Optimal foraging in bumblebees: Hunting by expectation

The foraging behaviour literature contains three hypotheses concerned with hunting by expectation. These suggest possible rules animals use to decide when to leave particular feeding sites and search in other places for food. Predictions of the three hypotheses were tested experimentally by varying the quality of plants (amount and distribution of nectar) encountered by bumblebees (Bombus appositus). Results support only a rate expectation hypothesis. Bees left multiflowered plants when the amount of nectar found in the first flower was below a threshold volume. Bees stayed on plants if they received greater than the threshold volume. This threshold nectar volume is close to the amount predicted if a bee forages to maximize its rate of net energy intake.     

Optimal diving behaviour for foraging in relation to body size

Overall, large animals dive longer and deeper than small animals; however, after the difference in body size is taken into account, smaller divers often tend to make relatively longer dives. Neither physiological nor theoretical explanations have been provided for this paradox. This paper develops an optimal foraging diving model to demonstrate the effect of body size on diving behaviour, and discusses optimal diving behaviour in relation to body size. The general features of the results are: (1) smaller divers should rely more heavily on anaerobic respiration, (2) larger divers should not always make longer dives than smaller divers, and (3) an optimal body size exists for each diving depth. These results explain the relatively greater diving ability observed in smaller divers, and suggest that if the vertical distribution of prey in the water column is patchy, there is opportunity for a population of diving animals to occupy habitat niches related to body size.     

Optimal foraging constrains macroecological patterns: body size and dietary niche breadth in lizards

Aim  To explore and identify probable mechanisms contributing to the relationships among body size, dietary niche breadth and mean, minimum, maximum and range of prey size in predaceous lizards.
Location  Our data set includes species from tropical rainforests, semi-arid regions of Brazil, and from deserts of the south-western United States, Australia and the Kalahari of Africa.
Methods  We calculated phylogenetic and non-phylogenetic regressions among predator body size, dietary breath and various prey size measures.
Results  We found a negative association between body size and dietary niche breadth in 159 lizard species sampled across most evolutionary lineages of squamate reptiles and across major continents and habitats. We also show that mean, minimum, maximum and range of prey size were positively associated with body size.
Main conclusions  Our results suggest not only that larger lizards tend to eat larger prey, but in doing so offset their use of smaller prey. Reduction of dietary niche breadth with increased body size in these lizards suggests that large predators target large and more profitable prey. Consequently, the negative association between body size and niche breadth in predators most likely results from optimal foraging. Though this result may appear paradoxical and runs counter to previous studies, resources for predators may be predictably more limited than resources for herbivores, thus driving selection for more profitable prey.     

Optimal foraging by the swallow (Hirundo rustica, L): Prey size selection

The foraging ecology of the swallow (Hirundo rustica) was investigated in the field and compared with predictions of optimal foraging theory. Prey items were selected primarily by size. The inclusion of an item in the diet depended on the absolute abundance of the high-ranking prey and not of the low-ranking ones. Small items of low profitability were, however, included when food was abundant and more small items were taken when they were relatively abundant. Energetics data are used to show that it is profitable in terms of net energy gain for the swallow to take a mixture of large and small items, whereas optimal foraging theory would predict exclusive specialization on large, high-ranking items. Other possible explanations for the inclusion of small items in the diet are discussed.     

Optimal foraging: Random movement by pollen collecting bumblebees

Summary Two bumblebee species, Bombus bifarius and B. flavifrons, forage randomly with respect to direction when gathering pollen on Potentilla gracilis. Bees avoid revisiting flowers by being able to differentiate recently visited from unvisited flowers. This recognition occurs while bees are flying over open flowers and appears to be a response to the amount of available pollen within flowers. Random foraging with respect to direction is the optimal strategy when the probability of flower revisitation is low. Bumblebees appear to be moving preferentially between nearest neighbors, again as predicted by foraging theory. This behavior causes the establishment of pollen patches in the P. gracilis population. Unlike other pollinators studied in similar situations, bumblebees on P. gracilis do not forage utilizing an area-restricted searching behavior. Because floral reward quality can be assessed at low cost by bees foraging on P. gracilis, their tendency to move to nearby flowers even after encountering a poor quality blossom apparently yields a higher rate of net energy intake than does area-restricted searching. The data indicate that bumblebees exhibit great plasticity in foraging behavior and that they are able to forage efficiently under a wide range of environmental conditions.     

Optimal foraging: food patch depletion by ruddy ducks

Summary I studied the foraging behavior of ruddy ducks (Oxyura jamaicensis) feeding on patchily distributed prey in a large (5-m long, 2-m wide, and up to 2-m deep) aquarium. The substrate consisted of a 4x4 array of wooden trays (1.0-m long, 0.5-m wide, and 0.1-m deep) which contained 6 cm of sand. Any tray could be removed from the aquarium and loaded with a known number of prey. One bird foraged in the aquarium at a time; thus, by removing a food tray after a trial ended and counting the remaining prey, I calculated the number of prey consumed by the bird. I designed several experiments to determine if ruddy ducks abandoned a food patch in a manner consistent with the predictions of a simple, deterministic, patch depletion model. This model is based on the premise that a predator should maximize its rate of net energy intake while foraging. To accomplish this, a predator should only remain in a food patch as long as its rate of energy intake from that patch exceeds the average rate of intake from the environment. In the majority of comparisons, the number of food items consumed by the ruddy ducks in these experiments was consistent with the predictions of the foraging model. When the birds did not forage as predicted by the model, they stayed in the patch longer and consumed more prey than predicted by the model. An examination of the relation between rate of net energy intake and time spent foraging in the food patch indicated that by staying in a patch longer than predicted, the ruddy ducks experienced only a small deviation from maximum rate of net energy intake. These results provided quantitative support for the prediction that ruddy ducks maximize their rate of net energy intake while foraging.     

Prey selection by plovers: Optimal foraging in mixed-species groups

Prey (earthworm) size selection was investigated in lapwings (Vanellus vanellus) and golden plovers (Pluvialis apricaria) feeding in mixed species flocks and compared with that predicted by an optimal foraging model based on energy intake. As well as the usual constraints of searching and handling time, our model incorporated the difficulty of capturing concealed prey, the orientation time needed to locate prey and the risk of theft by gulls (Larus ridibundus). When costs were taken into account, small worms turned out to be the most profitable. The relative profitability of size classes changed when gulls were present and birds shifted their intake accordingly so that they always took mainly the most profitable worms. Birds were expected to do best by taking the three most profitable size classes and the size range taken was consistent with this. In addition there was an inverse relationship between the probabilities of taking profitable and unprofitable worm sizes. Observations of birds were supported by field enclosure experiments which prevented birds feeding in certain areas. Departures from predictions of the model are interpreted as sampling errors due to birds using depth as an approximate indicator of worm size.     

Optimal foraging versus shared doom effects: interactive influence of mussel size and epibiosis on predator preference

In the western Baltic Sea, the highly competitive blue mussel Mytilus edulis tends to monopolize shallow water hard substrata. In many habitats, mussel dominance is mainly controlled by the generalist predator Carcinus maenas. These predator-prey interactions seem to be affected by mussel size (relative to crab size) and mussel epibionts.There is a clear relationship between prey size and predator size as suggested by the optimal foraging theory: Each crab size class preferentially preys on a certain mussel size class. Preferred prey size increases with crab size.Epibionts on Mytilus, however, influence this simple pattern of feeding preferences by crabs. When offered similarly sized mussels, crabs prefer Balanus-fouled mussels over clean mussels. There is, however, a hierarchy of factors: the influence of attractive epibiotic barnacles is weaker than the factor ‘mussel size’. Testing small mussels against large mussels, presence or absence of epibiotic barnacles does not significantly alter preferences caused by mussel size. Balanus enhanced crab predation on mussels in two ways: Additional food gain and, probably more important, improvement in handling of the prey. The latter effect is illustrated by the fact that artificial barnacle mimics increased crab predation on mussels to the same extent as do live barnacles.We conclude that crab predation preferences follows the optimal foraging model when prey belong to different size classes, whereas within size classes crab preferences is controlled by epibionts.     

Optimal foraging by bacteriophages through host avoidance

Optimal foraging theory explains diet restriction as an adaptation to best utilize an array of foods differing in quality, the poorest items not worth the lost opportunity of finding better ones. Although optimal foraging has traditionally been applied to animal behavior, the model is easily applied to viral host range, which is genetically determined. The usual perspective for bacteriophages (bacterial viruses) is that expanding host range is always advantageous if fitness on former hosts is not compromised. However, foraging theory identifies conditions favoring avoidance of poor hosts even if larger host ranges have no intrinsic costs. Bacteriophage T7 rapidly evolved to discriminate among different Escherichia coli strains when one host strain was engineered to kill infecting phages but the other remained productive. After modifying bacteria to yield more subtle fitness effects on T7, we tested qualitative predictions of optimal foraging theory by competing broad and narrow host range phages against each other. Consistent with the foraging model, diet restriction was favored when good hosts were common or there was a large difference in host quality. Contrary to the model, the direction of selection was affected by the density of poor hosts because being able to discriminate was costly.     

Optimal foraging by zooplankton within patches: the case of Daphnia

The motions of many physical particles as well as living creatures are mediated by random influences or 'noise'. One might expect that over evolutionary time scales internal random processes found in living systems display characteristics that maximize fitness. Here we focus on animal random search strategies [G.M. Viswanathan, S.V. Buldyrev, S. Havlin, M.G.E. Da Luz, E.P. Raposo, H.E. Stanley, Optimizing the success of random searches, Nature 401 (1999) 911-914; F. Bartumeus, J. Catalan, U.L. Fulco, M.L. Lyra, G.M. Viswanathan, Optimizing the encounter rate in biological interactions: Lévy versus Brownian stratagies, Phys. Rev. Lett. 88 (2002) 097901 and 89 (2002) 109902], and we describe experiments with the following Daphnia species: D. magna, D. galeata, D. lumholtzi, D. pulicaria, and D. pulex. We observe that the animals, while foraging for food, choose turning angles from distributions that can be described by exponential functions with a range of widths. This observation leads us to speculate and test the notion that this characteristic distribution of turning angles evolved in order to enhance survival. In the case of theoretical agents, some form of randomness is often introduced into search algorithms, especially when information regarding the sought object(s) is incomplete or even misleading. In the case of living animals, many studies have focused on search strategies that involve randomness [H.C. Berg, Random Walks in Biology, Princeton University, Princeton, New Jersey, 1993; A. Okubo, S.A. Levin (Eds.), Diffusion and Ecological Problems: Modern Perspectives, second ed., Springer, New York, 2001]. A simple theory based on stochastic differential equations of the motion backed up by a simulation shows that the collection of material (information, energy, food, supplies, etc.) by an agent executing Brownian-type hopping motions is optimized while foraging for a finite time in a supply patch of limited spatial size if the agent chooses turning angles taken from an exponential distribution with a specific stochastic intensity or 'noise width'. Search strategies that lead to optimization is a topic of high current interest across many disciplines [D. Wolpert, W. MacReady, No free lunch theorems for optimization, IEEE Transactions on Evolutionary Computation 1 (1997) 67].     

Optimal foraging on perilous prey: risk of bill damage reduces optimal prey size in oystercatchers

Intake rate maximization alone is not always sufficient in explainingprey size selection in predators. For example, bivalve-feedingoystercatchers regularly select smaller prey than expected ifthey aimed to maximize their intake rate. It has been proposedthat to these birds large prey are "risky," in the sense thatbirds may damage their bills when feeding on large bivalves.Large bivalves yield more energy, but according to this hypothesisthis is achieved at the expense of energy yield in the longterm when (1) the risk of bill damage increases with prey sizeand (2) foraging with a damaged bill is less effective. In accordancewith this hypothesis, we show that captive oystercatchers feedingon large cockles experienced a high probability of bill tipdamage, while bill damage was absent when cockles were small.Moreover, among free-living oystercatchers the prevalence ofbill damage was correlated with mean cockle size near the capturesite, and the data on captive birds fit in this pattern. Foodintake of captive oystercatchers feeding exclusively on cockleswas reduced by 23% after bill damage, and free-living birdswith damaged bills had 14 g lower mass. Because lower body masswas associated with higher mortality probability, these resultsindicate long-term costs associated with feeding on large cockles.We conclude that the risk of bill damage can potentially explainwhy oystercatchers avoid large bivalves and that oystercatchersmay maximize long-term intake rate by selecting prey sizes thatare "suboptimal" from a short-term rate-maximizing point ofview.     

Composition of organic matter in particle size fractionated pig slurry

Pig slurry is a heterogeneous mixture of different particle sizes that will have different mobility in soil. Therefore, a physically fractionated pig slurry sample was analysed, e.g. using pyrolysis-field ionisation mass spectrometry (Py-FIMS) in an effort to identify relationships between particle size and composition of organic matter. The presumably most mobile fractions in soils (<63 μm) accounted for ≈50% of slurry dry matter and were dominated by lignins, and N-containing compounds. Sterols were especially abundant in the larger-sized fractions, which corresponds to their reported distribution in soils and surface waters. The averaged molecular masses indicated similarities of fractions <10 μm to aquatic humic substances and increasing content of plant material with increasing particle size. A statistical analysis of the compound class distribution revealed that the analysis of three particle size fractions is essential for the assessment of the composition and properties of slurry constituents.     

Non-phagocytic uptake of intravenously injected microspheres in rat spleen: influence of particle size and hydrophilic coating

A recent development in prolonging the circulation time of drug carriers, such as liposomes and microspheres, has been to minimize their removal by macrophages of the reticuloendothelial system by covering their surface with hydrophilic polymers such as poloxamers, poloxamines and poly(ethyleneglycols). Here we demonstrate that this strategy may not necessarily prolong the circulatory half-life of drug carriers in all animal models. In rats, as opposed to rabbits, a non-phagocytic mechanism in the spleen may be triggered to remove efficiently from the blood drug carriers coated with hydrophilic coatings. Both the size of particle and its hydrophilic coating may act synergistically to trigger this non-phagocytic mechanism. In rats, a remarkable log to log relationship between particle size and spleen uptake was observed for both uncoated and polymeric coated microspheres. The potential implication of these observations in site-specific delivery of drug carriers is discussed.     

The utilization of organic matter in shallow marine sediments by an epibenthic deposit-feeding holothurian

The utilization of organic matter and constituent food items in shallow marine sediments by Parastichopus parvimensis (Clark), an epibenthic deposit-feeding holothurian, has been investigated.Organic matter ingested from sediments of varying organic content was used by P. parvimensis with 22 % efficiency. In experiments with ¹⁴C labelled food all microorganisms associated with both plant detritus and decomposed matter of animal origin were used with over 40 % efficiency. Species of fresh brown, red, green, and blue-green algae were not assimilated. Detritus derived from the brown alga Dictyopteris zonarioides (Farlow) was used with a low efficiency while detritus from red and green algae was not assimilated. These results indicate that P. parvimensis does not utilize the large energy reserve available as plant detritus in near shore bottom habitats off Santa Catalina Island before to its decomposition by bacteria and fungi.     

Optimal foraging and the traveling salesman

Optimal foraging models are examined that assume animals forage for discrete point resources on a plane and attempt to minimize their travel distance between resources. This problem is similar to the well-known traveling salesman problem: A salesman must choose the shortest path from his home office to all cities on his itinerary and back to his home office again. The traveling salesman problem is in a class of enigmatic problems, called NP-complete, which can be so difficult to solve that animals might be incapable of finding the best solution. Two major results of this analysis are: (1) The simple foraging strategy of always moving to the closest resource site does surprisingly well. More sophisticated strategies of “looking ahead” a small number of steps, choosing the shortest path, then taking a step, do worse if all the resource sites are visited, but do slightly better (less than 10%) if not all the resource sites are visited. (2) Short cyclical foraging routes resulted when resources were allowed to renew. This is suggested as an alternative explanation for “trap-lining” in animals that forage for discrete, widely separated resources.     

Optimal intraguild foraging and population stability

This article explores effects of adaptive intraguild predation on species coexistence and community structure in three species' food webs. Two Lotka-Volterra models that assume a trade-off between competition and predation strength are considered in detail. The first model does not explicitly model resource dynamics and is considered with both nonadaptive and adaptive intraguild predation; in the latter case predators choose their diet in order to maximize their instantaneous population growth rate. The second model includes resource population dynamics. Effects of adaptive intraguild predation on the community structure along a gradient in environment productivity are analyzed and compared with some experimental results of protist food webs. Conditions under which intraguild predation is adaptive are discussed for both models. It is proved that if intraguild predators are perfect optimizers then intraguild predation should decrease with increasing environmental productivity and adaptive intraguild predation is a stabilizing factor provided environmental productivity is high enough.     

Optimal foraging and ontogeny; food selection by Haplochromis piceatus

Summary We examined the influence of satiation level, prey density and light intensity on food uptake rate through the ontogeny of Haplochromis piceatus. Prey handling in the buccal cavity was found to be the main factor limiting prey uptake rate under light circumstances and at a sufficiently high prey density. Food uptake rate per unit body weight of different sizes of H. piceatus was equal when feeding on Chaoborus but decreased with increasing fish size when feeding on Daphnia magna. In choice experiments with Chaoborus and D. magna, prey selection by H. piceatus of all sizes was according to the predictions based on Charnov's 1976 model.