Predicting seasonal diet in the yellow-bellied marmot: success and failure for the linear programming model

Seasonal diet selection in the yellow-bellied marmot (Marmota flaviventris) was studied at two sites in Montana during 1991 and 1992. A linear programming model of optimal diet selection successfully predicted the composition of observed diets (monocot versus dicot) in eight out of ten cases early in the active season (April–June). During this period, adult, yearling and juvenile marmots selected diets consistent with the predicted goal of energy maximisation. However, late in the active season (July–August), the model predicted the diet composition in only one out of six cases. In all six late-season determinations, the model underestimated the amount of monocot in the diet. Possible reasons why the model failed to reliably predict diet composition late in the active season are discussed. Received: 26 April 1996 / Accepted: 12 June 1997     

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.     

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.     

高寒草甸生态系统牲畜种群的线性规划模型和最优化利用策略

本文研究了高寒草甸生态系统牲畜种群的线性规划模型和最优利用策略。以门源马场牧场的实际数据作为模型的一个例子,分别提出了藏羊、改良羊和牦牛的最优种群结构和最优出栏方案。在改良羊、藏羊、牦牛和马为主的牧场上,改良羊是牧场上的主要牲畜,牦牛和马保持其数量下限,藏羊全部淘汰。在藏羊、牦牛和马为主的牧场上,藏羊是牧场上的主要牲畜,牦牛和马保持其数量下限。按照线性规划模型方案经营,可提高经济收益,并减轻冬舂草场上牲畜的过多采食。价格分析说明青海省现行的畜产品价格体系需要调整。     

A comparison of restricted selection index and linear programming in sire selection

Summary The objective of restricted selection index is to enhance genetic change in one trait while restricting to zero change in a second trait. Linear programming is another, yet conceptually different, technique to maximize one function while enforcing limits on others. The objective of this research was to compare restricted selection index and linear programming in ability to maximize performance in one trait while limiting change in a second trait to zero. Results of a numerical study demonstrate that linear programming is a more effective method to limit correlated response than restricted selection index. On average, both methods limited response in a correlated trait to zero. However, the squared deviation of actual response in the restricted trait from zero was smaller with linear programming than with restricted selection index. Response to selection in the unrestricted trait is greater with restricted selection index than with linear programming.     

Foraging strategies and seasonal diet optimization of muskoxen in West Greenland

Various aspects of optimal foraging and seasonal diet composition of bulls (bachelor and dominant), cows, subadults, and yearlings of muskoxen Ovibos moschatus were investigated in West Greenland during the following seasons: calving, post-calving, summer, rut and mid-winter. The following hypotheses were tested: (1) muskoxen maximize daily energy intake during spring and summer, (2) dominant bulls monopolizing cows during the rutting season shift from an energy maximizing to a time minimizing foraging strategy in order to maximize the time available for reproductive activities, and (3) muskoxen employ a time minimizing foraging strategy during winter to conserve energy. As forage quality changed throughout the short Arctic growing season, muskoxen responded by changing the proportions of daily time spent feeding on graminoids (Cyperaceae, Poaceae) and dicots (Salix, Betula), respectively. This seasonal variation in the relative proportion of daily feeding time spent ingesting graminoids followed approximately the energy maximization prediction over the periods calving to rut. Neither time minimizing nor random foraging could explain the observed diets in this period, thus confirming hypothesis 1. Dominant bulls did not shift to the time minimizing strategy as predicted by hypothesis 2. However, during the pre-rutting and rutting seasons bulls deviated from the other sex/age classes by failing to obtain the daily maximum energy predicted by the model, as a result of a higher proportion of time allocated to agonistic and sexual behaviour. During winter, none of the sex/age classes employed a time minimizing strategy, so rejecting hypothesis 3. Instead, muskoxen were found to maximize Na intake, indicating that Na is of major importance for winter survival. The results emerging from a linear programming model with constraint settings varying over seasons confirm that the constraint parameters applied are indeed important limiting factors for muskoxen in natural populations.     

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.     

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.     

Optimization of biochemical systems by linear programming and general mass action model representations

A new method is proposed for the optimization of biochemical systems. The method, based on the separation of the stoichiometric and kinetic aspects of the system, follows the general approach used in the previously presented indirect optimization method (IOM) developed within biochemical systems theory. It is called GMA-IOM because it makes use of the generalized mass action (GMA) as the model system representation form. The GMA representation avoids flux aggregation and thus prevents possible stoichiometric errors. The optimization of a system is used to illustrate and compare the features, advantages and shortcomings of both versions of the IOM method as a general strategy for designing improved microbial strains of biotechnological interest. Special attention has been paid to practical problems for the actual implementation of the new proposed strategy, such as the total protein content of the engineered strain or the deviation from the original steady state and its influence on cell viability.     

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.     

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.     

Foraging in nature: foraging efficiency and attentiveness in caterpillars with different diet breadths

Abstract. 1. Seventy‐seven individual last‐instar caterpillars foraging in the field were examined for 6 h each. They represented four species of Arctiidae of similar size and habitat use. Two, Hypocrisias minima and Pygarctia roseicapitis, are specialists restricted to particular plant genera. The other two, Grammia geneura and Estigmene acrea, are extreme generalists that use many host plant species from multiple plant families. 2. Parameters of behavioural efficiency were monitored. Generalists spent more time walking, rejected more potential host plants, took longer to decide to feed after inspecting a plant, and took relatively more small feeding bouts compared with specialists. 3. This is the first test of differential foraging efficiency in the field in relation to diet breadth of insects and the data indicate that generalists are less efficient in their foraging activities and may suffer from divided attention. The need for attentiveness to enhance efficiency and thereby reduce ecological risk is discussed.     

Seed selection by dark-eyed juncos (Junco hyemalis): optimal foraging with nutrient constraints?

Summary Observations of the foraging behavior of six captive dark-eyed juncos (Junco hyemalis) are used to test the assumptions and predictions of optimal diet choice models (Pyke et al. 1977) that include nutrients (Pulliam 1975). The birds sequentially encountered single seeds of niger thistle (Guizotia abyssinica) and of canary grass (Phalaris canariensis) on an artificial substrate in the laboratory. Niger thistle seeds were preferred by all birds although their profitability in terms of energy intake (J/s) was less than the profitability of canary grass seeds. Of four nutritional components used to calculate profitabilities (mg/s) lipid content was the only characteristic that could explain the junco's seed preference. As predicted by optimal diet theory the probability of consuming niger thistle seeds was independent of seed abundance. However, the consumption of 71–84% rather than 100% of the seeds encountered is not consistent with the prediction of all-or-nothing selection. Canary grass seeds were consumed at a constant rate (no./s) independent of the number of seeds encountered. This consumption pattern invalidates a model that assumes strict maximization. However, it is consistent with the assumption that canary grass seeds contain a nutrient which is required in minimum amounts to meet physiological demands (Pulliam 1975). These experiments emphasize the importance of incorporating nutrients into optimal foraging models and of combining seed preference studies with studies of the metabolic requirements of consumers.     

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.     

Inheritance of optimal foraging behaviour in Columbian ground squirrels

Summary I examined the potential inheritance of the ability of Columbian ground squirrels (Spermophilus columbianus) to select an optimal diet. I calculated the diet that would maximize daily energy intake for each of 21 adult females and their litters, using a linear programming optimization model for each individual. The absolute value of the difference between an individual's predicted optimal diet and observed diet (deviation from an optimal diet) was used as a measure of an individual's foraging ability. The foraging ability of individuals was consistent over time and in different foraging environments, so I considered foraging ability to be a potentially heritable trait.Inheritance was determined from correlations of mother and offspring foraging ability. I experimentally removed some mothers just as they weaned their offspring so that offspring could not be influenced by their mother while learning to forage, while leaving the other mothers to raise their litters normally. In both cases, offspring strongly resembled their mother in foraging ability. However, offspring with mothers absent exhibited significantly larger deviations from their optimal diet. Offspring with mothers absent appeared to imitate their mother's diet during lactation, and this tendency partially explained their greater deviation. Consequently, offspring appear to inherit the ability to forage optimally from their mother, perhaps through observational learning or imitation. There may also be a genetic basis to foraging ability, but uncontrolled maternal effects in the experiment prevent a proper test for it.     

Searching on patch networks using correlated random walks: space usage and optimal foraging predictions using Markov chain models

We describe a novel representation of a discrete correlated random walk as the transition matrix of a Markov chain with the displacements as the states. Such a representation makes it possible to utilize results from the theory of absorbing Markov chains, to make biologically interesting predictions without having to resort to Monte Carlo simulations. Our motivation for constructing such a representation is to explore the relationship between the movement strategy of an animal searching for resources upon a network of patches, and its consequent utilization of space and foraging success. As an illustrative case study, we have determined the optimal movement strategy and the consequent usage of space for a central place forager utilizing a continuous movement space which is discretized as a hexagonal lattice. The optimal movement strategy determines the size of the optimal home range. In this example, the animal uses mnemokinesis, which is a sinuosity regulating mechanism, to return it to the central place. The movement strategy thus refers to the choice of the intrinsic path sinuosity and the strength of the mnemokinetic mechanism. Although the movement space has been discretized as a regular lattice in this example, the method can be readily applied to naturally compartmentalized movement spaces, such as forest canopy networks. This paper is thus an attempt at incorporating results from the theory of random walk-based animal movements into Foraging Theory.     

Forest savanna ecotone dynamics in India as revealed by carbon isotope ratios of soil organic matter

Linear programming models of diet selection (LP) have been criticized as being too sensitive to variations in parameter values that have not been or may not be able to be measured with a high degree of precision (small standard error). Therefore, LP's predictions have been questioned, even though the predicted diet choices agree very well with observations in 400 published tests. The philosophical and statistical aspects of this criticism of LP are reviewed in light of the ability to test any nontrivial ecological theory. It is argued that measures of error in field data may not meet simple statistical definitions, and thereby, may make sensitivity analyses that use the error measures overly conservative. Furthermore, the important issue in testing ecological theory may not be the statistical confidence in a single test, but whether or not the theory withstands repeated tests.