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ANTLION FORAGING: TRACKING PREY ACROSS SPACE AND TIME.

INTRODUCTION

Many predatory animals build traps to capture mobile prey. Well-studied examples include web-weaving spiders (e.g., Riechert and Gillespie 1986, Wise 1993), net-spinning caddisfly larvae (e.g., Hildrew and Townsend 1980, Richardson 1984, Malmqvist and Bronmark 1985), and pit-building antlion larvae (e.g., Wheeler 1930, Lucas 1982, Heinrich and Heinrich 1984). In addition to supplying food, the trap provides information about food availability at a given location and over a particular time interval. Because trap relocation ordinarily carries a significant energy cost (Griffiths 1980a, b, 1986, Lucas 1985, Linton 1995), and perhaps other costs such as increased risk of mortality (Simberloff et al. 1978, Lucas 1989, Griffiths 1992; but see Heinrich and Heinrich 1984 on risk-avoidance behavior), this approach to sampling prey over space and time can be expensive. Yet trap-building foragers may benefit substantially from tracking major shifts in prey availability through space and time. The discreteness of this trap construction - foraging - relocation process should enhance our ability to characterize foraging strategies and relate their efficacy to resource variability in time and space. In fact, many problems faced by biological systems can be reduced to the need to gather resources, distributed across space and time, as efficiently as possible.

Antlion larvae (Neuroptera: Myrmeliontidae), the focus of the present study, are generalist predators of arthropods that move along the soil surface. Larvae construct conical pits in the dry sandy or silty substrate and use them to capture prey. A large proportion of the antlion larval diet consists of ants, not because of any clear specialization or preference, but because ants are relatively abundant in the dry areas where antlions are found (Topoff 1977). Other prey frequently eaten by antlion larvae include spiders, beetles, isopods, flies, caterpillars, wasps, and mites (Turner 1915, Wheeler 1930, Heinrich and Heinrich 1984, Linton 1995).

Prey are captured when they fall into the pit, are dragged under the sediment surface, and are digested externally. Digested prey fluids are then extracted from the prey and consumed via grooved mandibles, which direct the fluids to the larva's mouth. Capture success with these prey varies; larger antlions with larger pits can generally capture a wider variety of prey types and sizes than can smaller antlions. Heinrich and Heinrich (1984) found that Myrmeleon immaculatus larvae captured an average of 8.8 prey/d in New England, whereas Cueta trivirgata in the Namib Desert captured an average of 2.3 prey/d similar of size (Marsh 1987). However, antlion larvae are capable of surviving for up to 3 months without eating (Heinrich and Heinrich 1984).

Combining the development of a predictive model with a laboratory experiment, we recently addressed the issue of foraging through space and time in a study of Myrmeleon immaculatus (Linton et al. 1991). Because antlion larvae sometimes move their pits as often as every 5 d in the few quantitative studies of their behavior in the field (Wilson 1974, Griffiths 1980b, Heinrich and Heinrich 1984, Linton 1995), we supposed that 3 d might provide a conservative estimate of the minimal time needed to evaluate a pit location. We further assumed that antlions were attempting to maintain or increase body mass; when the gain fell below the maintenance threshold for a 3-d period, an antlion would relocate its pit. The model produced the frequent pit relocations and peripheral pit distributions generally consistent with the laboratory data that we subsequently obtained (Linton et al. 1991).

One of us recently studied foraging by larvae of M. immaculatus at Sleeping Bear Dunes National Lakeshore (SBD-NL) in the northern lower peninsula of Michigan, USA (Linton 1995). Two parallel and adjacent 50-trap linear transects of artificial pitfall traps were established at each of two sites (Good Harbor Bay [GHB] and Sleeping Bear Bay [SBB]) [approximately]15 km apart. Pitfall traps consisted of a 9 cm diameter plastic cup buried flush to the soil surface and containing a downward-pointing plastic cone with its apex removed. The cone funneled captured prey into a smaller collecting cup containing preservative (Morrill 1975). These artificial traps effectively mimicked the pitfall traps of larval antlions, collecting and preserving the arthropod prey available to antlion larvae at the trap sites. The traps within each transect, spaced at 0.5-m intervals along a line parallel to the lake shoreline in vegetated dune habitat (Cowles 1899), were monitored daily over a 60-d period in each of two years (30 May-28 July 1986 and 31 May-29 July 1987, except that vandalism restricted the observations in Good Harbor Bay in 1987 to 31 May-14 July).

In addition to the space x time x taxon array of prey availability for antlions assembled from these data, pit densities, sizes, and relocation frequencies were also estimated. In this field system, antlions relocated their pits much less frequently than did the laboratory population in our previous study, rebuilding an average of 182 [+ or -] 20 cm (mean [+ or -] 1 SE; n = 42 observations) from the previous location, with an average movement interval of 67 [+ or -] 13 d (M. C. Linton, unpublished data; cf. Griffiths 1980b, Heinrich and Heinrich 1984, Matsura 1987, Matsura and Takano 1989). Analysis of the prey availability array yielded significant autocorrelations only on the smallest temporal scale considered (i.e., 1 d), but not on any of the within-transect spatial scales (0.5-25 m; Linton 1995).

A specific goal of the present study was to clarify why larval antlions in the Sleeping Bear system relocated their pits after several weeks rather than, for example, every few days (as in the laboratory study) or every few months. To accomplish this, we evaluated [greater than]5000 composite foraging strategies, using Monte Carlo simulations to estimate the expected net daily energy gain rate associated with each strategy, based on spatiotemporal prey availabilities measured in the field data. We expected to find that the foraging strategy yielding the highest gain rate, and other high-gaining strategies, would generate pit relocations about as frequently as observed in the field population. The key assumption underlying this expectation is that these larval antlions are capable of adopting a foraging strategy that maximizes (or nearly maximizes) net gain rate. Because antlion growth rate appears to be strongly food limited at Sleeping Bear Dunes National Lakeshore (Linton 1995) and at other sites studied to date (e.g., Griffiths 1980b, 1991, Furunishi and Masaki 1983, Lucas 1985, Gotelli 1993), maximally efficient foraging should increase larval growth rate. Because life cycle length is apparently flexible (Wheeler 1930, Furunishi and Masaki 1982), faster larval growth may increase fitness by reducing generation time or by reducing exposure to sources of larval mortality.

A general goal of this study is to present and use a conceptual framework concerning how trap-building predators might be expected to respond to spatial and temporal patterns of prey availability, a fluctuating spatiotemporal mosaic (Forman and Godron 1986). The patchiness of prey distributions over space and time is critically important in determining the best foraging strategies. When current site-specific gain rates provide information about the near future at the site or about nearby sites, then gain rate data are autocorrelated (see Chatfield 1996). Except in unusually long data sequences, autocorrelations are difficult to detect statistically, but even subtle correlative linkages may provide an edge to the forager whose strategy makes effective use of them.

In the following sections, we explain how prey availabilities were derived from pitfall trap data, describe the strategies to be evaluated, consider some implications of autocorrelation for optimal strategies, and indicate the way in which the simulations were parameterized and conducted. Then we present the simulation results, focusing mainly on the highest gain strategies and the features that characterize them, comparing against field results and predictions implied by the autocorrelation structure of the data. By contrasting results for two sites and by examining the implications of altering movement costs, we test predictions on the effects of prey availability and clarify the determinants of relocation frequency. Finally, we consider implications of the results and emphasize follow-up work and new directions that should further our understanding of how animals deal with spatiotemporal variation.

FILTERING THE PITFALL TRAP DATA

The 170 different size and taxonomic categories of arthropods identified from the trap transects were combined into 26 prey types, based on apparent similarity of handling by captive antlion larvae and on similarity in average biomass extracted by the larvae from the prey. Antlion profit from a prey type is affected by capture success, by the amount of biomass that is extractable, and, at unusually high prey densities, by handling time. Sclerotized exoskeletons and cuticles, which vary considerably in thickness among prey types, help to reduce the prey's profitability to antlion larvae via all three of these factors.

The average amount of food antlion larvae could extract from prey items found in the pitfall traps was determined in feeding experiments with captive antlions. Four types of prey accounted for a large percentage of the total number of prey (slightly more than 70%) and of the total extractable biomass (66%) captured in the traps, but two of these, scarab beetles (2% by numbers and 12% by biomass) and small/medium spiders (7% by numbers and 24% by biomass), were rarely captured by antlions in the field (M. C. Linton, personal observations). We therefore focused our simulation analysis on the availability of the other two prey types, caterpillars and grubs (hereafter pooled as "caterpillars," which contributed 2% of the total prey numbers but 18% of the biomass in the traps) and ants (60% by number and 12% of the biomass). All three instars of antlion larvae can capture these two prey types. Caterpillars represent a windfall of food (much more extractable biomass than the typical prey item) and may provide enough energy for an antlion larva to molt into the next instar or pupate from the final instar. Yet these larvae can grow steadily on as few as four average-sized ants per day (Linton 1995).

The "search path" width of a foraging antlion larva is the diameter of its pit, which is the extent of pit edge orthogonal to the direction of prey movement. We thus expected the capture rate of a pit to be proportional to pit diameter. Because antlion pits were not as wide as the transect traps used to determine prey availability, the daily trap captures overestimated the amount of prey available to individual antlions. Moreover, there was a seasonal increase in average pit size, reflecting antlion growth. We therefore generated expected pit diameter for each day from a linear regression of pit diameter against sampling date; the expected pit diameter, divided by the trap diameter, was then multiplied by the total number of prey to estimate the number available to an individual antlion pit on a given date.

To account for handling-time effects on the overall foraging rate of the antlion larvae, we further filtered the available prey estimates for each trap, using a standard type-2 functional response relationship (Holling 1959) and expressing the gain rate G in milligrams consumed per antlion per day:

G = [Epsilon]P/(1 + tP) (1)

where P is the number of ants or of caterpillars trapped per day, [Epsilon] is the extractable biomass in milligrams per ant or per caterpillar (0.057 and 39.6 mg/prey, respectively; Linton 1995), and t is the handling time per ant or per caterpillar (0.028 and 0.125 d/prey, respectively; Linton 1995).

On rainy days, neither antlion larvae nor their prey were active; by the next rain-free day, prey and antlion activity levels generally returned to normal (Linton 1995). Rain days were therefore simply removed from the data and ignored, under the assumption that any costs of metabolic maintenance and pit rebuilding would be independent of the foraging strategy being used, and therefore could not shift the ranking of gains among strategies.

STRATEGIES

For this analysis, we characterized antlion foraging strategies as consisting of four components, each quantified by a set of discrete, representative values.

1. Interval, the minimum number of days over which an antlion remains in place at a site. - We assumed that each day an antlion would gain the energy available at its present time and pit location and then would assess its weighted-average foraging gain over some number of immediately preceding days plus the present day (i.e., the interval). Thus, the antlion remained at the same location to complete its assessment for the duration of the interval, and stayed on thereafter until the gain rate was too low over the most current interval. We investigated intervals of duration 1, 3, 6, 10, 16, 25, 35, 45, and 55 days.

2. Weighting, the relative contribution of each day's foraging gain to the overall site assessment. - We assumed that the current day's foraging return provided the most important information for evaluating the present pit location, and geometrically discounted the contribution of preceding days to the weighted-average gain. Each day's gain is weighted by the weighting raised to the power n, where n is the number of days that have elapsed within the interval since the gain was obtained. For example, with an interval of 6 d and a weighting of 0.9, the present day's gain is multiplied by [0.9.sup.0] = 1, the previous day's gain is weighted by [0.9.sup.1] = 0.9, the gain achieved the day before that is weighted by [0.9.sup.2] = 0.81, and so on, until the gain from five days previously is weighted by [0.9.sup.5]. The weighted-average gain is then simply the sum of these weighted values divided by the sum of the weights. The weightings we analyzed were 1, 0.95, 0.9, 0.8, 0.7, 0.5, and 0.3.

The temporal window t over which the forager is assumed to assess its gain rate is defined by the interval i and the weighting w, taken together. In effect, the weighting determines a different type of interval having a duration that can be expressed as 1/(1 - w), the sum of the geometric series of weights. Because the shorter of these two interval durations determines the effective evaluation period, we express the overall window size as

t = min{i, 1/(1 - w)}. (2)

3. Threshold, the weighted-average foraging success during the interval, below which the antlion relocates its pit. - After each day's foraging, if the antlion has remained at the same location for at least the duration of the interval, then the weighted-average gain over the interval is compared with the threshold, and subthreshold gains trigger immediate pit relocation. This means that, all other things being equal, higher thresholds increase the relocation frequency, and lower thresholds reduce this frequency. Most threshold values that we used were derived by multiplying the overall mean mass gain per day (2.34 mg) by powers of two; we also used two extreme values, ensuring in these cases that the weighted-average gain was either never (zero) or always (300) below threshold. The values were 0, 0.146, 0.293, 0.585, 1.17, 2.34, 4.68, 9.36, 18.72, and 300 mg.

4. Displacement, the number of "steps" taken by an antlion in a random walk to a new pit location. - Pit relocation simply shifted an antlion to a different pitfall trap position along the transect in 0.5-m steps. Each step was taken with equal probability in either direction along the transect. An antlion attempting to move off the end of a transect would instead spend a step and remain at the end location. This rule ensures that an antlion starting from an unspecified, random location is equally likely to occupy any of the 50 pitfall trap locations at any future time. There is both a pit-rebuilding cost (0.781 mg), estimated using a relationship derived by Griffiths (1980a) for Morter obscurus, and a movement cost per step (0.065 mg per 0.5 m), roughly estimated by assuming that a typical movement path length in the field of 6 m corresponds to approximately the same energy expenditure as rebuilding a pit (M. C. Linton, unpublished data); these reduce the net energy gain during the day that an antlion relocates. We assume that the time spent moving and rebuilding has a negligible influence on the time available for foraging. Displacements that we evaluated were 1, 3, 5, 10, 15, 20, 30, 50, and 100 steps. Actual displacements achieved (because longer random walks generally include much doubling back) were approximately proportional to the square root of the displacement number.

IMPLICATIONS OF AUTOCORRELATION

Fig. 1 summarizes our expectations about relationships between these components of foraging strategy and scales of autocorrelation. For spatial patterns, when the scale of spatial autocorrelation in prey availability is large, then trap relocation distances should be extensive (i.e., large displacement), to escape what may be a relatively large unprofitable vicinity. Because long-distance relocations may prove costly in terms of movement energetics and predation risk, small-scale spatial autocorrelation is likely to result in smaller trap displacements when relocation is necessary. For temporal patterns, when the scale of temporal autocorrelation in prey availability is large, only a relatively small window of time may be needed to estimate near-future foraging profitability, whereas the high variability associated with small-scale temporal autocorrelation should necessitate a longer assessment window.

In contrast to the assessment window and displacement distance, relocation thresholds of gain rate may be determined less directly by spatial and temporal autocorrelation patterns. The threshold may generally tend to increase with window size to compensate for the enforced immobility of the evaluation period, and the threshold should decrease with displacement to contain the overall relocation costs. Taken together, the relationships summarized in Fig. 1 imply more frequent relocations when the spatial scale is large, although no clear predictions emerge for different scales of temporal autocorrelation (but see the Discussion). Moreover, the logic underlying these relationships assumes that relocation costs may play a large part in determining both how a trap builder gains spatiotemporal information and how it uses the information gained.

SIMULATIONS

The simulation algorithm is presented in Fig. 2. A computer program, written in Borland Pascal (available on request from the senior author), was used to implement the algorithm. The program began by accessing the data arrays and then looped through the 5670 strategies composed of all combinations of the four components [TABULAR DATA FOR TABLE 1 OMITTED] previously described. Each strategy was evaluated separately for each of the eight site-year-transect combinations; for each of the four site-year combinations over both transects within a site; for each site over years and transects; and overall across all sites, years, and transects. For each strategy and each site-year-transect combination, 1000 replicates were run. Each replicate represented an antlion that was started at a random locus within a 50-locus transect and was allowed to obtain the food reward available at its location on each of the days in the data set. Thus, results from this main analysis were derived from simulated foraging by 45 360 000 antlion larvae (5670 strategies x 8 site-year-transect combinations x 1000 replicate antlions). Additional analyses of this same magnitude were conducted to evaluate the role of rebuilding costs in determining optimal strategies, by multiplying the costs of movement and of pit reconstruction by 0, 0.1, 0.25, 0.5, 2, and 5.

A difficulty with this approach was deciding what information to provide an antlion about its immediate past foraging success at its starting date and location, because this information was not contained in the data set. Without such information, the antlion would be unable to relocate until a full interval of days had passed, which might introduce a substantial bias into the analysis. We attempted to minimize this problem in the following way. Each antlion began with an interval of information about its "virtual past" at the present location, derived by sampling with replacement from the first seven days of actual data for that location. This ensured that the antlion began with a plausible initial evaluation of the location, and might or might not initiate a pit relocation within the first interval of foraging. The number of days of data chosen for sampling to provide this virtual past seemed, in preliminary runs, to have little effect on the results; the 7-d period was therefore chosen arbitrarily.

RESULTS

Table 1 summarizes the outcome of the simulation analysis, with costs of movement set to the estimated values. Because the outcomes for within-site transects were very similar, these are not shown. The highest gain strategy overall featured a relatively long interval of 35 d, but with substantial discounting of preceeding data (weighting = 0.7) that implied a window of 3.33 d (Eq. 2); a relocation threshold at 1.17 mg/d, half of the grand-mean gain rate; and the minimal displacement of one 0.5-m step. A similar pattern is derived from the median values for each component from the top 32 strategies, representing those with gain rates within 1% of the highest rate: an interval of 45 d and weighting of 0.9 (i.e., a window of 10 d), threshold of 1.17 mg/d, and displacement of three 0.5-m steps.

Because the analysis of Linton (1995) indicated that scales of spatial and temporal autocorrelation are small (i.e., at or below the scales of spatial and temporal resolution in the data) for the SBD-NL transects, we can compare the previously discussed patterns with those expected according to the upper-left box of Fig. 1. We note that optimal displacements are small and assessment periods are relatively long, as expected. Moreover, a threshold of 1.17 mg/d (i.e., half of the overall mean) can be considered a fairly high value, in light of the substantial variability in the data and the relatively short window. In other words, the site assessment value needs only to fall below half of the overall mean value during a relatively brief assessment period to trigger relocation, not a particularly stringent requirement. Thus, these results seem generally consistent with the scheme in Fig. 1, although this in no way constitutes a rigorous test of these predictions (see Discussion).

The highest gain rate of 2.445 mg/d was achieved with a mean pit relocation frequency of 1.65 over the 60-d observation period and a total movement distance [TABULAR DATA FOR TABLE 2 OMITTED] of 0.5 m, generally consistent with the low relocation frequencies and short movement distances in field observations (Linton 1995). However, antlions that never relocated were able to do almost as well, achieving a highest gain rate of 2.388 mg/d, 97.7% of the gain achieved by those following the top strategy of occasional relocation. Particularly when relocation is energetically costly, a strategy of not relocating at all can apparently do nearly as well as a more complex, conditional relocation strategy.

In fact, the gain surface formed above orthogonal axes based on most pairs of the four strategy components is relatively flat [ILLUSTRATION FOR FIGURE 3 OMITTED], especially along weighting and threshold axes (e.g., [ILLUSTRATION FOR FIGURE 3D OMITTED]). Over all sites, years, and transects, 60% of all strategies investigated generated gain rates within 8% of the highest rate, and 90% generated gain rates within 18% of the highest. The results, however, are somewhat more sensitive to interval and displacement; in particular, short intervals and large displacements clearly result in too much energetically expensive pit relocation [ILLUSTRATION FOR FIGURE 3C OMITTED].

Note that the highest gain strategies for the two sites were quite similar to each other and to the overall best strategy, although these generated very different gain rates at the two sites, with a much greater gain and a negligible relocation frequency at Sleeping Bear Bay. Some rather different strategies generated the highest gains for the four different site-year combinations, however. At both sites, 1987 data produced much smaller assessment windows and lower relocation thresholds, yet relocations were somewhat more frequent. Despite these consistent differences between years, the best strategy at Sleeping Bear Bay generated a higher gain rate in 1986, whereas the best strategy at Good Harbor Bay achieved a higher gain rate in 1987.

When the costs of movement and pit rebuilding were completely eliminated from the model, the characteristics associated with the optimal foraging strategy shifted dramatically (Table 2). In this case, the highest gain strategy overall featured an interval of one day, as did all 25 other strategies achieving within 1% of the highest gain. Moreover, the threshold for the highest gain strategy was very low (0.146 mg/d) and the displacement was maximal (100 0.5-m steps per relocation). Thus, a 7.6% higher gain rate was attained by lengthy cost-free moves after each day of negligible foraging gain, relative to the gain rate attained when relocation is energetically expensive.

The overall pattern of optimal foraging strategies vs. relocation costs is illustrated in Fig. 4A. As costs rise from 0% to 10% of the estimated values, interval, window, and threshold remain low, but displacement drops sharply. Additional costs increase window and interval and further decrease displacement. Interestingly, threshold rises with cost to its maximum at the estimated cost values, and then declines sharply for still higher costs. These trends result in high relocation frequencies with costs at or below 10% of the estimates, a sharp and then more gradual, general decline with further increases, and then essentially a cessation of pit relocation as the threshold plummets with a long interval [ILLUSTRATION FOR FIGURE 4B OMITTED].

DISCUSSION

A surprising result from the simulations was the flatness of the foraging gain surface, particularly when the cost of movement was included. A variety of strategies, including never moving at all, led to very similar feeding prospects. The distribution of prey in the dunes environment at Sleeping Bear Dunes National Lakeshore would sufficiently support antlions with many of the foraging strategies consistent with infrequent relocation, including those actually observed.

At SBD-NL, the locations of antlion pits are not significantly correlated with prey abundance, as measured by unfiltered pitfall trap data (Linton 1995); larvae of Myrmeleon immaculatus actually seem to track sources of shade or cover more strongly than sources of food (Klein 1982, Lucas 1989, Linton 1995). Once in the shade, an antlion larva may not move again during that feeding/growing season. This preference for shade or cover does positively influence feeding, by protecting the pit from rain and wind damage. Reducing or eliminating exposure to direct sun may also have important implications for thermo- and hydroregulation. The larva may generally increase its total foraging time by having its pit functional for longer periods, and may reduce the physiological demands and pit maintenance costs associated with wind, rain, and intense solar radiation. The importance of this observation seems clear for larvae that, by not moving at all, can gain 97.7% of the maximum gain when relocation is costly and 92.7% of the maximum when movement is cost free. Additional work on these physiological effects might suggest that foraging models like ours would gain considerable predictive power from incorporating habitat structure and dependence on physiological state.

Our simulation results suggest that antlions may relocate their pits only infrequently at Sleeping Bear Dunes National Lakeshore because of high relocation costs. Once these costs are reduced sufficiently, the optimal strategy shifts sharply in favor of a very brief site assessment, lower relocation threshold, larger displacement, and frequent relocations. This dramatic change can be understood as a response to spatial and temporal autocorrelations in foraging gain rate that, although largely undetectable by standard statistical methods, are nevertheless present and important.

Ideally, an antlion's pit should be relocated whenever the expected gain from moving exceeds the cost. Even a positive temporal autocorrelation of only one day indicates that a low foraging gain today will tend to be repeated tomorrow, making immediate relocation advantageous whenever the overall expected daily gain for the habitat exceeds today's gain by more than the relocation cost. To ensure that the new location is less likely to suffer from the low prey availability of the current site, however, displacement should be great enough to reduce or eliminate any positive spatial autocorrelation with the current site, as long as movement costs are not excessive. Thus, the characteristics of the optimal strategy when relocation costs are very low are consistent with the spatiotemporal patchiness of prey availability apparent in Fig. 5. With significant relocation costs in place, however, it is simply too expensive for antlions to take full advantage of the information provided by the autocorrelation structure of prey availability in the habitat.

Note that this interpretation hinges on the magnitude of relocation cost relative to expected net foraging gain from relocating. This means that increasing the variance of gain rate over space and time has an effect on characteristics of the optimal foraging strategy comparable to reducing the relocation cost. Moreover, greater prey availability is often correlated with greater variance of prey availability, as in Tables 1 and 2. We might therefore generally expect to find more frequent trap relocations associated with greater prey availability, a pattern apparent in site and site-year comparisons for Table 2, where relocation costs are excluded, but not for Table 1.

This seemingly counterintuitive association between more frequent trap relocation and higher prey availability has been observed in the long-jawed orb-weaving spider Tetragnatha elongata, and has been attributed to two entirely different mechanisms. Comparisons of creek- and lakeside populations of T. elongata showed that prey are more abundant near the lake, where spiders relocate their webs almost every night, whereas individuals in the creek population maintain the same web for at least several days before relocating (Caraco and Gillespie 1986, Gillespie and Caraco 1987, Smallwood 1993). Caraco and Gillespie explain the difference based on the distinction between risk-prone (creek) and risk-averse (lake) behavior by spiders maximizing their chances of being able to produce an egg sack within a season of fixed duration. In contrast, Smallwood emphasizes the importance of site-specific differences in the intensity of aggressive interactions among conspecifics; higher prey availability draws more spiders, which therefore interact and move around more often. Having life cycles of flexible duration (Wheeler 1930, Furunishi and Masaki 1982) makes antlions less likely candidates for risk-sensitive foraging; sand-tossing associated with pit-building, however, can apparently increase relocation frequencies at very high densities (P. Dillon, personal communication), in closer accord with the mechanism proposed by Smallwood. At the relatively low antlion densities and prey availabilities typical of temperate zone antlion habitat, however, it seems likely that it is the costs of pit relocation that will generally keep relocation frequencies low.

In the SBD-NL system, there were clear differences in prey availability between the sites at Good Harbor Bay and Sleeping Bear Bay, and among the site-year data sets. These and other differences generated some variation among the best foraging strategies for these cases. Because the two sites are physically similar and only [approximately]15 km apart along the lakeshore, it seems unlikely that the populations at these sites differ genetically in characteristics that would influence foraging behavior. Perhaps comparisons of genetically isolated populations would reveal adaptations in which foraging behavior becomes genetically tuned to the local environment. In any case, comparative studies across populations differing in the mean and variance of prey abundance and in the scales of spatial and temporal autocorrelation would allow the approach taken here to be tested, improved, and extended.

In the laboratory, antlions may be induced to adopt a foraging strategy consistent with the spatiotemporal distribution of prey offered to them. In a 30-d experiment, we recently showed that larvae would move their pits initially every few days and then less often to exploit fine-scale differences in prey availability within containers 40 cm in diameter (Linton et al. 1991). The situation that we posed for them had small-scale spatial, but large-scale temporal, autocorrelation in prey availability, and their foraging strategies generally fit the characteristics in the lower-left box of Fig. 1. It may be typical of such situations that the relocation frequency starts very high and then declines, as we observed, particularly when a location with a consistently high gain rate can be found.

We note that antlion larvae observed in the laboratory cannot automatically be assumed to have useful information at the beginning of the observation period about the spatiotemporal characteristics of the foraging problem posed for them, unlike those observed for some arbitrary interval in the field. This may help to explain the greater initial movement frequency in the previous laboratory study. In any case, there is clearly much scope for additional laboratory studies to provide new insight into how foraging strategies respond to patterns of prey availability.

Conceptualizing foraging problems as finding how best to move simultaneously along spatial and temporal axes may prove useful in a wide variety of biological systems. Perhaps the systems best studied in this way to date are insect pollinators and flowers (Pyke 1979, Waddington and Heinrich 1979) and the seasonal migrations of large herds of grazing mammals (Baker 1978). Plant systems can sometimes be viewed in a similar way, particularly clonal plants that extend stolons to initiate new ramets (Slade and Hutchings 1987a, b). However, these cases are complicated by exploitation-regeneration dynamics of the resources, whereas the prey resources of trap-building predators can generally be considered renewable and non-exploitable. The relatively simple dynamics of the trap-builder systems may increase our chances of eventually understanding them in depth.

ACKNOWLEDGMENTS

We thank Brad Dickey, Richard Hanschu, Marcel Holyoak, and two anonymous referees for helpful comments and suggestions on this analysis. P. H. Crowley acknowledges the National Science Foundation for grant support (EHR 91-08764) and the National Center for Ecological Analysis and Synthesis for providing an excellent research environment that helped to advance this project.

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Author:Crowley, Philip H.; Linton, Mary C.
Publication:Ecology
Geographic Code:00WOR
Date:Oct 1, 1999
Words:6446
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