Optimal Foraging
Optimal foraging was initially defined as the understanding of the factors affecting nonhuman foraging behavior, in which animals will increase their intake of resources and decrease their energy costs.1 However, its applications in the human realm were quickly observed.
The major hurdle to overcome was that humans differ from non-humans in their foraging skills. Humans will pursue game for a longer period of time, sometimes poisoning or bleeding the animal slowly until it is weak. This creates a high energy cost for the return of meat. Human resource processing can occur when resources cannot be directly sought, for instance after dark or during inclement weather. Resource processing is not always performed by the same person who acquired the resource. Some foragers' processing costs are reduced to zero because of this trade-off. Also the amount of resources acquired is important to humans, because excess resources could relate to multiple wives or status in a society. All of these human characteristics have to be taken into account when producing human optimal foraging models.2
Optimal foraging has been interpreted by anthropologists in many ways, and they have created several models to explain people’s behavior. None of the models is correct in all situations and the model usually reflects back on the society the anthropologist has studied. However, several models have become more universal and will be discussed further. One of the major principles of the models is that the diversity in human diets cannot be attributed to perceptual abilities, prey-capturing appendages, or to predator size.
All models of optimal foraging have a basic framework of goals, currency, a set of constraints, and a set of options. The goal is usually the maximization of foraging efficiency. The currency is almost always calories; however, recently proteins, fats, and carbohydrates have been seen more prevalently in intensive diet studies. Some common constraints are time allotted for foraging activities or the digestive capabilities of the consumers. Some possible options are the availability of potential food and other activities demanding time away from foraging, such as childrearing or tool making. All the models propose how resources will be used. In general the cost of acquiring food is calculated by the resource's mobility, the density of the resource, the degree of aggregation, and the maximum distance at which it is acquired. Since human nutrition requirements change by activity level, age and body size the models cannot be applied to all people of a groups at all times and therefore are the average of foraging abilities.3
Truly, efficiency of work is not determined only by the calories gained by such work, but the calories used to get such gains must also be taken into account. Time input can give a basic estimate (and is usually the estimate used in optimal foraging models), but different physical activities will result in different caloric use in the same amount of time. Unfortunately, unless much more sophisticated techniques are developed for measuring caloric expenditure, such analyses will be at worst impossible and at best inaccurate.
Linear Programming Model
The linear programming model of optimal foraging became popular in the 1970s because it was a mathematical approach. The linear programming model provided a method for solving multiple linear equations for any number of variables. It can simultaneously evaluate a diet in terms of other elements. The linear model gives a realistic analysis of the diet, because humans require a variety of vitamins, minerals and calories to survive. The graphs and predictions it produces can take into account estimates on resource processing, digestion rates, and tool-manufacture and maintenance times. This can demonstrate the cost of obtaining an item as a function of density. For example, when an item is harvested the density of it decreases in the environment, therefore increasing the cost for obtaining it again. The lines on the graphs should then be curvilinear instead of linear, due to this change in density over time.4The forager will continue to utilize a resource until the curvilinear line’s tangent becomes parallel to the mean environmental return rate.5
The model assumes that the resources are all sought at one time and not over a period of days, months or years. The linear programming model is a good mathematical start to determine whether a forager is looking for resources optimally, but it should not be the final step in the evaluation. Other methods provide a more in-depth analysis and comparative look at diet.6
Diet-Breadth Model
The diet-breadth model predicts only whether a resource will be taken by a forager when it is encountered. The acquisition of resources is broken down into search costs and handling costs. Search cost is defined as the time to locate a resource and handling cost as the time to harvest or hunt and process the resource. Returns are calculated per unit time. The resources are ranked for post-consumer return rate, the amount of energy gathered per unit time after the encounter.
The search cost of a resource can change due to external factors, such as the introduction of horses into an area or information gathered from other groups. The handling cost can also change with improved technology, such as nets or shotguns. This model is best at predicting how a society will react when new objects or ideas are introduced, the old ways are not as productive, or the weather changes abruptly. The return rates of resources can also change with a forager's personal skills or with the seasons; for example, the amount of fat on an animal fluctuates during the year. It can also evaluate a change in density or search techniques independent of handling time, the processing or procuring technology.
The model predicts relative measures or averages. The model makes several assumptions including that a forager will choose foods based on quality and density. When a resource is encountered, the forager will decide to harvest it or not. It assumes the goal of all foragers is to maximize their overall energy return rate. The model has a concept of opportunity cost in which there is a loss of energy during the pursuit of a resource when something of higher return could be available. According to the diet-breadth model, as high ranked resources become rarer in an area the diet breadth would expand to include lower ranked resources. The abundance of a resource cannot be the only determinant to predict if it is utilized. For example, certain plants may be very abundant in an area; however, they provide little caloric or nutritional needs and therefore are harvested only after sources of better nutrition are exhausted.
The decision to include a resource relies on the abundance of higher ranked resources. The model predicts diet diversity, but not how frequently a resource is seen in the diet. Higher ranked items will be taken if they are encountered, but if they are encountered less frequently they will make up a smaller portion of the diet. People are not perfect and are not always rational actors, so they frequently violate the model because of cultural taboos.
Some problems may be encountered with the diet-breadth model, as it assumes that the environment and resources are homogeneously distributed. In reality, resources are not encountered randomly and at the same frequency that they exist in the environment. Also, the forager is not a perfect predictable model either. The search for resources is rarely random, because foragers usually have a path or goal in mind before they leave the camp. The diet-breadth model is not perfect, but it does provide a multi-variable approach to determining resource selection.7
This graph comes from Hawkes et al. 1982, an analysis of optimal foraging of the Ache of Paraguay that used
both the patch choice model and the diet-breadth model (referred to by Hawkes et al. as the optimal diet model).
Patch Choice Model
The patch-choice model assumes that resources are encountered in patches and are not homogeneously distributed in the environment. The patches are encountered separately and randomly. The model assumes that a forager does not return to a patch until it has rejuvenated and that the time spent traveling between patches is non-productive. It tries to determine which resource patches should be included in the diet.
The model is set up very similarly to the diet-breadth model in that resources are ranked in terms energetic returns per unit time. The patch-choice model differs from the diet-breadth model in that the time spent searching is included in the overall return rate. It tries to determine when it is efficient to quit searching a patch and move to another one. Initially, a patch has great density and diversity; however, this decreases over time. Moving to a new patch restores the original rate of encounter but costs energy and time to travel and the predictability of the other patch is unknown. The patch-choice model employs the marginal value theorem which states that foragers will move out of a resource patch when the rate of return for that patch falls below the average rate the environment as a whole, not when the returns from the patch have fallen to zero.
This model can never be tested in a natural setting because foragers do not encounter or choose their patches randomly. Also, the travel time between patches is not nonproductive, but can provide resources along the way and give clues to what other resources may be around, for example animal tracks encountered during a move indicate what type of fauna may be present in the new patch. A forager chooses the highest return rate patches given their known environment.8
Mathematical Modeling of the Patch-Choice Model
Because the patch-choice model of optimal foraging predicts resources in non-homogeneous patches and considers time and distance between patches, the search pattern a group of foragers uses to utilize resources can be analyzed and modeled mathematically. Search patterns can be modeled using several familiar statistical models, including the Gaussian (or Normal) distribution, the uniform distribution, and the exponential distribution.9
Clifford T. Brown and his associates postulate that a fourth model, Lévy flights, is the best model of optimal foraging behavior. In order to test this hypothesis, the authors analyzed data published by J.E. Yellen in 1977, which described the movements and residence times of the Dobe Ju/’hoansi during 1968. Using calipers and a map included in Yellen’s book, they measured the distances between camps, in the order they were occupied. The residence times were also measured, in order to be compared against the same statistical model. The researchers applied the Lévy flight model, as well as the three other statistical models mentioned above, in order to ascertain the best fit for the data. The data appeared to conform to the power law set out by the Lévy flight model, and the R2 coefficient indicated a good fit. The normal distribution, uniform distribution, and exponential distribution did not produce a good fit for the data set. They concluded that the Ju/’hoansi’s foraging patterns were best described by the Lévy flight model.10 This model has also been shown to model the optimal foraging behavior of some non-human primates.11
Figures 1 and 2, from Brown 2007, show the adherence of wait time in patches and distances between patches to the power law of the Lévy flight model.
Glasser's Model
J.W. Glasser suggests that consumers will be facultative foragers and that discrimination between resource choices only occurs when resources are abundant. Some consumers are obligate consumers and either specialize in a few resource types or consume resources in proportion to their frequencies in the environment. He predicts that obligate strategies will be more efficient in acquiring resources than the facultative consumers, because they do not have to process decisions about what to choose to pursue.
His disagreement with the other major theories is that it is logically incorrect to assume that a discriminating forager does so randomly. His model proposes that if foragers learn where resources are present and how to utilize them more efficiently, their energetic cost will be decreased with experience. If the forager becomes more efficient at acquiring these resources, they will not need to search for them as much. This would create less of a strain on the resource and it would be able to replenish itself more efficiently, so the next time the forager needed it, the resource would be at the previous level of abundance. This would create a positive feedback loop between the forager and the resources utilized. The forager would require less and the resource would always be abundant.
Glasser theorizes that consumers should either be specialists or generalists. They should be specialists when the resources are relatively common and generalists when they are relatively rare. If the resources are variable, the facultative strategy should be employed, specializing during abundant time and being more generalist in times of scarcity. All consumers should search for valuable resources when others are abundant. His theory is much more complex than the others and has several contingency plans for each type of consumer in every environment.12
Modern Foraging Behavior
In past environments, hominids had acquired an advantage to consume or over-consume resources during times of plenty. They evolved several strategies to store both energy and macro- and micronutrients. The modern environment provides an abundance of calories and thus provides opportunity for obesity. More than 1.1 billion adults worldwide are overweight or obese. More than 22 million children and adolescents are over weight, and this number is growing at an increasing rate. Many changes have been seen since the Paleolithic diets of our ancestors, including an increase in the availability of resources, a reduction in travel time between food patches, a reduction in the energy expended during that travel, and food processing has altered the intrinsic nutritional value of the food that is consumed.
The advent of food processing has reduced our need for stronger gastric capacity and the production of certain enzymes, has shortened the gut transitional time, and has introduced parasites and toxins into the food. In modern humans, the quantity consumed and the frequency of consumption has increased substantially. The metabolic efficiency that would have helped humans survive in past environments has led to the normality of excessive weight gain. Foraging in our modern environment requires little energy expenditure and produces big energy payoffs.
(Image from The LifeStyle Company Article: Fast Food or Fast Fat?)
Several factors account for our ease of obtaining high calorie packages of resources. Search time in the environment is significantly reduced because of helpful cues from billboards and ads telling us where to eat. Travel time is reduced because there are a high density of resources in a certain area - several fast food chains in a city block, restaurants, grocery stores, and vending machines - as well as modern modes of transportation requiring little energy input from the user. Resource availability is assured because all restaurant chains have the same menus, so the consumer knows what they are expecting to discover before they decide to forage. The time spent in the patch looking for resources has been reduced - companies rely on brand name recognition - and this allows a forager to quickly acquire the desired resource with certainty of what it is. Food preparation time has been reduced due to pre-made and pre-packaged foods. These processed foods are calorie-dense and low in fiber and other bulky components, and thus can be consumed in larger proportions.
Energy-dense fast foods provide more calories per dollar than more expensive fruits and vegetables. This provided the paradox of low-income families having higher obesity rates than upper class families. Also, lower capita neighborhoods have a higher frequency of fast food restaurants than higher income neighborhoods. In obesogenic environments, there is an endless supply of food and no decreasing rate of return. Foragers can maximize their net energy gain by super-sizing their meals. The efficiency of capture in fast food restaurants is high and the risk, car accidents and food poisoning, are very low. This makes them a very good investment in ecological terms. Also, humans' physiological capacity for satiation has been reduced because our species had to subsist on sometimes limited diets in the past. This allows us to continue eating after we are full, especially if there is variety involved in the meal. Satiation does not occur because the palate does not get bored of eating the same taste repeatedly. Humans are very poor at estimating a portion size. This could be due to the phenomenon that in times of plenty one would need to eat until the resource is gone, without limiting food intake. However, in modern society this inability to judge portions has allowed our eating to extend far beyond what is necessary. In summation, humans have physiologically adapted to the feast and famine way of life and in Western society there is always enough for a feast. Our inability to determine portion sizes and sense our own satiation has led to over consumption, while our energy storage abilities and sedentary lifestyles provide the perfect avenue for obesity.13
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