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 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.     

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.     

Optimal foraging of a herbivorous lizard,the green iguana in a seasonal environment

Food selection was studied in free living green iguanas (Iguana iguana) throughout the year in a semiarid environment, Curaçao (Netherlands Antilles). Food intake was determined by direct observations and converted into biomass intake. Comparison between intake and biomass availability of the various food items revealed that the lizards were selective, and that changes in seasonal food availability led to periodic switching of food plants. The extent to which nutrient constraints determine iguana feeding ecology was investigated. Potential constraints were the requirements for water, digestible crude protein, and metabolizable energy. By using a linear programming model that incorporates characteristics of the food (chemical composition, energy content, item size) and requirements and constraints of the green iguanas (nutrient and energy requirements digestive tract capacity, feeding rate) it was possible to identify which factors determine food choice over the year. During the dry period, when the iguanas had no access to drinking water they consumed flowers to increase water intake, though the amount of flowers consumed was too low to cover maintenance requirements for either energy or protein. After the young leaf flush, following the early rains in May, the biomass increased, free surface water was available during showers, and the linear programming solutions indicate that food selection conformed to the protein maximization criterion. Reproduction in green iguanas shows an annual cycle, in which oviposition takes place at the end of the dry season, when intake is below maintenance levels. Females show a 8–10 month gap between acquisition of most of the protein required for egg synthesis and the act of laying. Thus, as in avian and mammalian herbivores, food availability during a period prior to the energy and protein demanding reproductive season of iguanas determines reproductive success.     

Optimal foraging and fitness in Columbian ground squirrels

Summary Optimal diets were determined for each of 109 individual Columbian ground squirrels (Spermophilus columbianus) at two sites in northwestern Montana. Body mass, daily activity time, and vegetation consumption rates for individuals were measured in the field, along with the average water content of vegetation at each ground squirrel colony. I also measured stomach and caecal capacity and turnover rate of plant food through the digestive tract for individuals in the laboratory to construct regressions of digestive capacity as a function of individual body mass. Finally, I obtained literature estimates of average daily energy requirements as a function of body mass and digestible energy content of vegetation. These data were used to construct a linear programming diet model for each individual. The model for each individual was used to predict the proportion of two food types (monocots and dicots) that maximized daily energy intake, given time and digestive constraints on foraging. Individuals were classified as optimal or deviating, depending on whether their observed diet was significantly different from their predicted optimal diet. I determined the consequences of selecting an optimal diet for energy intake and fitness. As expected, daily energy intake calculated for deviators (based on their observed diet proportion) was less than that for optimal foragers. Deviating foragers do not appear to compensate for their lower calculated energy intake through other factors such as body size or physiological efficiency of processing food. Growth rate, yearly survivorship, and litter size increase with calculated energy intake, and optimal foragers have six times the reproductive success of deviators by age three. Optimal foraging behavior, therefore, appears to confer a considerable fitness advantage.     

Optimal foraging and community structure: implications for a guild of generalist grassland herbivores

Summary A particular linear programming model is constructed to predict the diets of each of 14 species of generalist herbivores at the National Bison Range, Montana. The herbivores have body masses ranging over seven orders of magnitude and belonging to two major taxa: insects and mammals. The linear programming model has three feeding constraints: digestive capacity, feeding time and energy requirements. A foraging strategy that maximizes daily energy intake agrees very well with the observed diets. Body size appears to be an underlying determinant of the foraging parameters leading to diet selection. Species that possess digestive capacity and feeding time constraints which approach each other in magnitude have the most generalized diets. The degree that the linear programming models change their diet predictions with a given percent change in parameter values (sensitivity) may reflect the observed ability of the species to vary their diets. In particular, the species which show the most diet variability are those whose diets tend to be balanced between monocots and dicots. The community-ecological parameters of herbivore body-size ranges and species number can possibly be related to foraging behavior.     

Optimal and central-place foraging theory applied to a desert harvester ant,Pogonomyrmex californicus

Summary Certain predictions of optimal- and central place-foraging theory were tested on the desert harvester ant, Pogonomyrmex californicus. Colonies were offered three different sizes of oat seed and found to maximize net energy intake (ei) over time (t _i ) by harvesting the seed sizes with the highest e _i /t _i rank. Two aspects of t _i were measured that were assumed constant in previous studies. The handling components of t _i (time required to manipulate the seed and travel time back to the colony with the food) were measured and found to be positively correlated with seed size. The manipulation success rate (the percentage of handled seeds successfully picked up) decreased with increased seed size. These results point out how important it is to measure all parameters of e _i /t _i rather than to assume constancy with both prey type and foraging distance. The relative abundance of less preferred food types was important in determining the proportion of preferred types in the diet. The food supply of eight colonies was manipulated experimentally over a 25-day period. Four deprived colonies were constrained within aluminum enclosures to prevented foraging. The remaining four satiated colonies were given food ad libitum. The niche breadths of the treated colonies were then compared to controls, but found not to differ significantly. Seed baits were offered at three distances from the colony to test whether selectivity increased with disance. Contrary to theoretical predictions, all colonies harcested about the same proportion of each seed size at each distance.     

Positive complexity-stability relations in food web models without foraging adaptation

May's [1972. Will a large complex system be stable? Nature 238, 413-414] local stability analysis of random food web models showed that increasing network complexity leads to decreasing stability, a result that is contradictory to earlier empirical findings. Since this seminal work, research of complexity-stability relations became one of the most challenging issues in theoretical ecology. We investigate conditions for positive complexity-stability relations in the niche, cascade, nested hierarchy, and random models by evaluating the network robustness, i.e., the fraction of surviving species after population dynamics. We find that positive relations between robustness and complexity can be obtained when resources are large, Holling II functional response is used and interaction strengths are weighted with the number of prey species, in order to take foraging efforts into account. In order to obtain these results, no foraging dynamics needs to be included. However, the niche model does not show positive complexity-stability relations under these conditions. By comparing to empirical food web data, we show that the niche model has unrealistic distributions of predator numbers. When this distribution is randomized, positive complexity-stability relations can be found also in the niche model.     

Optimal central-place foraging by beavers: Tree-size selection in relation to defensive chemicals of quaking aspen

Summary At a newly occupied pond, beavers preferentially felled aspen smaller than 7.5 cm in diameter and selected against larger size classes. After one year of cutting, 10% of the aspen had been cut and 14% of the living aspen exhibited the juvenile growth form. A phenolic compound which may act as a deterrent to beavers was found in low concentrations in aspen bark, and there was no significant regression of relative concentration of this compound on tree diameter. At a pond which had been intermittently occupied by beavers for over 20 years, beavers selected against aspen smaller than 4.5 cm in diameter, and selected in favor of aspen larger than 19.5 cm in diameter. After more than 28 years of cutting at this site, 51% of the aspen had been cut and 49% of the living aspen were juvenileform. The phenolic compound was found in significantly higher concentrations in aspen bark than at the newly occupied site, and there was a significant negative regression of relative concentration on tree diameter. The results of this study show that responses to browsing by trees place constraints on the predictive value of standard energy-based optimal foraging models, and limitations on the use of such models. Future models should attempt to account for inducible responses of plants to damage and increases in concentrations of secondary metabolites through time.     

Specializations and limitations in the utilization of food resources by the carp,Cyprinus carpio: a study of oral food processing

Synopsis The wide variety of aquatic food is considered to be instrumental for the diversification in fish species. Yet their abilities and inabilities of handling food are poorly known. For these reasons the food processing and feeding repertoire of the adult carp, Cyprinus carpio, fed on a variety of food types, were analyzed by light and X-ray cinematography of the head parts and by electromyography of the head and body muscles during feeding. Nine stereotyped movement patterns (particulate intake, gulping, rinsing, spitting, selective retention of food, transport, crushing, grinding and deglutition) compose the feeding process, their sequence and frequency were adjusted to the type of food. Following quantitative morphological analysis at macroscopic, light- and electronmicroscopical level, the relations between the functioning and architecture of the feeding apparatus were established. The structure and dimensions of the mouth opening, the protrusible upper jaw, the slit-shaped pharyngeal cavity, the palatal and postlingual organ, the branchial sieve, the pharyngeal masticatory apparatus and the distribution of taste buds, mucous cells and muscle fibers along the oropharyngeal surface were the directive structural characters used for estimating the abilities in food processing. The specializations for utilizing food items and its limitations, derived from structural and functional data, are compared with diet data found in the literature in order to evaluate the relative position of the carp in competition for food in the aquatic environment. It is established that the ‘omnivorous’ carp is specialized in effective handling of several categories of aquatic food, even when these are mixed with non-food (bottom invertebrates <4% SL in diameter) since the palatal organ enables the carp to separate food from non-food. This includes very hard-skinned food items, processed with the powerful pharyngeal jaws of the fish, and to a lesser extent zooplankton (>250 μm). The carp is at the same time very limited in processing long and struggling prey (e.g. fish) as well as vegetable matter, due to the lack of oral teeth and the specialized morphology of its pharyngeal chewing apparatus. These feeding abilities agree with diet data from literature. The reported herbivorism of carp illustrates its opportunism in feeding behaviour. Specialization in feeding is discussed and the necessity to take into account the total series of post-capture feeding actions for a more complete view on trophic specialization. Food intake and the intra-oral food processing of carp are bound to the structures of its sensory, central processing and effector apparatus and to the plasticity in their functioning. These together determine its feeding efficiency in exploiting the available aquatic food resources. Next to ethological and ecological studies functional morphology is another important tool to explain the trophic interactions of fish.     

Optimal foraging and community structure: The allometry of herbivore food selection and competition

I address the selection of plants with different characteristics by herbivores of different body sizes by incorporating allometric relationships for herbivore foraging into optimal foraging models developed for herbivores. Herbivores may use two criteria in maximizing their nutritional intake when confronted with a range of food resources: a minimum digestibility and a minimum cropping rate. Minimum digestibility should depend on plant chemical characteristics and minimum cropping rate should depend on the density of plant items and their size (mass). If herbivores do select for these plant characteristics, then herbivores of different body sizes should select different ranges of these characteristics due to allometric relationships in digestive physiology, cropping ability and nutritional demands. This selectivity follows a regular pattern such that a herbivore of each body size can exclusively utilize some plants, while it must share other plants with herbivores of other body sizes. I empirically test this hypothesis of herbivore diet selectivity and the pattern of resource use that it produces in the field and experimentally. The findings have important implications for competition among herbivores and their population and community ecology. Furthermore, the results may have general applicability to other types of foragers, with general implications for how biodiversity is influenced.     

Slug foraging behaviour: Attraction to food items from a distance

Slug foraging paths recorded using time lapse video techniques under infra-red light were fitted to a correlated random walk model. Analyses were carried out on slugs in arenas where no food was present, as well as those containing commercial molluscicides at two rates of application. Slugs were found to search randomly in empty arenas and those containing commercial metaldehyde baits, but deviated from random search patterns when in the presence of commercial methiocarb bait. Differential attraction from a distance is suggested as a cause of these differences.     

Predicting synergistic effects of resources and predators on foraging decisions by juvenile Steller sea lions

Many theoretical and experimental studies suggest that synergistic interactions between resources and predators influence foraging decisions and their fitness consequences. This framework, however, has been ignored almost completely by hypotheses on causes of the population decline of Steller sea lions (SSLs) (Eumetopias jubatus) in western Alaska. By comparing predictions from a dynamic state variable model to empirical data on the behaviour of individuals instrumented with satellite-linked time-at-depth recorders, we develop and find preliminary support for the hypothesis that, during winter in Prince William Sound, juvenile SSLs (a) underutilise walleye pollock, a predictable resource in deep strata, due to predation risk from Pacific sleeper sharks, and (b) underutilise the potential energy bonanza of inshore aggregations of Pacific herring due to risk from either killer whales, larger conspecifics, or both. Further, under conditions of resource scarcity—induced by overfishing, long-term oceanographic cycles, or their combination—trade-offs between mortality risk and energy gain may influence demographic parameters. Accordingly, computer simulations illustrated the theoretical plausibility that a decline of Pacific herring in shallow strata would greatly increase the number of deep foraging dives, thereby increasing exposure to sleeper sharks and mortality rates. These results suggest that hypotheses on the decline of SSLs should consider synergistic effects of predators and resources on behaviour and mortality rates. Empirical support for our model, however, is limited and we outline tasks for empirical research that emerge from these limitations. More generally, in the context of today’s conservation crises, our work illustrates that the greater the dearth of system-specific data, the greater the need to apply principles of behavioural ecology toward the understanding and management of large-scale marine systems. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Food selection of semifree common marmosets (Callithrix jacchus): Indications for optimal foraging

In this investigation a group of common marmosets (Callithrix jacchus) consisting of two parents and their six progeny of various ages were allowed free access to an open-air enclosure, which was equipped with a heated hut, roofed veranda, external cage, and a runway system made of roofing slats and a few small trees. Feeding places, sitting boards and sleeping boxes were distributed throughout the whole area. This investigation covered a total of 254 hours of observation. The hut and its immediate vicinity can be considered as being the core area of the home-range, as the maximum frequencies of both feeding and location occurred there. Through the experimental variation in the type of foods provided at specific feeding places, it was obvious that the closeness of the feeding place to the hut was more important to the marmosets than the type of food placed there. The marmosets apparently reduced the energy output when searching for food by minimizing the distance to the food patches.     

Expression of conditioned preference for low-quality food in sheep is modulated by foraging costs

Past positive experiences can increase herbivores’ motivation to eat low-quality foods. However, this is not always translated into a higher preference for low-quality foods in choice tests among foods of higher nutritional quality. Foraging behavior is also affected by properties of the feeding context because the quality and abundance of foods in nature change in time and space. We hypothesized that in a choice situation, the expression of a past positive experience with a low-quality food is modulated by the costs associated with selecting a high-quality food option. A total of 24 sheep were randomly assigned into two groups (n=12). During conditioning phase, one group (CS+; i.e., conditioned group) was fed with oat hay (a low-quality food) for 20 min and immediately after a ration of soybean meal (a nutritious food), whereas the other group was also fed with oat hay but the offer of soybean meal was delayed 5 h (CS−; i.e., control group). After conditioning, we assessed sheep motivation to eat the oat hay in an experimental arena in which accessibility to alfalfa hay (a high-quality food) was increasingly restricted. When alfalfa hay was readily accessible, CS+ and CS− sheep almost exclusively selected this food, showing a small and similar preference for oat hay. However, when accessibility to alfalfa hay decreased, intake and selection of oat hay was greater in the CS+ sheep than in the CS− sheep. The latter was a consequence of differential changes in behavior between groups; for example, sheep in CS+ spent more time foraging oat hay and were more likely to switch to oat hay if they had previously been eating alfalfa hay than sheep in CS−. Our results show that behavioral expression of the conditioned preference for a low-quality food depends on parameters of the feeding context (e.g., availability). We suggest that this can be the link between learning models and optimal foraging models of diet selection.     

Optimal foraging and intraspecific diet differences in the lizard Cnemidophorus sexlineatus

Summary Previous studies have shown that adult and juvenile six-lined racerunners, Cnemidophorus sexlineatus, consume different sizes and taxa of arthropod prey. the purpose of this study was to determine if these differences could be explained in terms of energy cost and benefit parameters as related by the optimal diet model. Handling times and encounter rates with each of five categories of prey were determined by direct observation of lizard foraging behavior in the field. Energetic cost of search and energy content of prey were estimated from data in the literature. Mean values of all these parameters were used in the classic optimal diet model to determine which prey types yield the greatest rate of net energy gain for adult and juvenile racerunners. Grasshopper-like insects were the most valuable prey for adults, whereas plant and ground arthropods were the most valuable prey for juveniles. These findings correspond to the age-class specific diet differences.Each age-class adopts foraging tactics that increase the chance of finding the most valuable prey. Adult racerunners move hastily over a large area to find the relatively rare, but large and mobile grasshopper prey. Juveniles move much more slowly, and carefully investigate twigs and leaves to find smaller, cryptic plant and ground arthropods. However these foraging tactics do not preclude the taking of less valuable prey items, should they be encountered. This is because it is energetically better on average to eat the prey item rather than skipping it to search for better prey, except for the case of juvenile racerunners eating grasshoppers. That juvenile racerunners will attempt to capture and consume even very large grasshoppers is contrary to the expectations derived from the optimal diet model. This behavior may be the result of the foraging rule of thumb racerunners use to find their prey.     

Seasonal and spatial shifts in copepod diets within tropical estuaries measured by fatty acid profiles

Fatty acids are the main components of lipids and are necessary for the production and permeability of cell membranes, playing an essential role in the physiological responses of organisms. The biochemical composition of zooplankton might be used as bio-indicators of the trophic status of aquatic ecosystems. Aiming to fill the gap of knowledge in tropical estuaries, the main aim of this study was to test if the fatty acid profiles can reveal spatial and temporal shifts in the diet of copepods and therefore can be used as indicators of the trophic status of estuarine systems. We investigated the fatty acids composition of copepod species and their possible food sources along the salinity gradient of two tropical estuaries (Paraíba do Norte and Mamanguape estuaries, northeastern Brazil), during the rainy and dry seasons. We found clear seasonal differences regarding fatty acids composition and concentration in copepods, with maximal concentrations and diversity of total fatty acids during the rainy season. The copepods species were mainly carnivorous in the dry season and omnivorous in the rainy season and, in both estuaries, the diet of most copepods was dependent on food availability. The fatty acid profiles suggest that, in general, feeding patterns of zooplankton change spatially and temporally, reflecting the shifts in their food sources abundance (i.e., dominance among diatoms and flagellates, terrestrial detritus and small animals). We observed a residual proportion of terrestrial detritus and green algae in the diets and these items were only present in the dry season. Furthermore, the food sources in the Paraiba do Norte estuary, a system with high levels of anthropogenic disturbance, showed lower feeding quality, with lower essential fatty acids concentrations. Our study showed that fatty acid profiles can be used as ecological indicator to assess seasonal and spatial shifts in the trophic ecology of copepods in tropical estuaries and to distinguish systems with different levels of human impact in a fast and accurate way.     

Predicting trophic relations in ecological networks: A test of the Allometric Diet Breadth Model

Few food web theory hypotheses/predictions can be readily tested using likelihoods of reproducing the data. Simple probabilistic models for food web structure, however, are an exception as their likelihoods were recently derived. Here I test the performance of a more complex model for food web structure that is grounded in the allometric scaling of interactions with body size and the theory of optimal foraging (Allometric Diet Breadth Model—ADBM). This deterministic model has been evaluated by measuring the fraction of trophic relations it correctly predicts. I contrasted this value with that produced by simpler models based on body sizes and found that the quantitative information on allometric scaling and optimal foraging does not significantly increase model fit. Also, I present a method to compute the p-value for the fraction of trophic interactions correctly predicted by the ADBM, or any other model, with respect to three probabilistic models. I find that the ADBM predicts significantly more links than random graphs, but other models can outperform it. Although optimal foraging and allometric scaling may improve our understanding of food webs, the ADBM needs to be modified or replaced to find support in the data.     

Growth and development of Calanus chilensis nauplii reared under laboratory conditions: testing the effects of temperature and food resources

We assessed growth and development of naupliar stages of Calanus chilensis Brodsky 1959, under a combination of three temperatures and two food levels in laboratory conditions. Both food supply and temperature significantly affected naupliar growth and development. High food, measured as chlorophyll a (Chl a) concentration, was 40 μg l⁻¹, on average, and yielded temperature-dependent growth rates in the range of 0.13-0.17 day⁻¹. Low food was about 1.2 μg chlorophyll a l⁻¹ and retarded or arrested development and drastically reduced the growth rate to the range of 0.05-0.09 day⁻¹. To test whether these experimental results were consistent with field data, we used published information on temperature and chlorophyll a variability in northern Chile and developed a combined temperature/food-dependent model to diagnose naupliar growth in the field through a 2-year seasonal cycle including the 1997-1998 El Niño conditions. We concluded that in the upwelling region off northern Chile, C. chilensis might seldom encounter conditions of food shortage, as those applied in the laboratory. Thus, naupliar growth of this species may be primarily controlled by environmental temperature and this might also be the case for the dynamics of the entire population inhabiting the coastal upwelling zone.