Circularity in linear programming models of optimal diet

The linear programming model of optimal diet for herbivores has been criticized for being biologically unrealistic, for being too successful given statistical realities, and for being circular. I try to clarify the issue of circularity. Circularity arises if constraint lines are estimated from average values for governing parameters, when the assumed constraints are not effective. This may occur (1) under benign season conditions when consumers do not maximize their food intake, because of costs associated with food processing and storage, or (2) when an unidentified constraint limits intake. To evaluate hypotheses about the factors controlling diet composition, it must be shown that (1) consumers respond appropriately to variation in the parameters controlling constraint settings, and (2) the assumed constraints are close to their maximum (or minimum) settings.     

Optimal diet choice for large herbivores: an extended contingency model

1. A more general contingency model of optimal diet choice is developed, allowing for simultaneous searching and handling, which extends the theory to include grazing and browsing by large herbivores.
2. Foraging resolves into three modes: purely encounter-limited, purely handling-limited and mixed-process, in which either a handling-limited prey type is added to an encounter-limited diet, or the diet becomes handling-limited as it expands.
3. The purely encounter-limited diet is, in general, broader than that predicted by the conventional contingency model.
4. As the degree of simultaneity of searching and handling increases, the optimal diet expands to the point where it is handling-limited, at which point all inferior prey types are rejected.
5. Inclusion of a less profitable prey species is not necessarily independent of its encounter rate and the zero-one rule does not necessarily hold: some of the less profitable prey may be included in the optimal diet. This gives an optimal foraging explanation for herbivores' mixed diets.
6. Rules are shown for calculating the boundary between encounter-limited and handling-limited diets and for predicting the proportion of inferior prey to be included in a two-species diet.
7. The digestive rate model is modified to include simultaneous searching and handling, showing that the more they overlap, the more the predicted diet-breadth is likely to be reduced.     

Sequential and simultaneous choices: Testing the diet selection and sequential choice models

We investigate simultaneous and sequential choices in starlings, using Charnov's Diet Choice Model (DCM) and Shapiro, Siller and Kacelnik's Sequential Choice Model (SCM) to integrate function and mechanism. During a training phase, starlings encountered one food-related option per trial (A, B or R) in random sequence and with equal probability. A and B delivered food rewards after programmed delays (shorter for A), while R (‘rejection’) moved directly to the next trial without reward. In this phase we measured latencies to respond. In a later, choice, phase, birds encountered the pairs A–B, A–R and B–R, the first implementing a simultaneous choice and the second and third sequential choices. The DCM predicts when R should be chosen to maximize intake rate, and SCM uses latencies of the training phase to predict choices between any pair of options in the choice phase. The predictions of both models coincided, and both successfully predicted the birds’ preferences. The DCM does not deal with partial preferences, while the SCM does, and experimental results were strongly correlated to this model's predictions. We believe that the SCM may expose a very general mechanism of animal choice, and that its wider domain of success reflects the greater ecological significance of sequential over simultaneous choices.     

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.     

On estimating energetic values of prey: implications in optimal diet models

Summary The accurate estimation of the amount of energy contained within a food item which is available to a predator is essential in tests of optimal foraging theories. Many studies of optimal foraging measure gross energy content of prey directly by bomb calorimetry. I suggest that a more realistic and accurate estimate of true prey value is available by calculating energy associated with the organic constituents of prey, and then subtracting away energy associated with insoluble and indigestible components. This methodology allows for a much more precise estimate of prey value (useable energy) and therefore a more realistic test of optimal foraging models.     

Altitudinal and seasonal variations in the diet of Japanese macaques in Yakushima

Altitudinal and seasonal variations in the diet of Japanese macaques in Yakushima, southwestern Japan, were studied for 2 years by means of fecal analysis. The altitudinal range of fecal samples collected was 30 m to 1,203 m above sea level, and it was divided into three zones: low-zone forest (0–399 m), middle-zone forest (400–799 m), and high-zone forest (800 m–1,230 m). There was a considerable altitudinal and seasonal variation in the macaques' diet. Seed/fruit and animal matter were eaten more in the lower zones, whereas more fiber and fungi were consumed in the higher zones. In all of the zones, they ate seed/fruits the most in autumn (September–November) and the least in spring (March–April). They ate fibrous food the most in spring and the least in autumn. Macaques relied on seed/fruits heavily in the lower zone for a longer period than in the higher zones. Macaques in the high-zone forest ate almost no seed/fruit foods from March to May. Altitudinal variations in availability of seed/fruit foods seem to have influenced the altitudinal variations in diet. Total basal area of seed/fruit-food trees, species richness of seed/fruit-foods, main seed/fruit-food types available, and annual fleshy-fruit production all decreased with increasing altitude. Both interannual variation and annual cyclicity of diet were found in all zones. Electronic Publication     

Optimal foraging by a suspension-feeding copepod: responses to short-term and seasonal variation in food resources

Laboratory radioisotope experiments were used to investigate the effects of phytoplankton seasonal succession on the selectivity and clearance rates of a suspension-feeding copepod in two Indiana lakes. Responses to particle size and quality were tested by allowing adult female Diaptomus birgei feeding in natural seston to select between a small (6×7 m) flagellate (Chlamydomonas reinhardii) and a large, poor quality food (heat-killed Carteria olivieri, 22×25 m). Short-term responses were tested in one lake by additional treatments in which copepods were acclimated for 5–6 h in filtered lake water (starved) or natural seston with added Chlamydomonas (enriched). Copepods from both lakes fed selectively on the small live flagellate during the spring bloom of edible phytoplankton but fed selectively on the larger, poor quality particle during the clear water phase when food was scarce. These results are interpreted as an interaction between the concentration-dependent selectivity for high quality foods predicted by optimal diet theory and a perceptual bias for large-sized particles. Selectivity for high-quality food was intermediate and clearance rates were depressed when total phytoplankton abundance was high but dominated by filamentous cyanobacteria. In each experiment copepods also responded to the short-term manipulations by exhibiting weaker discrimination against the poor quality particle in the starvation treatment and stronger discrimination in the enriched treatment. A two-way mixed model ANOVA revealed substantial short term (37%) and seasonal (53%) components to the total variance in selectivity. Clearance rates were also influenced by both phytoplankton succession and the short-term resource manipulations. As expected, clearance rates on the poor quality food were more sensitive to the abundance of alternative foods. These results show how the feeding behavior of a freshwater copepod is modulated by both seasonal and short-term variation in natural food.     

Experimental analysis of diet specialization in the snail kite: the role of behavioral conservatism

We examined factors maintaining extreme diet specialization in the snail kite (Rostrhamus sociabilis), a medium-sized hawk which feed almost exclusively on Pomacea snails, by determining why during some months kites eat crabs (Dilocarcinus dentatus) in the Ilanos of Venezuela. We offered snails and crabs of different sizes to wild free-flying birds to develop estimates for a prey choice model. Handling times of Pomacea doliodes snails averaged 90±39 s and were positively correlated with snail size. Handling times for crabs (x=353±130 s) were significantly longer and exhibited greater variation than for snails, and were not correlated with crab size. Edible crab tissues had greater dry weights and contained more energy (25.37 kJ/g) than tissues of snails (16.91 kJ/g). Total energy of crabs was much greater than that of snails, and total energy of both foods was highly related to body length. We constructed an allometric equation for profitability of snails and crabs. Snails were more profitable than all but the largest crabs, but estimates of variance in profitability were greater for crabs. Predictions from the model were tested by offering crabs that represented equal, greater and much greater profitability than snails, to determine whether kites chose prey according to profitability. Only 15.6% of 289 food items chosen were crabs. Half of the 18 kites tested did not eat crabs and only 3 birds switched from snails to more profitable crabs. Four fledglings showed no preference for snails. The role of neophobia in food choice was investigated by offering unfamiliar snails (Pomacea urceus) to kites. Kites exhibited neophobic behaviors, and 5 of 12 birds chose not to capture P. urceus. Two-thirds of the 12 snails chosen were rejected immediately, but the others were handled efficiently (x=133±89 s). Although morphological adaptations allow kites to specialize on snails, the costs of specialization were overcome for kites when the profitability of alternative food increased sufficiently. Our results suggest a role for behavioral conservatism, in the form of risk-averse foraging and neophobia, in maintaining severe diet specialization in the snail kite.     

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.     

Foraging strategy in a subterranean rodent,Spalax ehrenbergi: a test case for optimal foraging theory

Summary The foraging behavior of the subterranean mole rat Spalax ehrenbergi (Rodentia, Spalacidae) was tested according to the framework of optimal foraging theory. We compared the frequencies of food species hoarded in storage chambers of mole rats with the frequencies of these species occurring in the vicinity of the mole rats' nest mounds during the winter and spring seasons. In addition, we examined the food composition of several summer nest mounds. Laboratory observations were conducted in order to test the foraging behavior of mole rats under simulated subterranean conditions. The mole rat is a generalist and collects a variety of food species. Out of 33 plant species that were hoarded by mole rats in the 21 studied nest mounds, 61% (n=20) were geophytes, 21% (n=7) perennial herbs, 15% (n=5) annual herbs and 3% (n=1) dwarf shrubs. The frequency of each collected species in the 16 winter and spring nest mounds is in general accordance with its frequency in the mole rat's territory. This implies that the mole rat randomly samples the food reserve of its territory without special preference or directed search for a particular species. The collection or avoidance of any food item is not dependent on the presence or absence of any other food item. We suggest that the foragin generalism of the mole rat is a product of the constraints of a subterranean niche — the necessity to hoard food as much as possible in a limited time period and the high energetic investment of tunneling to the food items.     

北京地区大足鼠耳蝠主要食物及其食性组成的季节变化

20 0 2年 5月至 2 0 0 3年 11月初 (冬眠期除外 ) ,约每两周一次 (每次调查持续 1- 2晚 )于北京房山霞云岭乡四合村蝙蝠洞 (115°5 9′N ,39°4 3′E)捕捉觅食后返洞的大足鼠耳蝠 (Myotisricketti) ,通过 2 8次野外调查收集了 342个粪便样品 ,分析了其食物组成的频率差异。北京地区大足鼠耳蝠主要捕食宽鳍 (Zaccoplaty pus) (在总样品中的频率为 6 0 2 % )、鲫鱼 (Carassiusauratus) (5 8% )和洛氏 (Phoxinuslagowskii) (2 3% )三种淡水鱼 ;还捕食至少 7个目的昆虫 ,分别为鞘翅目 (2 0 2 % )、鳞翅目 (12 6 % )、同翅目 (9 6 % )、蜉蝣目(4 1% )、半翅目 (5 6 % )、双翅目 (3 5 % )和膜翅目 (2 6 % )。两年中三种淡水鱼的总频率与昆虫的总频率差异显著 ;年内数据比较显示 ,鱼类和昆虫频率 2 0 0 2年差异不显著 ,2 0 0 3年差异显著。大足鼠耳蝠雨季和旱季食物种类基本无差异 ,但鱼类和昆虫在其食物组成中有年内波动 ,即大足鼠耳蝠旱季多以鱼类为食 ,雨季捕获昆虫的数量相对增加。据两年的研究结果 ,证实北京房山霞云岭大足鼠耳蝠的食物主要组成部分是三种鱼类 ,而宽鳍为主要食物成分的原因是其多在水体浅层活动而易被大足鼠耳蝠捕获。从能量收支平衡的角度推测大足鼠耳蝠在雨季捕食昆虫可能     

Mean-variance sets for dietary choice models: simplicity in a complex world

Summary This paper presents a series of simulations designed to determine optimal diet breadth under shortfall avoidance models. Profitability and encounter rate functions were varied, and means and variances of energy intake rate were generated using a simple simulation procedure. The resulting mean-variance sets assumed three distinct shapes: u-shaped, arched, and looped. These simulations show that certain mean-variance sets allow the forager to employ simple behavioural rules to determine the optimal diet breadth. This situation occurs when low ranking diet items have small handling times, and these conditions may be quite common. In other cases, mean-variance sets may be too complicated to allow for easy behavioural rules designed to minimize starvation probability. The ability to characterize foraging problems into a limited series of mean-variance set types benefits workers examining the evolution and maintenance of foraging strategies, since these sets have clear implications for the ability of animals to develop simple behavioural rules. Unfortunately data are lacking on the profitability and encounter rate distributions animals face in nature.     

Individual variation in the ability of Columbian ground squirrels to select an optimal diet

Summary Columbian ground squirrels (Spermophilus columbianus) were examined for ability to select a diet that maximizes daily energy intake (optimal diet) under free-living field conditions. The optimal diet for each squirrel was determined given constraints (e.g. body size, feeding time) on individual foraging behavior. Most squirrels (63%) consumed a diet not significantly different from one that would maximize their daily energy intake. The remainder (37%) approached an energy maximized diet but appeared to make some incorrect foraging decisions. Both males and females appeared to approach energy maximized diets. An individual's deviation from its optimal diet is relatively constant within a season and not significantly affected by immediate environmental influences such as food abundance, thermal conditions and social environment. The energy cost of deviating from an optimal diet may be large enough to affect fitness. These results suggest that the ability to select an optimal diet can be viewed as a behavioral trait that might be subject to natural selection.     

Adaptive omnivory and species coexistence in tri-trophic food webs

The commonness of omnivory in natural communities is puzzling, because simple dynamic models of tri-trophic systems with omnivory are prone to species extinction. In particular, the intermediate consumer is frequently excluded by the omnivore at high levels of enrichment. It has been suggested that adaptive foraging by the omnivore may facilitate coexistence, because the intermediate consumer should persist more easily if it is occasionally dropped from the omnivore's diet. We explore theoretically how species permanence in tri-trophic systems is affected if the omnivore forages adaptively according to the "diet rule", i.e., feeds on the less profitable of its two prey species only if the more profitable one is sufficiently rare. We show that, compared to systems where omnivory is fixed, adaptive omnivory may indeed facilitate 3-species persistence. Counter to intuition, however, facilitation of 3-species coexistence requires that the intermediate consumer is a more profitable prey than the basal resource. Consequently, adaptive omnivory does not facilitate persistence of the intermediate consumer but enlarges the persistence region of the omnivore towards parameter space where a fixed omnivore would be excluded by the intermediate consumer. Overall, the positive effect of adaptive omnivory on 3-species persistence is, however, small. Generally, whether omnivory is fixed or adaptive, 3-species permanence is most likely when profitability (=conversion efficiency into omnivores) is low for basal resources and high for intermediate consumers.     

Effect of predation risk on the presence and persistence of yellow-bellied marmot (Marmota flaviventris) colonies

Habitat selection may have population level consequences and ultimately may influence a population's local persistence or extinction. We capitalized on a long-term study (1962–2004) of yellow-bellied marmots Marmota flaviventris in and around the Rocky Mountain Biological Laboratory, Gothic, Colorado, USA, and compared habitat characteristics associated with food availability and predation risk to explain variation in persistence of marmots at 27 sites, and their absence at 22 additional, randomly selected sites. We classified sites as persistent, intermittent or null based on whether there was a history of extinction; intermittent sites periodically went extinct and null sites never had marmots. Logistic regression analyses revealed that environmental variables associated with visibility and safety, rather than food, correctly classified sites as persistent or non-persistent as well as persistent or intermittent. Discriminant function analysis that included the null sites revealed that the same visibility-related characteristics predicted where marmots were found. These results highlight the importance of variation in safety among sites in predicting long-term population persistence, as well as a species' distribution.     

蜘蛛位置对成功捕获猎物和球型网图案的影响

静坐在球型网的中心,蜘蛛可能遭受天敌的攻击并暴露在不利的天气条件下,如风和雨。然而,栖居于网的中心使蜘蛛比隐藏在隐蔽场所中的蜘蛛能更迅速地察觉并捕获猎物,这是因为猎物的位置仅能被位于网中心的蜘蛛所确定。对在隐蔽场所中的蜘蛛而言,提高对猎物捕获率的方式之一是尽量减少隐蔽所与网中心的距离。而且,网中心与隐蔽所之间较短的距离使蜘蛛能更迅速地逃离危险境况。我使用既在网中心、又在隐蔽场所的硬类肥蛛(Larinioides sclopetarius Clerck),来检验这两种行为如何影响对猎物的捕获成功率。隐藏在隐蔽场所中的蜘蛛更经常忽略猎物,使猎物也有比较多的逃离机会,这样,与在网中心的蜘蛛相比,猎物的损失率就更高。另外,研究了隐蔽场所的位置对球型网图案的影响。在大多数球型网中,网中心上方的区域比网下方小,丝也比较少,形成了结构不对称的网;隐蔽场所通常在网的上方。当隐蔽场所的位置在实验中被倒转时,就形成了非典型的球型网。最后,L．sclopetarius建造的网有很突出的边缘非对称性,与隐蔽场所相邻的区域面积较小,而远离隐蔽场所的区域面积较大,这也可解释为减少了隐蔽场所和网中心之间的距离[动物学报50(4)：559-565．2004]。     

Sexual and seasonal variation in the diet and foraging behaviour of a sexually dimorphic carnivore, the honey badger (Mellivora capensis)

The honey badger, or ratel, Mellivora capensis has not been well studied despite its extensive distribution. As part of the first detailed study, visual observations of nine habituated free-living individuals (five females, four males) were used to investigate seasonal, annual and sexual differences in diet and foraging behaviour. Theory predicts that generalist predators 'switch' between alternative prey species depending on which prey species are currently most abundant, and diet breadth expands in response to decreased availability of preferred food types. There were significant seasonal differences in the consumption of eight prey categories related to changes in prey availability but no seasonal differences in food intake per kg of body mass. As predicted, the cold-dry season diet was characterized by low species richness and low foraging yield but high dietary diversity, while the reverse was true in the hot-dry and hot-wet seasons. In accordance with these predictions, results suggest that the honey badger maintains its intake level by food switching and by varying dietary breadth. Despite marked sexual size dimorphism, male and female honey badgers showed no intersexual differences in prey size, digging success, daily food intake per unit body weight or foraging behaviour. Results do not support the hypothesis that size dimorphism is primarily an adaptation to reduce intersexual competition for food.     

Predation risk and habitat selection in the persistence of a remnant caribou population

Summary A small caribou herd of 24–77 animals resided on Pic Island (1138 ha) in Lake Superior from 1976 to 1984. Most of the caribou populations on the adjacent mainland had gone extinct earlier in this century. We tested three hypotheses for the persistence of this remanant population: (1) there was more forage available on the island than the mainland, (2) the animals on the island were isolated from white-tailed deer and did not develop the meningeal worm infection, and (3) there was less predation by wolves on the island. Forage was more abundant on the mainland than on Pic Island. The eggs of meningeal worms were not found in the feces of deer on the mainland or Pic island. Wolves seldom visited the island and when they did there was escape habitat available for the caribou. We concluded that the herd persisted because of this reduced predation risk and that the animals were prepared to select a reduced variety and phytomass of forage to remain for long periods in the relatively safe island habitat. When the animals did visit the mainland to feed they sclected forbs that provided a large bite size. On the island food supplies were too meager to select plants that gave a large bite size and the caribou spent long intervals feeding. Caribou by using habitats with a large phytomass and selecting for large bite size should minimize their time feeding which would allow them more time to watch for predators.