Abstract

Foragers of Melophorus bagoti often return to previously rewarding sites to search for more food items. They are opportunistic scavengers that exploit both protein and carbohydrate food sources. Under natural foraging conditions, protein food items are distributed sparsely and randomly, whereas carbohydrates come in patches that are often renewable. This makes for vastly different foraging scenarios that a single forager is confronted with. In theory, foraging performance can be greatly improved if foragers are able to adjust their strategy to different food item distributions. This could be achieved through individual foraging experience or by employing pre-existing, intrinsic foraging strategies. We investigated this by offering both kinds of food with the same distribution: as a renewable food source at a fixed location. After removal of the food source, outbound foragers displayed an area-restricted search centered on its location. Searches for protein had a greater spread than those for carbohydrates, which matches the natural distribution pattern of these food types. However, searches for both kinds of food follow the same general strategy, which is best described as a Brownian-like walk. We suggest that the observed adaptive behavior is a result of differential learning effort.

INTRODUCTION

Foraging ants have to cope with two major difficulties: how to find food and how to find the way back to the nest. Here we focus on how ants search for food items. In nature, food sources can occur at very different densities (sparse or dense) and distributions (patchy or randomly distributed), and food sources can be renewable or depletive ( Stephens and Krebs 1986 ; Bell 1991 ). Certain types of food, however, have typical distribution patterns. Nectar from flowers, for example, usually comes in patches as one plant often has several flowers, and the food source is generally renewable as the nectar is replenished; the same is true for honeydew excretions from aphids. Dead insects on the other hand are usually randomly distributed as they remain where the insect happened to die, and they are depletive.

Many animals have specialized in the exploitation of food sources whose distribution in space has a typical pattern; it is conceivable that there is considerable selection pressure for search strategies that increase the encounter rate with food and therefore their foraging efficiency ( Pyke 1984 ; Bell 1990 ; Ydenberg 1998 ). A large number of studies have focused on identifying optimal search strategies for a diverse array of foraging scenarios, and also on finding evidence of these strategies in the movements of naturally foraging animals (e.g., Hoffmann 1983 ; Bartumeus et al. 2005 ; Lomholt et al. 2008 ; Sims et al. 2008 ; Scharf et al. 2009 ; Papastamatiou et al. 2011 ). They usually concern free-roaming foragers that have no prior knowledge of the distribution of food items. But some animals also return to a location where they have previously found food, as it could offer a continued food supply, for instance a food patch, a large food item, or a renewable food source (e.g., Schmid-Hempel 1984 ; Crist and MacMahon 1991 ). They are able to learn the location of this food source, and their foraging behavior is shaped by experience. If they fail to locate this site, they engage in area-restricted searching behavior ( Pyke 1984 ; Stephens and Krebs 1986 ). Their search path is commonly made up of loops that repeatedly bring the animal back to the area where the food is most likely located. Similar selection pressure toward search efficiency can be expected here. Previous work on the ant Formica schaufussi has shown that foragers adapt some parameters of their search paths to the type of food previously encountered at that location: carbohydrate food leads to tighter searches of longer duration than protein food ( Traniello et al. 1992 ; Fourcassié and Traniello 1994 ). They show this pattern after only one previous visit to the site and it does not change much after repeated offering of the same food type ( Fourcassié and Traniello 1993 ). The authors suggest that the foraging ants have a “resource-related predisposition” that allows them to adjust their search effort to the different distribution patterns of carbohydrates and proteins in nature. However, the nature of this predisposition remains unclear; it may depend on extrinsic (e.g., learning, perceptual) or intrinsic (e.g., genetic, predetermined) mechanisms ( Bell 1990 ). Fourcassié and Traniello (1994) suggest two possible extrinsic mechanisms. Firstly, search path properties may depend on olfactory stimuli that are used to detect food items. In ants, the detection radius for protein food is greater than for carbohydrate food; a search pattern for protein odors would thus cover a larger area ( Pyke 1983 ). Secondly, the tightness of search may depend on the invested learning effort. A higher learning effort would result in a more precise memory of the food location and thus a tighter search pattern. A possible intrinsic mechanism could be based on predefined, innate search strategies or “movement rules” that are optimized to find food items with a typical distribution in time and space (like carbohydrates or protein). Encounter of a specific food type could trigger the use of the appropriate strategy in the subsequent search. Advances that have been made in recent years in the field of optimal search theory enable us to investigate the use of different movement strategies.

In theoretical models of searching, the basic movement pattern of a searching animal is generally considered to be made up of segments of straight movement and incidents of reorientation, and to be based on a random walk ( Bell 1991 ). The lengths of the straight segments are drawn at random from probability distributions. Depending on the distribution of food items, models based on certain mathematical distributions can be more successful at locating these items than others. Commonly proposed foraging models are variants of the Brownian walk, based on a Gaussian distribution, and the Lévy walk, which is based on a heavy-tailed (and scale free) power law distribution ( Shlesinger and Klafter 1986 ; Viswanathan et al. 1996 , 1999 ). Although the question of Lévy walks in nature is still being debated (see for example Edwards 2011 ; James et al. 2011 ), several empirical studies appear to provide evidence of such movements in animals ( Sims et al. 2008 ; Humphries et al. 2010 ; Hays et al. 2012 ). It has been proposed that Lévy walks could be a widespread searching strategy among central place foragers such as ants and bees ( Reynolds et al. 2007a , 2007b ; Reynolds and Rhodes 2009 ). Two recent studies of Melophorus ants ( Schultheiss and Cheng 2011 ; Schultheiss P, Wystrach A, Legge ELG, Cheng K, submitted manuscript), however, showed that they do not use a Lévy strategy when searching for their nest entrance.

Our experiments investigate the searching behavior of Melophorus bagoti foragers that are attempting to locate a previously experienced, stationary, and nondepleting food source. By offering two different types of food that have very different distribution patterns in nature, we can test if the ants search for these in different manners. We can also investigate if different movement strategies are used in searching for different types of food. Furthermore, these results will add to our as yet limited knowledge about search strategies in central place foragers.

MATERIAL AND METHODS

Study species and study site

Melophorus bagoti is widespread in the semi-arid grassland deserts of inland Australia. Foraging ants are diurnal and highly thermophilic ( Christian and Morton 1992 ) and venture out solitarily to find dead insects, seeds, and sugary plant excretions ( Muser et al. 2005 ; Schultheiss et al. 2010 ). Due to their special thermal niche they are the only ants that forage during the hot part of the day. They are exceptional navigators and can use both visual navigation and path integration (a mechanism that keeps track of the distances and directions walked) to find their way around ( Narendra 2007a , 2007b ; Cheng et al. 2009 ). Foragers repeatedly visit the same foraging areas ( Muser et al. 2005 ), and establish habitual routes between the foraging area and the nest ( Kohler and Wehner 2005 ; Wystrach et al. 2011 ).

The study site is located ca. 10 km south of Alice Springs and has an average annual precipitation of 287mm (Australian Bureau of Meteorology, Melbourne). The vegetation is made up of Triodia sp. hummock grassland (now largely replaced by the invasive grass Cenchrus ciliaris ), interspersed with bushes of Hakea eyreana , Acacia spp., and occasional large Eucalyptus spp. trees. Nests of M. bagoti occur at a density of ca. 3 per hectare ( Schultheiss et al. 2010 ). Experiments were conducted on one ant colony from December 2009 to February 2010.

Experimental setup

Adjacent to the nest entrance, an area of 10 m × 10 m was cleared of all vegetation, and a grid of 1 m × 1 m squares marked out with tent pegs and string. The nest entrance was enclosed, with an opening providing access to the testing area where a Petri dish feeder (distance: 5 m) was placed at the center of the test area and provided food ad libitum . It contained one of two possible types of food for several weeks at a time: cookie crumbs (“carbohydrates”) or fresh pieces of mealworms (“protein”). Although both food types also contain lipids, and mealworms also contain carbohydrates that will be more accessible when cut up, the main components of the two foods are carbohydrates and protein, respectively. Foragers that discovered the feeder returned to it readily to pick up another food item, thus shuttling back and forth between the feeder and the nest entrance frequently. Ants were marked with a day-specific color at the feeder, and allowed to continue foraging for a minimum of 2 days before testing. For a test, the nest entrance was fully enclosed and the feeder removed. (Returning foragers could still enter the enclosure from outside.) When a forager appeared at the nest opening, it was lifted out and set down just outside the enclosure, where it could continue its foraging run. Aided by the grid squares, its foraging path was then recorded on paper for about 3min, or until the ant left the grid or returned to the nest. This setup may have resulted in unnatural behavior of protein-fed foragers, as they rarely encounter renewable protein sources in nature. It does, however, enable us to investigate the mechanisms that shape the behavior of searching ants.

Data analysis

All ants that displayed a path of at least 15 m length within the test field were considered as displaying searching behavior. The searching ants tended to move in rather straight lines and changed direction quite abruptly. Digitization of the search paths could be limited to these turning positions, which retain most of the information. The starting point of a search was defined as a change in direction of 90° or more, with the turn completed within 0.2 m, and the distance to the next point being at least 0.2 m; for subsequent turning points the critical angle was reduced to 45°. This procedure results in a simplified version of the full search path but retains most of the information, and has been shown to deliver robust results in a previous study ( Schultheiss and Cheng 2011 ). It also breaks down the paths into a series of straight segments of different length, connected by turns of varying angle. The structure of search paths from the two groups of ants (“carbohydrate” and “protein”) was compared in regard to (a) spread, (b) segment length, and (c) turning angle and changes of these parameters within each group were also investigated. Spread was measured as the median or mean distance of the turning points from the original feeder position in the middle of the test area (position 0/0), segment length was defined as the shortest distance between two turning points, and turning angle was defined as deviation from the straight direction. For comparisons between groups, Mauchly’s sphericity test was used to test for equality of variances. Where necessary, Greenhouse-Geisser or Huynh-Feldt corrections were applied, leading to fractional degrees of freedom.

A straightness index was calculated for the initial outbound journey that led the ant close to the feeder location. This approach path was defined as starting once the ant entered the test grid and terminating once the ant reached the line through the feeder perpendicular to the feeder-nest line ( y = 0). The index was computed by dividing the beeline between these positions by the actual length of the path taken by the ant.

The movement strategy of searching ants was investigated by calculating frequency distributions of search path segment lengths and finding models that fit the data best. Both exponential and power law models were considered. We followed the procedure laid out in Edwards et al. (2007) and Edwards (2011) , which uses the raw, unbinned data to calculate maximum likelihood estimates (MLEs) of model exponents. This method was used to fit models with and without an upper bound to the whole series or the tail end (defined as starting at a = 2.6 m), respectively. Bounded models are more realistic when investigating biological systems, as maximum segment length will be limited by physiological or ecological constraints. The upper bound was defined as the maximum value of the distribution. A goodness-of-fit test ( G -test with Williams’s correction, Sokal and Rohlf 1995 ) was then performed on the preferred model, to see if it adequately describes the data. In addition, we analyzed our data with the method of Sims et al. (2007 , 2008 ), which uses log-binned, normalized (LBN) data. We are aware that this procedure is considered less exact than MLE calculations ( Edwards 2008 , AM Edwards, personal communication). However, performing this kind of analysis here enables the direct comparison with previously published data on the nest searching behavior of M. bagoti ( Schultheiss and Cheng 2011 ). Further information about model fitting procedures can be found in the Supplementary Material .

RESULTS

Structure of search paths

Ants that were tested had experience of the unlimited, stationary food source (carbohydrate or protein) for at least 2 days. During this time, they learnt the location of this food source and returned to it frequently. Carbohydrate- and protein-fed ants returned to the feeder with similar frequency. When the feeder was removed, 86% of carbohydrate foragers (total n = 57) and 87% of protein foragers (total n = 60) returned to the area where it was located and displayed an area-restricted search that was centered on the previous feeder location ( Figures 1 and 2 ). The spread of these searches was slightly different between groups: ants trained to a carbohydrate-rich food source displayed tighter searches than ants trained to a protein-rich food source (O’Brien’s test for homogeneity of variance: F1,86 = 4.3, P < 0.05; Welch’s ANOVA: F1,75.84 = 5.0, P < 0.05) ( Figure 3a ). It must be noted though that the variance between individual ants was quite large in both groups, and there was also considerable overlap between the two. Figure 3b shows the straightness of the initial approach path from the nest entrance to the feeder position. Foragers in the protein group had significantly lower straightness indices ( t -test: t (99) = 2.4, P < 0.05). Looking into the behavior of ants within each group, further differences become evident. Foragers looking for carbohydrate food started their search close to the feeder ( Figure 2 ) and then slowly moved outward, away from the feeder location ( Figure 4a ). This increase in spread was significant (repeated measures ANOVA: F8.1,299.6 = 4.5, P < 0.001) and followed a significant linear trend ( F1,37 = 17.3, P < 0.001). Ants looking for protein food began their search at a greater distance from the feeder ( t -test: t (68.5) = −3.7, P < 0.001), quickly moved closer, and then stayed at a similar average distance to it ( Figures 2 and 4b ). Overall, no significant change in spread was observed (repeated measures ANOVA: F6.1,236.4 = 1.9, P = 0.08). As the search unfolded, ants in both conditions also showed a gradual increase in segment length ( Figure 4c4d ; two-way ANOVA: F13.7,1030 = 1.8, P < 0.05, with no differences between groups, F1,75 = 1.2, P = 0.29). The increase followed a significant linear trend ( F1,75 = 16.0, P < 0.001). At the same time, no changes were apparent in their turning angles (two-way ANOVA: F22,1650 = 0.7, P = 0.8, and no differences between groups, F1,75 = 1.4, P = 0.2; measured over 25 turning points, ants with fewer turning points being excluded from the analysis; n values as in Figure 4 ).

Figure 1

Examples of search paths performed by Melophorus bagoti foragers. Ants were trained to a nondepletive food source, which was removed before the test. The open circle marks the previous location of the food source, and the star marks the nest entrance. The ant in (a) had experience of a carbohydrate food source and in (b) of a protein food source.

Figure 1

Examples of search paths performed by Melophorus bagoti foragers. Ants were trained to a nondepletive food source, which was removed before the test. The open circle marks the previous location of the food source, and the star marks the nest entrance. The ant in (a) had experience of a carbohydrate food source and in (b) of a protein food source.

Figure 2

Overview plots showing the positions of turning points as the search unfolds in (a)–(e) carbohydrate and (f)–(j) protein foragers. Single plots from left to right show the positions of the 1st, 4th, 8th, 16th, and 25th turning points. In each subplot, the feeder position is located at the center, marked by the crossing of the gray lines (carbohydrates: n = 37, protein: n = 40).

Figure 2

Overview plots showing the positions of turning points as the search unfolds in (a)–(e) carbohydrate and (f)–(j) protein foragers. Single plots from left to right show the positions of the 1st, 4th, 8th, 16th, and 25th turning points. In each subplot, the feeder position is located at the center, marked by the crossing of the gray lines (carbohydrates: n = 37, protein: n = 40).

Figure 3

Differences in search path parameters between groups. (a) Search spread of the first 20 m of search path in the two groups (carbohydrates: n = 43, protein: n = 45). Boxes show medians and upper and lower quartiles; whiskers extend to the upper and lower deciles. Paths with less than 20 m path length were excluded from the analysis. (b) Straightness index of the initial approach path from the nest entrance to the target position. A perfectly straight path will have an index of 1 (carbohydrates: n = 49, protein: n = 52).

Figure 3

Differences in search path parameters between groups. (a) Search spread of the first 20 m of search path in the two groups (carbohydrates: n = 43, protein: n = 45). Boxes show medians and upper and lower quartiles; whiskers extend to the upper and lower deciles. Paths with less than 20 m path length were excluded from the analysis. (b) Straightness index of the initial approach path from the nest entrance to the target position. A perfectly straight path will have an index of 1 (carbohydrates: n = 49, protein: n = 52).

Figure 4

Changes in search path parameters as the search unfolds. Error bars show standard deviation, and black lines show best fitting linear functions. Ants with less than 25 turning points or less than 24 segments were excluded from the analysis (carbohydrates: n = 37, protein: n = 40). Average distance of turning points from zero (the previous feeder location) in (a) carbohydrate foragers and (b) protein foragers. Average length of search path segments in (c) carbohydrate and (d) protein foragers.

Figure 4

Changes in search path parameters as the search unfolds. Error bars show standard deviation, and black lines show best fitting linear functions. Ants with less than 25 turning points or less than 24 segments were excluded from the analysis (carbohydrates: n = 37, protein: n = 40). Average distance of turning points from zero (the previous feeder location) in (a) carbohydrate foragers and (b) protein foragers. Average length of search path segments in (c) carbohydrate and (d) protein foragers.

Movement strategy

We then fit models to the segment length distributions to investigate the underlying movement strategy. Within each group, all analyses are based on the same data (derived from n = 49 paths for the carbohydrate group, and n = 53 paths for the protein group). Figure 5 gives an overview of the distributions. It shows a high frequency of short segments that rapidly drops off as the segment length increases. This general pattern, however, is broken by the large values in the second bin, showing segment lengths of 0.4–0.6 m; for carbohydrate foragers, these values are even higher than those in the first bin. This pattern is interesting, but cannot be meaningfully explained by general searching models. For the following model fitting procedures, we therefore only consider segments with a minimum length ( xmin ) of 0.6 m or larger.

Figure 5

Overview of the segment length distributions from both groups. Data were put in bins of 0.2 m width, starting with the minimum segment length of 0.2 m. Carbohydrate group: n = 1785 segments, protein group: n = 1846 segments.

Figure 5

Overview of the segment length distributions from both groups. Data were put in bins of 0.2 m width, starting with the minimum segment length of 0.2 m. Carbohydrate group: n = 1785 segments, protein group: n = 1846 segments.

Figure 6 and Table 1 show the results from the analysis following the MLE method ( Edwards et al. 2007 ; Edwards 2011 ). Results from the analysis following the LBN method ( Sims et al. 2007 , 2008 ) can be found in the Supplementary Material ( Supplementary Figure S1 and Supplementary Table S1 ). The tables include several values that are calculated for model selection. Akaike’s Information Criterion (AIC) is used to find the best model in a group (we use the more accurate AICc which includes a correction term); the preferred model has the smallest AIC value. The AIC weight measures the weight of evidence for each model, and the evidence ratio compares the weight of evidence for each model to that of the best one, thus giving a measure of relative likelihood.

The results of the MLE analysis show that, for both conditions, exponential models are strongly preferred over power law models ( Table 1 ). Unbounded exponential models deliver the best results, but bounded exponential models remain viable options in both cases. Goodness-of-fit tests show that the unbounded exponential models describe the data adequately in both groups ( G -test: P = 0.058 for carbohydrate foragers, P = 0.230 for protein foragers). To further investigate possible Lévy walk characteristics, we repeated the analysis with just the tail end of the distribution ( Table 1 ). In both groups, there is no clear preference of one model type over the other, possibly due to the small number of segments that constitute the tail end. But in any case, the estimates for the power law exponent µ are well outside the range of Lévy walks (1 to 3; Viswanathan et al. 1999 ). The LBN method delivers quite similar results for models fit to the whole series ( Supplementary Figure S1 ). Although the picture is not quite as clear, a single exponential model describes the distribution adequately in both conditions ( Supplementary Table S1 ).

DISCUSSION

Foragers of M. bagoti make use of both protein and carbohydrate food sources, which have very different distribution patterns in nature. We offered both kinds of food with the same distribution, as a renewable food source, to see if food type alone can trigger different searching behavior, and if differences are due to the use of divergent search strategies.

In our experiments, Melophorus foragers readily learnt the location of a renewable food source (carbohydrate or protein), and displayed a systematic search for it when removed. This search path was centered on the previous food location ( Figures 1 and 2 ) and was made up of loops of varying size; this looping structure repeatedly brought the ant back close to the target area. Interestingly, the type of food previously available at that location had an effect on the behavior of ants: their initial approach path to the protein food source was less straight ( Figure 3b ), and the spread of searches for protein-rich food was larger than that for carbohydrate-rich food ( Figure 3a ). As both food types were offered with the same distribution in space, these differences have to be due to some quality of the food. Several possibilities come to mind as to how these differences are achieved:

  1. 1. The ants could simply be better at learning the location of carbohydrate food than of protein food, and thus be more confident about the location of the food. Carbohydrate resources are typically clumped, so that the chances of another food reward at that site are high. Natural protein, on the other hand, occurs scattered over large areas and is not replenished, so that learning the location of a protein source is usually not beneficial. If learning were “strategic” or dependent on motivation then carbohydrate foragers might create more accurate spatial memories. Given the costs associated with learning and memory ( Dukas 1998 , 2008 ; Hoedjes et al. 2011 ), it makes functional sense to tailor the amount of learning and the robustness of memory and their associated costs to the expected need for learned information (see also Traniello et al. 1992 ; Fourcassié and Traniello 1993 , 1994 ).

  2. Better learning in turn should cause a tighter search pattern, in which the spread of the search pattern is based on probabilistic expectations of the reward location. In this view, better learning creates an expected distribution of reward location with less uncertainty (less spread), and search spread is tuned to match these expectations. Ants with a higher degree of uncertainty about a location are known to display larger searches ( Merkle et al. 2006 ), and there is evidence that their path meander increases ( Wystrach et al. 2011 ). The paths of our protein foragers showed both these features ( Figure 3a , 3b ). The stronger meander in the approach paths of protein foragers had further consequences on the search path properties. Carbohydrate foragers moved close to the target position before starting their search, which then slowly expanded outward ( Figures 2 and 4a ). Protein foragers, on the other hand, walked to the target in a more tortuous way, to the effect that our search criteria were often met before reaching the target. The approach path was then concluded with the first few search segments before the rest of the path was centered on the target ( Figure 2 ). In fact, the meandering approach path may already be part of the actual search for protein. Foragers would then appear to “switch” from an intrinsic, forward-drifting search strategy to an extrinsic, learnt-place strategy in the vicinity of the target ( Figure 4b ). This behavior may increase the chances of finding other protein-rich food items on the way to the target, as a tortuous path covers a larger area than a straight path.

  3. The suggestion that ants may be able to learn strategically can be tested experimentally by first training all foragers to a carbohydrate food source; in a second step, one group continues to experience this carbohydrate food source, whereas another group is trained to protein food at the same location (see Fourcassié and Traniello 1993 ). If learning is strategic, both groups of foragers should then have a similarly accurate memory of the food location, and will search with a similar strategy.

  4. 2. The differences in search spread may be explained by the type of stimulus that is used to locate the food. The foragers may in fact be searching for odor cues that will lead them to the food source. Because the detection radius for protein food is larger than that for carbohydrate food ( Pyke 1983 ), efficient searches for protein odors will cover a larger area. The decrease in straightness of protein foragers’ paths when approaching the reward site ( Figure 3b ) could also be interpreted as the behavior of ants scanning for an odor plume. Odor is known to play a significant part in the navigational toolkit of desert ants and is used in both foraging ( Wolf and Wehner 2005 ) and homing ( Steck et al. 2009 ). Such a hypothesis may be tested by controlling the odors emanating from the feeder, by sealing the feeder except for letting ants in or by provisioning foods that emit odor but cannot be picked up (e.g., enclosed in a fine mesh).

  5. 3. Foragers looking for the protein food may “give up” the search faster and move away from that area, thereby increasing their search spread. Unfortunately, “giving up time” could not be measured directly, as the internal state of the ant is unknown to us: she could well be still moving around in the test area, but not looking for the experimental food source any more. We find, however, no evidence of earlier “giving up” behavior (i.e., moving outward, away from the zero position) when looking at the average spread of the unfolding search in that condition ( Figure 4b ). If ants looking for protein would indeed move away from the target earlier, we should also see a sharper increase in the segment lengths of their unfolding search paths. This is not the case, as segment length increase was similar in both the conditions ( Figure 4c , 4d ).

  6. 4. The ants could indeed have different, pre-existing foraging strategies available to them, and use of the appropriate one may be triggered by the food type they previously encountered. If this is the case, we should see some differences in their movement strategies. On the other hand, if the ants do not have different intrinsic strategies to choose from, both groups should display the same movement strategy. This will be shaped by the actual, experienced distribution of food items, which was the same in both conditions.

  7. The movement strategy was investigated by looking at the segment length distributions. In Figure 5 , we saw that segments with a length of 0.4–0.6 m occurred more frequently than expected. This may reflect some systematic aspect of their search strategy, for example, an intermittent, small-scale search at the precise feeder location, or may alternatively be due to a systematic sampling error in our methods. In any case, the effect appeared in both groups, and at a similar scale. The remainder of the segment length distribution (≥0.6 m in length) was further analyzed.

Model fits over the whole series show a very clear preference of exponential over power models in both conditions ( Figure 6 and Table 1 ). Curve progression is quite smooth in both groups, suggesting that the data are well described by a single function. Adding an upper bound to the exponential model does not further improve model fits. The calculated slope of the exponential model is very similar in both food conditions ( Table 1 ), evidence that both groups have similar foraging strategies. Results from the LBN method of model fitting are comparable (see Supplementary Material ). This supports the idea that, for Melophorus foragers, the search strategy is shaped by the actual distribution of food items, and is not derived from some pre-existing foraging strategy (see point 4 above). The exponential movement strategy is very similar to the freely roaming Brownian walk, but as the search paths of ants are looping rather than freely roaming, their movements are best described as a “Brownian-like walk.” Exponential search strategies are also used by Melophorus foragers for locating the nest entrance after successful foraging runs ( Schultheiss and Cheng 2011 ; Schultheiss P, Wystrach A, Legge ELG, Cheng K, submitted manuscript). This too is a single target, the location of which the ants had previously learnt.

Figure 6

Inverse cumulative frequency distribution plots of segment lengths, for (a) carbohydrate and (b) protein foragers. Note that axes are logarithmic. Values below xmin are shown in gray, and are not considered for function fits. Lines show best fitting functions over the whole series, using the MLE method; red = exponential, orange dashed = bounded exponential, blue = power law, light blue dashed = bounded power law. n values for segments ≥ xmin : 1122 for carbohydrates, 1106 for protein.

Figure 6

Inverse cumulative frequency distribution plots of segment lengths, for (a) carbohydrate and (b) protein foragers. Note that axes are logarithmic. Values below xmin are shown in gray, and are not considered for function fits. Lines show best fitting functions over the whole series, using the MLE method; red = exponential, orange dashed = bounded exponential, blue = power law, light blue dashed = bounded power law. n values for segments ≥ xmin : 1122 for carbohydrates, 1106 for protein.

Table 1

Statistical parameters of curve fitting using the MLE method, for functions fit to the whole series (shown in Figure 6 ) and to the tail end of the distribution only

 Exponent 95% CI log-likelihood AICc AIC weight Evidence ratio 
Function fit to whole series       
Carbohydrates       
 Exp  λ MLE = 1.047  0.987–1.109 −1070.874 2145.726 0.514 
 ExpB  λ MLE = 1.040  0.979–1.103 −1069.908 2145.838 0.486 1.058 
 PL  µ MLE = 2.260  2.187–2.335 −1180.794 2365.567  9.402 e–49  5.467 e47 
 PLB  µ MLE = 1.959  1.868–2.051 −1112.766 2231.553  1.186 e–19  4.334 e18 
 Protein       
 Exp  λ MLE = 1.100  1.037-1.166 −1000.513 2005.004 0.663 
 ExpB  λ MLE = 1.097  1.033–1.164 −1000.168 2006.358 0.337 1.968 
 PL  µ MLE = 2.287  2.212–2.364 −1122.060 2248.100  1.081 e–53  6.131 e52 
 PLB  µ MLE = 2.029  1.937–2.122 −1067.403 2140.828  2.128 e–30  3.117 e29 
Function fit to tail end       
Carbohydrates       
 Exp  λ MLE = 0.999  0.845–1.168  −147.301  298.689 0.373 1.467 
 ExpB  λ MLE = 0.948  0.780–1.130  −145.877  297.922 0.548 
 PL  µ MLE = 4.347  3.835–4.917  −153.808  311.704 0.001 982.967 
 PLB  µ MLE = 3.779  3.150–4.441  −147.823  301.814 0.078 
 Protein       
 Exp  λ MLE = 1.102  0.920–1.307  −112.823  229.744 0.188 2.964 
 ExpB  λ MLE = 1.083  0.892–1.293  −112.460  231.119 0.094 5.896 
 PL  µ MLE = 4.740  4.122–5.435  −112.966  230.030 0.162 3.421 
 PLB  µ MLE = 4.421  3.711–5.183  −110.686  227.571 0.556 
 Exponent 95% CI log-likelihood AICc AIC weight Evidence ratio 
Function fit to whole series       
Carbohydrates       
 Exp  λ MLE = 1.047  0.987–1.109 −1070.874 2145.726 0.514 
 ExpB  λ MLE = 1.040  0.979–1.103 −1069.908 2145.838 0.486 1.058 
 PL  µ MLE = 2.260  2.187–2.335 −1180.794 2365.567  9.402 e–49  5.467 e47 
 PLB  µ MLE = 1.959  1.868–2.051 −1112.766 2231.553  1.186 e–19  4.334 e18 
 Protein       
 Exp  λ MLE = 1.100  1.037-1.166 −1000.513 2005.004 0.663 
 ExpB  λ MLE = 1.097  1.033–1.164 −1000.168 2006.358 0.337 1.968 
 PL  µ MLE = 2.287  2.212–2.364 −1122.060 2248.100  1.081 e–53  6.131 e52 
 PLB  µ MLE = 2.029  1.937–2.122 −1067.403 2140.828  2.128 e–30  3.117 e29 
Function fit to tail end       
Carbohydrates       
 Exp  λ MLE = 0.999  0.845–1.168  −147.301  298.689 0.373 1.467 
 ExpB  λ MLE = 0.948  0.780–1.130  −145.877  297.922 0.548 
 PL  µ MLE = 4.347  3.835–4.917  −153.808  311.704 0.001 982.967 
 PLB  µ MLE = 3.779  3.150–4.441  −147.823  301.814 0.078 
 Protein       
 Exp  λ MLE = 1.102  0.920–1.307  −112.823  229.744 0.188 2.964 
 ExpB  λ MLE = 1.083  0.892–1.293  −112.460  231.119 0.094 5.896 
 PL  µ MLE = 4.740  4.122–5.435  −112.966  230.030 0.162 3.421 
 PLB  µ MLE = 4.421  3.711–5.183  −110.686  227.571 0.556 

Maximum likelihood estimates (MLEs) of function exponents were calculated according to Edwards et al. (2007) and Edwards (2011) ; the log-likelihood of the estimate is also given. 95% confidence intervals (CI) were obtained with the profile likelihood-ratio test ( Hilborn and Mangel 1997 ). Calculation of AICc, AIC weight, and evidence ratio follows Burnham and Anderson (2002) . The tail end of the segment length distribution starts at a = 2.6 m for both groups (carbohydrates: n = 147, protein: n = 125). Exp = exponential, ExpB = bounded exponential, PL = power law, PLB = bounded power law.

In order to further test for the existence of a heavy-tailed Lévy walk, separate models are also fit to the tail end of the segment length distribution. Here it is not possible to choose between the different types of models, as there is an almost equal amount of evidence for both exponential and power models ( Table 1 ). Nevertheless, the slope estimates of all power models and their 95% confidence intervals are outside the range of Lévy walks, where 1 < µ ≤ 3 ( Viswanathan et al. 1999 ). In this, Melophorus differs from honeybees, which have been shown to use a Lévy strategy to locate a food source ( Reynolds et al. 2007b ). This difference may, however, be due to differences in experimental procedure: while Reynolds et al. (2007b) tested the bees in an almost featureless open field, our ants were tested in their natural visual surrounding which is cluttered with visual features. It is possible that a systematic search aided by visual navigation and path integration rules out Lévy patterns. Also, the mechanism giving rise to Lévy movements in airborne honeybees may not operate in ants that walk over rough ground.

In conclusion, our study shows that M. bagoti foragers search differently for different food types. Although food distribution was identical for both groups, searches for carbohydrates were more concentrated than for protein, and the approach path to carbohydrates was much straighter. This predisposition of behavior is matched to the natural distribution patterns of food items, as carbohydrate food sources are constant in space and renewable, whereas protein food sources are not. As all foragers had at least 2 days of experience of the experimental food source, the differences in searching behavior are likely to be based on an intrinsic mechanism, and are not due to individually different foraging experience. Our analyses further show that the observed differences between the groups are not a result of the use of different intrinsic movement strategies. Foragers in both groups displayed strategies that are based on exponential distributions, similar to a Brownian walk; there is no evidence for the use of Lévy walks in either group. Although we suggest that differences are due to a decreased learning effort in protein foragers, the details remain to be investigated.

Supplementary Material

Supplementary material can be found at http://www.beheco.oxfordjournals.org/

Funding

This work was supported by a graduate scholarship from Macquarie University to P.S. and the Australian Research Council (grant number DP110100608 to K.C).

Acknowledgments

We thank CSIRO Ecosystem Sciences Alice Springs and the Centre for Appropriate Technology (CAT) for providing field facilities. We are also grateful to Andrew Allen for statistical support.

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