Hunter-gatherer foraging: A linear programming approach

Abstract

A linear program model is developed to examine how much effort huntergatherers should devote to hunting vs gathering. This foraging model contains a foraging time, a digestive capacity, and a nutritional constraint which determine the optimal solution to a given human foraging goal: nutritional maximization, foraging time minimization, risk aversion, or food storage maximization. The model is compared with the most commonly used foraging models in anthropology and is shown to be more appropriate for hunter-gatherers. Using data on present day hunter-gatherers, the model's solution is shown to indicate quantitatively that these people tend to either maximize their energy or protein intake rather than minimize their time spent providing for their energy and protein needs. The model also predicts diet proportions, absolute food intake, time spent foraging, and sexual division of labor. A general version of the model is developed where the hunting and gathering cropping rates are made functions of environmental primary production. The solutions to this model agree with world patterns of hunter-gatherer diets, foraging time, and sexual division of labor. Moditications of the model to investigate risk-averse foraging and food storage are also presented, and the model is applied to determine when agriculturelpastorahsm might be adopted and how hunter-gatherer body size might be selected. Although the model appears closely to predict observed hunter-gatherer foraging, the model's sensitivity and the quality of the data available make its uncritical acceptance unwarranted at this time. 6 1987 Academic press, 1~.

Predator Functional Responses: Discriminating Between Handling and Digesting Prey

“…Examples have been reported from mollusks (veliger larvae: ; common or blue mussel [ Mytilus edulis ], Bayne et al [1989]), crustaceans ( Branchipus schaefferi, Streptocephalus torvicornis, Dierckens et al [1997]; Calliopius laeviusculus, DeBlois and Leggett [1991]; Daphnia spp., , McMahon and Rigler [1963], ; Calanus pacificus, Frost [1972]; other copepods: Paffenhöfer et al [1982], Christoffersen and Jespersen [1986], , Jonsson and Tiselius [1990]), insects ( Chaoborus spp. larvae, reviewed by ; the grasshoppers Circotettix undulatus, Dissosteira carolina, Melanoplus femur‐rubrum, and Melanoplus sanguinipes, Belovsky [1986 b ]; dusty wing larvae [ Conwentzia hageni ], green lacewing larvae [ Chrysopa californica ], red mite destroyer larvae [ Stethorus picipes ], Fleschner [1950]), birds (Woodpigeons [ Columba palumbus ], Kenward and Sibly [1977]; Oystercatchers [ Haematopus ostralegus ], Kersten and Visser [1996]; hummingbirds [ Selasphorus rufus ], Hixon et al [1983], Diamond et al [1986]), and mammals (moose [ Alces alces ], Belovsky [1978]; pronghorn antelopes [ Antilocapra americana ], bison [ Bison bison ], elk [ Cervus elaphus ], yellow‐bellied marmots [ Marmota flaviventris ], mule deer [ Odocoileus hemionus ], white‐tailed deer [ Odocoileus virginianus ], bighorn sheep [ Ovis canadensis ], Columbian ground squirrels [ Spermophilus columbianus ], Rocky Mountain cotton tails [ Sylvilagus nuttali ], Belovsky [1986 b ]; cattle [ Bos taurus ], Campling et al [1961]; beavers [ Castor canadensis ], Belovsky [1984 b ], Doucet and Fryxell [1993], Fryxell et al [1994]; Thomson's gazelles [ Gazella thomsoni ], Wilmshurst et al [1999]; human beings [ Homo sapiens ], Belovsky [1987]; snowshoe hares [ Lepus americanus ], Belovsky [1984 c ]; meadow voles [ Microtus pennsylvanicus ], Belovsky [1984 a ]; muskoxen [ Ovibus moschatus ], Forchhammer and Boomsma [1995]; sheep [ Ovis aries ], Blaxter et al [1961]; shrews [ Sorex araneus, S. caecutiens, S. isodon ], ).…”

Predator Functional Responses: Discriminating Between Handling and Digesting Prey

“…Examples have been reported from mollusks (veliger larvae: ; common or blue mussel [ Mytilus edulis ], Bayne et al [1989]), crustaceans ( Branchipus schaefferi, Streptocephalus torvicornis, Dierckens et al [1997]; Calliopius laeviusculus, DeBlois and Leggett [1991]; Daphnia spp., , McMahon and Rigler [1963], ; Calanus pacificus, Frost [1972]; other copepods: Paffenhöfer et al [1982], Christoffersen and Jespersen [1986], , Jonsson and Tiselius [1990]), insects ( Chaoborus spp. larvae, reviewed by ; the grasshoppers Circotettix undulatus, Dissosteira carolina, Melanoplus femur‐rubrum, and Melanoplus sanguinipes, Belovsky [1986 b ]; dusty wing larvae [ Conwentzia hageni ], green lacewing larvae [ Chrysopa californica ], red mite destroyer larvae [ Stethorus picipes ], Fleschner [1950]), birds (Woodpigeons [ Columba palumbus ], Kenward and Sibly [1977]; Oystercatchers [ Haematopus ostralegus ], Kersten and Visser [1996]; hummingbirds [ Selasphorus rufus ], Hixon et al [1983], Diamond et al [1986]), and mammals (moose [ Alces alces ], Belovsky [1978]; pronghorn antelopes [ Antilocapra americana ], bison [ Bison bison ], elk [ Cervus elaphus ], yellow‐bellied marmots [ Marmota flaviventris ], mule deer [ Odocoileus hemionus ], white‐tailed deer [ Odocoileus virginianus ], bighorn sheep [ Ovis canadensis ], Columbian ground squirrels [ Spermophilus columbianus ], Rocky Mountain cotton tails [ Sylvilagus nuttali ], Belovsky [1986 b ]; cattle [ Bos taurus ], Campling et al [1961]; beavers [ Castor canadensis ], Belovsky [1984 b ], Doucet and Fryxell [1993], Fryxell et al [1994]; Thomson's gazelles [ Gazella thomsoni ], Wilmshurst et al [1999]; human beings [ Homo sapiens ], Belovsky [1987]; snowshoe hares [ Lepus americanus ], Belovsky [1984 c ]; meadow voles [ Microtus pennsylvanicus ], Belovsky [1984 a ]; muskoxen [ Ovibus moschatus ], Forchhammer and Boomsma [1995]; sheep [ Ovis aries ], Blaxter et al [1961]; shrews [ Sorex araneus, S. caecutiens, S. isodon ], ).…”

Macronutrient modifications of optimal foraging theory: An approach using indifference curves applied to some modern foragers

“…In most linear programing models, the rate of intake of a single nutrient, e.g., energy or protein, is assumed to be maximized, subject to meeting the specified nutrient constraints (Reidhead, 1979). When the intake rate maximizing strategy for two resources leads to mutually exclusive optimal foraging strategies, the optimal mix must be determined by some other specified nutrient or non-nutrient constraint (for an example where the constraint that determines the optimal mix of energy and protein is stomach volume see Belovsky, 1987).…”

“…Finally, the approach, as it has been applied thus far, has been post hoc. Since subsistence patterns show neither energy nor pro-tein maximization, multiple constraints are added to the model one at a time until a close fit to the observed foraging pattern is obtained (Belovsky, 1987). Since the number of possible constraints is unlimited, and constraints and their values are invoked on a case-specific basis, not surprisingly, a specific model can be developed to account for every possible observed diet.…”

Artefact analysis

“…Examples of simulation methods in archaeology are unfortunately limited but are of great interest: Doran (1970), Thomas (1972), Ammermann and Cavalli-Sforza (1973), Wobst (1974), Zubrow (1975), Hassan (1977), Jochim (1976), Hodder ed. (1978, Renfrew and Cooke (1979), Sabloff (1981), Keene (1979), Belovsky (1987), Doran (1990), etc.…”

Predator Functional Responses: Discriminating Between Handling and Digesting Prey

“…Examples have been reported from mollusks (veliger larvae: ; common or blue mussel [ Mytilus edulis ], Bayne et al [1989]), crustaceans ( Branchipus schaefferi, Streptocephalus torvicornis, Dierckens et al [1997]; Calliopius laeviusculus, DeBlois and Leggett [1991]; Daphnia spp., , McMahon and Rigler [1963], ; Calanus pacificus, Frost [1972]; other copepods: Paffenhöfer et al [1982], Christoffersen and Jespersen [1986], , Jonsson and Tiselius [1990]), insects ( Chaoborus spp. larvae, reviewed by ; the grasshoppers Circotettix undulatus, Dissosteira carolina, Melanoplus femur‐rubrum, and Melanoplus sanguinipes, Belovsky [1986 b ]; dusty wing larvae [ Conwentzia hageni ], green lacewing larvae [ Chrysopa californica ], red mite destroyer larvae [ Stethorus picipes ], Fleschner [1950]), birds (Woodpigeons [ Columba palumbus ], Kenward and Sibly [1977]; Oystercatchers [ Haematopus ostralegus ], Kersten and Visser [1996]; hummingbirds [ Selasphorus rufus ], Hixon et al [1983], Diamond et al [1986]), and mammals (moose [ Alces alces ], Belovsky [1978]; pronghorn antelopes [ Antilocapra americana ], bison [ Bison bison ], elk [ Cervus elaphus ], yellow‐bellied marmots [ Marmota flaviventris ], mule deer [ Odocoileus hemionus ], white‐tailed deer [ Odocoileus virginianus ], bighorn sheep [ Ovis canadensis ], Columbian ground squirrels [ Spermophilus columbianus ], Rocky Mountain cotton tails [ Sylvilagus nuttali ], Belovsky [1986 b ]; cattle [ Bos taurus ], Campling et al [1961]; beavers [ Castor canadensis ], Belovsky [1984 b ], Doucet and Fryxell [1993], Fryxell et al [1994]; Thomson's gazelles [ Gazella thomsoni ], Wilmshurst et al [1999]; human beings [ Homo sapiens ], Belovsky [1987]; snowshoe hares [ Lepus americanus ], Belovsky [1984 c ]; meadow voles [ Microtus pennsylvanicus ], Belovsky [1984 a ]; muskoxen [ Ovibus moschatus ], Forchhammer and Boomsma [1995]; sheep [ Ovis aries ], Blaxter et al [1961]; shrews [ Sorex araneus, S. caecutiens, S. isodon ], ).…”

Macronutrient modifications of optimal foraging theory: An approach using indifference curves applied to some modern foragers

“…In most linear programing models, the rate of intake of a single nutrient, e.g., energy or protein, is assumed to be maximized, subject to meeting the specified nutrient constraints (Reidhead, 1979). When the intake rate maximizing strategy for two resources leads to mutually exclusive optimal foraging strategies, the optimal mix must be determined by some other specified nutrient or non-nutrient constraint (for an example where the constraint that determines the optimal mix of energy and protein is stomach volume see Belovsky, 1987).…”

“…Finally, the approach, as it has been applied thus far, has been post hoc. Since subsistence patterns show neither energy nor pro-tein maximization, multiple constraints are added to the model one at a time until a close fit to the observed foraging pattern is obtained (Belovsky, 1987). Since the number of possible constraints is unlimited, and constraints and their values are invoked on a case-specific basis, not surprisingly, a specific model can be developed to account for every possible observed diet.…”

Artefact analysis

“…Examples of simulation methods in archaeology are unfortunately limited but are of great interest: Doran (1970), Thomas (1972), Ammermann and Cavalli-Sforza (1973), Wobst (1974), Zubrow (1975), Hassan (1977), Jochim (1976), Hodder ed. (1978, Renfrew and Cooke (1979), Sabloff (1981), Keene (1979), Belovsky (1987), Doran (1990), etc.…”

Predator Functional Responses: Discriminating Between Handling and Digesting Prey

“…Examples have been reported from mollusks (veliger larvae: ; common or blue mussel [ Mytilus edulis ], Bayne et al [1989]), crustaceans ( Branchipus schaefferi, Streptocephalus torvicornis, Dierckens et al [1997]; Calliopius laeviusculus, DeBlois and Leggett [1991]; Daphnia spp., , McMahon and Rigler [1963], ; Calanus pacificus, Frost [1972]; other copepods: Paffenhöfer et al [1982], Christoffersen and Jespersen [1986], , Jonsson and Tiselius [1990]), insects ( Chaoborus spp. larvae, reviewed by ; the grasshoppers Circotettix undulatus, Dissosteira carolina, Melanoplus femur‐rubrum, and Melanoplus sanguinipes, Belovsky [1986 b ]; dusty wing larvae [ Conwentzia hageni ], green lacewing larvae [ Chrysopa californica ], red mite destroyer larvae [ Stethorus picipes ], Fleschner [1950]), birds (Woodpigeons [ Columba palumbus ], Kenward and Sibly [1977]; Oystercatchers [ Haematopus ostralegus ], Kersten and Visser [1996]; hummingbirds [ Selasphorus rufus ], Hixon et al [1983], Diamond et al [1986]), and mammals (moose [ Alces alces ], Belovsky [1978]; pronghorn antelopes [ Antilocapra americana ], bison [ Bison bison ], elk [ Cervus elaphus ], yellow‐bellied marmots [ Marmota flaviventris ], mule deer [ Odocoileus hemionus ], white‐tailed deer [ Odocoileus virginianus ], bighorn sheep [ Ovis canadensis ], Columbian ground squirrels [ Spermophilus columbianus ], Rocky Mountain cotton tails [ Sylvilagus nuttali ], Belovsky [1986 b ]; cattle [ Bos taurus ], Campling et al [1961]; beavers [ Castor canadensis ], Belovsky [1984 b ], Doucet and Fryxell [1993], Fryxell et al [1994]; Thomson's gazelles [ Gazella thomsoni ], Wilmshurst et al [1999]; human beings [ Homo sapiens ], Belovsky [1987]; snowshoe hares [ Lepus americanus ], Belovsky [1984 c ]; meadow voles [ Microtus pennsylvanicus ], Belovsky [1984 a ]; muskoxen [ Ovibus moschatus ], Forchhammer and Boomsma [1995]; sheep [ Ovis aries ], Blaxter et al [1961]; shrews [ Sorex araneus, S. caecutiens, S. isodon ], ).…”

Macronutrient modifications of optimal foraging theory: An approach using indifference curves applied to some modern foragers

“…In most linear programing models, the rate of intake of a single nutrient, e.g., energy or protein, is assumed to be maximized, subject to meeting the specified nutrient constraints (Reidhead, 1979). When the intake rate maximizing strategy for two resources leads to mutually exclusive optimal foraging strategies, the optimal mix must be determined by some other specified nutrient or non-nutrient constraint (for an example where the constraint that determines the optimal mix of energy and protein is stomach volume see Belovsky, 1987).…”

“…Finally, the approach, as it has been applied thus far, has been post hoc. Since subsistence patterns show neither energy nor pro-tein maximization, multiple constraints are added to the model one at a time until a close fit to the observed foraging pattern is obtained (Belovsky, 1987). Since the number of possible constraints is unlimited, and constraints and their values are invoked on a case-specific basis, not surprisingly, a specific model can be developed to account for every possible observed diet.…”

Artefact analysis

“…Examples of simulation methods in archaeology are unfortunately limited but are of great interest: Doran (1970), Thomas (1972), Ammermann and Cavalli-Sforza (1973), Wobst (1974), Zubrow (1975), Hassan (1977), Jochim (1976), Hodder ed. (1978, Renfrew and Cooke (1979), Sabloff (1981), Keene (1979), Belovsky (1987), Doran (1990), etc.…”