful (16–18). Ecologically contact rate is low, increased movement works against gregariza- based forecasting models for S. gregaria and other locust species tion by separating individuals, whereupon they begin to resolita- show more promise (19–26). These models have been based on rize. At high-contact levels, however, the smaller variance in the properties of populations not individuals. Gregarization is cumulative contact further increases the rate of gregarization in known to depend on the type of vegetation cover (24). Our the population. Phase-dependent rates of movement thus have experiments and simulations show how vegetation architecture the effect of homogenizing the phase of the population both when and distribution at the smallest spatial scales (i.e., ranges of it is solitarious and when it is gregarious. centimeters to meters, corresponding to locust behavior over Population Density. Of key importance in swarm formation minutes and hours), as well as locust densities, can influence is the interaction between the distribution of resources and gregarization. The differences in distribution we examined are changes in the size of the locust population in a given area. In not detectable at the larger scales which provide the focus of many the wild, gregarization is usually associated with a local monitoring strategies. To improve control programs, local data, increase in population size through breeding and concentra- including the fractal dimension of resource or a related measure, tion (13). The experiment shows that gregarization is greater should be collected and incorporated into existing models and at the higher density of locusts. The model indicates that in a monitoring programs. locally scattered habitat (low fractal dimension), gregarization increases only gradually with population size, whereas in This work was supported by grants from the Biotechnology and locally concentrated habitats (high fractal dimension), gre- Biological Sciences Research Council (to M.C. and S.J.S.), Fonds pour garization occurs suddenly when the mean amount of contact la Formation des Chercheurs et l’Aide a`la Recherche from the exceeds the threshold required for gregarization (Fig. 3). government of Quebec (to E.D.), the United Nations Development Fund (to S.J.S.), and the Wellcome Trust (to D.C.K.).

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