Foraging for optimal pastsJoachim L. Dagg, Eschborn, Germany

jdagg@gmx.de

Abstract. The so-called diet and patch models were foundational for evolutionary studies of foraging ecology. The diet model analyzed an organism’s choice between at least two different food or prey items. The patch model asked how much time a forager should invest in exploiting a resource patch that offered diminishing returns before moving on to search for another patch. Concerning sources of inspiration, however, some pioneers of optimal foraging theory explicitly denied an input from economics, others explicitly credited marginalist economics, while the majority remained tacit on this issue. An inquiry into the historical sources reveal an interesting patter.

As far as diet (prey or food choice) is concerned, at least two models existed. One was the, probably homegrown, so-called contingency model of diet choice, the other was imported from marginal utility theory of economics. The import could not be operationalized in a way allowing predictions about feeding behavior. It was, therefore, used as a framework for interpreting data on food choices and gaining insights about the relative value of food items. The contingency model was hypothetico-deductive instead. It allowed predictions of behavior that could be tested. It was, therefore, the more popular among the peers and the pioneering publications have become citation classics, whereas the publications importing marginal utility theory int foraging ecology are largely forgotten.

The situation is different for the patch model. At face value, only one homegrown model exists that was discovered independently at least twice. A closer look reveals obscure links suggesting knowledge dispersal from marginal productivity theory of economics towards optimal foraging or mating theory, respectively, along routes of private and unpublished communications. These communications were between alma mater and student in the case of Eric Charnov and between father and son, in the case of Geoffrey Parker.

This study suggests two concusions: 1. models that are operationalized in a way allowing hypothetico-deductive research are more popular among researchers than others requiring a more inductive an interpretive approach.2. The sciences are interlinked far more closely and deeply than mere citations would suggest. Sometimes a knowledge transfer that is crucial for a discovery can occur as an informal and private communication.

Key-words: optimal foraging theory; optimal mating theory, marginal utility, marginal productivity; economics

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mailto:jdagg@gmx.de

1 IntroductionThe so-called diet and patch models were foundational for evolutionary studies of foraging ecology (Ydenberg et al 2007, 8f, 12). The diet model analyzed an organism’s choice between at least two different food or prey items. The patch model asked how much time a forager should invest in exploiting a resource patch that offered diminishing returns before moving on to search for another patch. The research articles pioneering these models, however, show an interesting pattern. Whereassome pioneers explicitly deny an input from economics (e.g., MacArthur & Pianka 1966; Schoener 1987, 35f), others explicitly credit economic models and theorems as their sources of inspiration (e.g., Rapport 1971; 1980; Rapport & Turner 1977; Covich 1972; 1974; pers. comm.), but most are silent on this question.

The following shows that the explicit transfer of an economic model of marginal utility into a diet model of foraging ecology has not been as successful as the alternative diet model, which probably developed independently in ecology. Differences in operationalization and predictive power are suggested as reasons for this difference in success. For the patch model, however, two obscure paths of knowledge dispersal along routes outside the published record could be tracked down and verified. This emphasizes the inter-relatedness of sciences and highlights the fact that many kinds of informal knowledge exchange exist. Before that can be done, however, the economics in question need to be introduced.

2 Marginal utilityAs marginal values are particularly relevant to optimal foraging theory, the marginal utility theory of economics is a good place to start. Therefore, the following takes a closer look at early proponents of marginal utility theory. In 1854, Hermann Gossen stated the law that the utility of a good diminishes with its consumption. Gossen conceived this diminishing gain in psychological terms of pleasure (Genuss) rather than caloric intake or fertilization success, but later economists replaced pleasure by utility.

“Die Größe eines und desselben Genusses nimmt, wenn wir mit Bereitung des Genusses ununterbrochen fortfahren, fortwährend ab, bis zuletzt Sättigung eintritt.” (Gossen 1854, 4f) “The magnitude of one and the same pleasure diminishes continually if we keep enjoying it incessantly, until satiation eventually commences.” (My translation)

Gossen’s second law stated that a consumer should stop enjoying a good, when it still just gives the same marginal pleasure as any of the other goods would.

“Der Mensch, dem die Wahl zwischen mehren Genüssen frei steht, […] muß, […] um die Summe seines Genusses zum Größten zu bringen, sie alle theilweise bereiten, und zwar in einem solchen Verhältnis, daß die Größe eines jeden Genusses in dem Augenblick in welchem seine Bereitung abgebrochen wird, bei allen noch die gleiche bleibt.” (Gossen 1854, 12) “In order to maximize the sum of its pleasure, the person that can choose between several goods has to enjoy each one only partially, in such a proportion that the pleasure at the moment of terminating to enjoy one good is of the same magnitude as of all the others.” (Mytranslation)

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Pareto (1919, 180) modeled this graphically (see fig. 2.1). Indifference curves map ratios of goods, for example, apples, A, and bananas, B, that will have the same utility for consumers and hence render them indifferent to variation in the ratio.

Fig. 2.1: The indifference curves t to t’’’ define ratios of the goods A and B that yield equal utility to a consumer. The budget line mn shows which ratios the consumer could actually afford. The optimal choice is the ratio c’’.

Indifference curves are usually convex to the origin because a consumer that has a lot of bananas and no apples (n) will trade more bananas for one apple than one that already has apples and vice verse for one that has many apples (m) and no bananas. An indifference map is the cluster of indifference curves for varying utility levels. A budget line represents the ratios of the goods a consumer can actually afford with a certain budget. The tangential point where the budget line touches one of the indifference curves defines the optimal ratio of goods that will maximize utility for that consumer. Unlike in figure 1, budget lines will often be concave to the origin, because the price of a good rises with its consumption as an adjustment to either increased demand or decreasedsupply. Finally, the consumption curve that connects the optimal ratios ci (fig. 1) curls away from good B meaning that people will consume relatively less of that good as their affluence rises.

This has become a standard model of optimal consumer choice (Meyers 1948, ch. 7; Friedman 1953, 100-103; Becker 1962), which can be found in all textbooks. Economists can determine the preferences of consumers to different bundles of goods empirically, for example, by using questionnaires. They can construe the corresponding indifference curves from the results and use the model for predicting consumer behavior when princes or taxes for certain goods change (e.g., Boulding 1966, 620).

The model has also been used in foraging ecology by interpreting the indifference curves as representing combinations of prey or food items yielding equal returns per time needed to pursue or handle them and the budget line as representing those combinations of food/prey that a forager could actually catch with a given time budget. However, indifference curves could not be determined in advance, in order to predict the feeding patterns resulting from varying conditions in food or time budgets. Those researchers, who did take this economic model as their point of departure (e.g., Covich 1972; 1974; Rapport 1971; 1980; 1981), left the biological utility of food items implicit in the change of the feeding patterns observed, when the food or time budgets varied. That is, they used the model as a framework for interpreting the observed relations between conditions and feeding pattern. Their model was a tool of analysis not prediction. Conversely, those who did explicate and rank the profitability of food/prey items in advance, in order to test hypotheses about behavior, seem to have developed this so-called contingency model independentlyof economics (e.g., Charnov 1976a; cf. Schoener 1987, 12f).

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3 Marginal productivityAnother theory of particular relevance to the history of foraging theory can be found in Eugen von Böhm-Bawerk’s Positive Theory of Capital, first published in German in 1889 and in English in 1891 (I used the photographic reprint of the English version from 1930). Böhm-Bawerk’s point of departure into his economic studies were two problems about capital interest (Tomo 1995; 1997). The ex ante problem concerned the question why an interest rate was put on a loan. Böhm-Bawerk disagreed with his supervisor Menger’s theory that is was a charge for the use of money or Marx’s that it was a means of capitalists for exploiting laborers. The agio (discount) theorem proposed, instead, that a good to be consumed or used in the future was valued less than the same good to be consumed or used at present. The ex post problem concerned the question why the debitor was usually able to pay the interest. Here, Böhm-Bawerk suggested that the capital investment allows roundabout ways of production that could increase not only the amount of goods produced but also the value of the goods produced. This is referred to as the period-of-production or value surplus theorem (Tomo 1995; 1997).

These aspects of the optimal period of production and discount of Böhm-Bawerk’s theory have been mathematized and modeled by Knut Wicksell (1893[1970], 120-130 and figure at p. 122)and Irving Fisher (1907, 25-28, §9 and fig. 1; 1930, 57-58, §6 and chart 16) respectively. Surprisingly, these models of Wicksell and Fisher turn out to be the ultimate predecessors of the optimal mating model of Parker (1974; Parker and Stuart 1976) and the optimal foraging model of Charnov (1976b), respectively. This article traces the subterranean roots by which these vintage models of marginalist economics percolated into ecology and, there, got “discovered” as models forthe optimal duration of mating (Parker 1974; Parker and Stuart 1976) or of exploiting a resource patch (Charnov 1976b).

3.1 Wicksell (1893) on the optimal period of production Knut Wicksell’s Über Wert, Kapital und Rente was first published in 1893. An English translation was published in 1954 and reprinted in 1970. Wicksell built on Böhm-Bawerk (1891), who had Wicksell (1893) managed to construe the investment of capital into an endeavor of production as units of time invested by plotting an inverse of the interest rate on the abscissa of his graphical model. An inverse of any interest rate (x%/year) will yield an amount of time in years.

Wicksell analyzed a case, in which workers borrow all the capital required to set up a production process, so that the rate of interest on that capital, z, equals their fixed costs. If the wholecapital invested in the endeavor was borrowed at the beginning, the interest had to be paid for the whole period, t, that the endeavor lasted. But if capital was taken up in installments, the time during which that interest had to be paid could be reduced at most by half.

He then asked, “how long a period of production these workers are to choose with most advantage to themselves” (Wicksell 1970, 120). Wicksell actually wanted to maximize the wages l of the workers by finding the optimal production time t. He illustrated his analysis in the form of a graphic (fig. 3.1), which is strikingly similar to the now emblematic graph illustrating the marginal value theorem in behavioral ecology (fig. 9.1). As the period during which the interest must be paid can be halved by borrowing in installments (see above), the tangent meets the abscissa at the inverse of z/2 rather than z.

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Fig. 3.1.: Wicksell’s graphical model first published in 1893 (Wicksell 1970, 122).

In his Finanztheoretische Untersuchungen (Wicksell 1900, 40), the productivity curve begins at the origin, because Wicksell came to believe that workers cannot produce anything without some capital. He also discussed the effect of a tax being placed on the production and illustrated it with a lowered production curve and tangent. Wicksell (1935, 180, fig. 14) used a similar graphic model in order to illustrate the relationship between capital, interest and time using the example of wine gaining value with time.

George Joseph Stigler (1941, 279) explained Wicksell’s theory as follows: “We may postulate a given number of workers who may borrow any required sum of capital at a given rate of interest. They produce all necessary tools and equipment and use these up completely in the production period. These laborers seek to maximize their annual wages, which with interest equal the annual product, since in a static state there will be no profits and land is a free good.” Stigler (1941, 281) also featured the graphical illustration.

Fig. 3.2: Stigler’s reproduction of Wicksell’s graphical model (Stigler 1941, 281, fig. Viii).

Later, Joan Robinson (1953-54, fig. 2; 1956, pp. 411-420) adapted Wicksell’s model in orderto predict the effects of technical progress on wages and profit. Carl Uhr (1962, 66) described the relation between invested capital and the optimal period of prodicing goods in Wicksell’s model as follows: “With a certain quantity of labor and land given, and all of the capital invested in advances,capital could be expressed as a function of time, namely of the length of the production period during which it suffices to sustain laborers and landowners.” Hirshleifer (1967, 191) called Wicksell’s formalization of a theory relating wages, capital stock, interest and the period of production “one of the most famous developments in the history of economic thought.” That is, the economists carried on Wicksell’s (1893) way of modeling marginal productivity right into the time, when behavioral ecology started as a new way of doing ethology with an economic thrust.

Two things about Wicksell’s analysis and graphic model differ from later installments in behavioral ecology (e.g., Parker 1974; Smith & Fretwell 1974; Parker & Stuart 1976). First,

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Wicksell used an inverse of the interest rate to determine the intersection point of the tangent with the x-axis. This suggests that the workers should terminate the process earlier as the interest rate on invested capital rose. It makes sense, however, because the workers should not even borrow the money to start the endeavor, if the interest rates were too high. In foragers or males, on the other hand, an exceptionally long search time does not mean that the individual should not even start exploiting/mating a found resource patch/female. This is so, because the time spend searching is thereal cost being paid, whereas in Wicksell’s model the cost being paid is interest and this cost is transformed into a time equivalent by calculating it inverse.

Second, Wicksell determined the portion of the revenue that can be apportioned to wages as the value, l, from the origin to the intersection of the tangent with the y-axis, the remainder going to pay the fixed costs. This is not possible for mating or foraging behavior, because the costs and benefits have different currencies. In optimal mating theory, for example, the gain is in terms of fertilized eggs, the expenditure in energy used for searching. This difference in currencies was a formidable problem for behavioral ecology (Ydenberg et al. 2007, 15) and the solution was to find trade-offs in state variables instead (e.g., time spent searching vs. time spent mating).

The above-mentioned differences suggest that Wicksell has not been a direct source of inspiration for optimal mating theory. Furthermore, the graphical model of Wicksell has not becomeas emblematic in economics as figure 4 has in behavioral ecology. Nevertheless, this model must have entered operations research or industrial engineering and thus reached Geoffrey Parker’s father, a chemical engineer and biochemist. He gave his son the crucial tip for modeling optimal mating time according to this optimal period of production theory (e.g., Parker 1974, 157, fn 1, 164;2010, 443; pers. comm.) without Geoffrey Parker having ever seen the source from economics, operations research, or chemical engineering.1 In fact, the tip that Allan Parker gave to his son suggests a re-interpretation of Wicksell’s model. The inverse of the interest rate was replaced by a real amount of time being needed to set up a production-process within a chemical plant, where capital (natural, human, industrial) was already in place and the fixed set-up time was the only cost to be considered. Hence, this lost source of Alan Parker was already one step closer to the optimal mating model than Wicksell’s. Otherwise, the optimal period of production was determined in a way identical to Wicksell’s, by marking the time investment on the negative half of the X-axis, plotting the gain function within the positive (+/+) quadrant of the coordinate system, and drawing atangent from the time-investment point that touched the gain function.

3.2 Fisher (1907) on the marginal value of expected incomeFisher (1907, chap. II) distinguished the interest being fixed in a loan contract as explicit from the implicit interest. The implicit interest is the discounting that is tacitly made in any transaction. For example, an orchard producing, on average, an annual crop of apples worth $1,000 will not be worth $20,000, because the orchard is expected to yield that income for 20 years and nothing thereafter. Instead, the prize indicates that the interest rate implicit in the transaction has been 5%. The future incomes have been discounted by that rate. Hence, the implicit interest is the agio or discount. However, Fisher inversed Böhm-Bawerk’s productivity theory in claiming that the income(e.g., crops of a land) produces capital and not the inverse. That is, the capital (e.g., money) invested

1 The actual source of Alan Parker is unknown (Geoffrey Parker, pers. com.), but any textbook considering a real time-investment in setting up a process and returns diminishing with time would be a likely candidate.

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in an endeavor does not somehow produce value (as in Böhm-Bawerk’s theory), but the value of theexpected income (discounted by the implicit interest rate) produces capital.

“The paradox that, when we come to the value of capital, it is income which produces capital, and not the reverse, is, then, the stumbling-block of the productivity theorists.” (Fisher 1907, 15)

Fisher went on to illustrate this inverted productivity theory of capital with a model for the optimal waiting time until harvesting a forest. This graphical model uses the actual rate of interest, in order to find the tangent to the growth curve that mrks the optimal waiting time, instead of takingan inverse of the interest rate as a time-investment to be marked at the negative branch of the x-axis.

Fig, 3.3: The future yields, B’, B’’, T, are discounted by the interest rate, in order to get the present values, C’, C’’, t, of that expected income. The tangent interest rate marks the optimal waiting time (Fisher 1907, 25, fig. 1).

A point of note, here, is that Fisher’s inversion of the theoretical cause-effect relation between capital and productivity also changed his usage. He avoided the term marginal productivityand instead circumscribed what we would today recognize as a concept of marginal value:

“For, of various optional employments of his capital, the investor selects the one which offers the maximum present value.” (Fisher 1907, 25, see also 159, 162, 167)

“The individual selects from the eligible list (of prospective income-streams varying in distribution, in time and otherwise) the income-stream which has in present estimation, whether truly or falsely, the maximum present value. If alternatives are numerous and vary continuously from each other, this condition is equivalent to the condition that the marginal rate of estimated return on sacrifice shall equal the rate of interest.” (Fisher 1907, 162)

Later (Fisher 1930, 57) called it the marginal rate of return over cost. This point of usage and the particular example of the optimal waiting time until harvesting a trees will become significant, again, when we turn to the marginal value theorem of Eric Charnov (1976b). Suffice it to say that, again, economists (e.g., Boulding 1966, ch 30; Bierman 1968; Hishleifer 1970) carried on Fisher’s way of modeling marginal value (or return over cost) right into the time, when behavioral ecology started as a new way of doing ethology with an economic thrust.

Before behavioral ecology took off, however, these marginalist models came under attack within economics as requiring a degree of foresight that cannot be had in any real market. This eclipse of the marginalist tradition between the 1940s and 60s has lead to the deplorable situation that even those behavioral ecologists, who are aware of a more recent heritage of their science from economics, are usually not aware of the deeper roots of their science in economics.

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4 The marginalist controversyMarginalist theory was based on the assumption that individuals (firms) acted rationally so as to maximize their utility (profit). One of the first to attack the foresight concerning interest that was implied in Fisher’s theory was Seager (1912; see also reply by Fisher 1913 and comment by Seager 1913). The so-called marginalist controversy, however, erupted much later. It roughly lasted from 1940s to the 1950s (Mongin 1997; Screpanti & Zamagni 2005, 413). Some empirical results suggested that firms did not maximize their profits. The price-setting of firms was not marginalist (Hall & Hitch 1939), profit possibilities were left unexploited until costs changed (Lester 1946), andfirms made decisions infrequently and in response to expected policies by competitors not profits (Lester 1946). Tintner (1941a, b) denied that the idea of maximizing utility or profit even made any sense as a guide for action in an unpredictable economic system, because it would require a foresight that cannot be had. It is interesting to note that Hall & Hitch already mentioned, parenthetically, the resolution that the defenders of marginalism would later settle on:

“in pricing they [executives of firms] try to apply a rule of thumb which we shall call ‘full cost’, and that maximum profits, if they result at all from the application of this rule, do so as an accidental (or possibly evolutionary) by-product.” (Hall & Hitch 1939, 18f)

Later scholars of economics (e.g., Alchian 1950; Enke 1951, Friedman 1953, 3-43) did, indeed, employ a selection argument in defense of the established economic theory (see also Vromen 2011). In the long run, only the firms that did maximize profits will survive economically and only the individuals that did maximize their utility will rise in the hierarchy and become affluent. The result looks as if individuals and firms act rationally and maximize utility or profits, even if their actions were random and their foresight nill.

“In an economic system the realization of profits is the criterion according to which successful and surviving firms are selected. […] Realized positive profits, not maximum profits, are the mark of success and viability. It does not matter through what process of reasoning or motivation such success was achieved. The fact of its accomplishment is sufficient. This is the criterion by which the economic system selects survivors: those who realize positive profits are the survivors; those who suffer losses disappear.” (Alchian 1950, 213, original emphasis)

“In the long run, however, if firms are in active competition with one another rather than constituting a number of isolated monopolies, natural selection will tend to permit the survival of only those firms that either through good luck or great skill have managed, almost or completely, to optimize their position and earn the normal profits necessary for survival. In these instances the economist can make aggregate predictions as if each and every firm knew how to secure maximum long-run profits.” (Enke 1951, original emphasis)

“Let the apparent immediate determinant of business behavior be anything at all—habitual reaction, random chance, or whatnot. Whenever this determinant happens to lead to behavior consistent with rational and informed maximization of returns, the business will prosper and acquire resources with which to expand; whenever it does not, the business will tend to lose resources and can be kept in existence only by the addition of resources from outside. The process of “natural selection” thus helps to validate the [maximization-of-returns] hypothesis—or, rather, given natural selection, acceptance of the hypothesis can be

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based on the judgment that it summarizes appropriately the conditions for survival.” (Friedman 1953, 22)

At that point, economics was the receiver and evolutionary biology the source delivering an argument for economic selection employed in order to justify the assumptions of rational choice andutility maximization in marginalist theories.

5 The imperialist outreach of economistsSome from the next generation of economists took the validity of neoclassical theory for granted and used it as a base for expanding the domain of it into other territories. Thus, Tullock (1970; 1971a; b) applied marginal utility theory, demand-supply diagrams, and externalities to explain the prey-switching of general predators, the food patch exploitation of coal tits, and pasture management respectively; Becker (1974; 1976) applied social income (instead of inclusive fitness) to sociobiological problems and Hirshleifer (1977) expanded on this. Returning from these forays, they claimed an imperialist agenda:

“The combined assumption of maximizing behavior, market equilibrium, and stable preferences, used relentlessly and unflinchingly, form the heart of the economic approach as I see it. They are responsible for the many theorems associated with this approach [Examples omitted]. The economic approach is clearly not restricted to material goods and wants, nor even to the market sector.” (Becker 1976, 5)

“[I]t is ultimately impossible to carve off a distinct territory for economics, bordering upon but separated from other social disciplines. Economics interpenetrates them all, and is reciprocally penetrated by them. There is only one social science. What gives economics its imperialist invasive power is that our analytical categories – scarcity, cost, preferences, opportunities, etc. – are truly universal in applicability. Even more important is our structured organization of these concepts into the distinct yet intertwined processes of optimization on the individual decision level and equilibrium on the social level of analysis. Thus economics really does constitute the universal grammar of social science.” (Hirshleifer1985, 53, emphasis added)

These claims already show the break-lines that other researchers attacked later. For example,Boulding (1986) took the claim to conquer political and other sciences seriously only to diagnose the utter failure of this approach to solve any of their problems (e.g., the risk of a nuclear war or maximum credible accident, the desperate condition of the ‘third world,’ the environmental crisis). Worse still, it could not even cure its own pathologies of the financial system. That is, he refused to regard the market conditions as a given environment about which nothing can be done. Unlike animal species that adapt to their environment as well as possible, but are still powerless against their ultimate extinction, this passive attitude against economic conditions was no option. Still deeper, Heilbroner (1991) criticized that this ostensibly passive attitude against the market and its pathologies reflects a commitment to a capitalist ideology.

Simon (1986) pointed out that this neoclassical approach is based on assumptions, which aretaken for granted rather than tested empirically. Imperial economists have only shown that the theorems and models of neoclassical economics can be applied to all sorts of problems in other sciences. They have done armchair economics. That does not mean that these explanations would

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withstand a comparison if other approaches based on different assumptions were tried. In particular,Simon had opened the black-box of decision-making earlier and found that rationality was bounded and utility was not maximized but needs were only “satisficed” (e.g., Simon 1955; 1979). Etzioni (2011) reviews a new research programme, behavioral economics, challenging the neoclassical assumptions of rational choice and utility maximisation. Coming full circle, this new behavioral approach to economics took its research methods from other sciences like psychology. For example,at the occasion of receiving the Nobel Memorial Prize in Economic Sciences, Daniel Kahneman said:

“Tversky and I viewed our research primarily as a contribution to psychology, with a possible contribution to economics as a secondary benefit. We were drawn into the interdisciplinary conversation by economists who hoped that psychology could be a useful source of assumptions for economic theorizing, and indirectly a source of hypotheses for economic research.” (Kahneman 2003, 1449)

One of the economists mentioned by Kahneman, Richard D. Thaler, later won the same Prize for “integrating economics with psychology.” (see Committee for the Prize in Economic Sciences in Memory of Alfred Nobel 2017)

The evolutionary defense of neoclassical assumptions by earlier economists like Friedman and Alchian, however, did not only send their heirs on conquests but also had a direct effect on ecologists. Some saw that the assumptions of rational economic choice and utility maximisation do not need to be taken literally and can, therefore, also apply to animals. Hence, they started to apply economic models to optimal foraging theory before the conquerors even arrived at the scene. Among other things, this free exchange of ideas with marginalist economics has lead to a successfulresearch programme of optimal foraging theory within behavioral ecology. Interestingly, the most advanced research within this programme also studies choices of animals that are irrational by erstwhile economic assumptions and tries to reinterpret and reintegrate these findings in an extended explanatory framework (Huneman & Martens 2017). This suggests that the attacks undermining marginalist assumptions in economics (e.g., by Simon, Kahneman or Thaler) have been received in behavioral ecology as well. The following will not treat this actual research, however, but only the historical diet (marginal utility) and patch (marginal productivity) models.

6 Independent developmentsAs already mentioned at the end of section 2, the so-called contingency model among the diet models probably developed among ecologists without input from economics (Schoener 1987, 12f). The claims of independence, however, were extended beyond that model to the whole science. MacArthur & Pianka (1966) implied simultaneous but independent developments in economics and biology leading to similar models.

“There is a close parallel between the development of theories in economics and population biology.” (MacArthur & Pianka 1966, 603)

Responding to claims that marginalist economics provided major stimuli for optimal foraging theory (Schoener 1987, 31), Thomas Schoener was more explicit in his denial of such an influence.

“Almost everyone would agree that there are striking resemblances between OFT [optimal foraging theory] and certain aspects of economic theory. To what extent are these

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resemblances convergences and to what extent are they casual [sic]?—the direction of course being from economics to ecology.

The answer appears fairly clear when one considers who the principal early theorists were. Except for papers by Rapport (1971), Covich (1972), and in part Hamilton and Watt (1970), explicit reference to economic theory is largely lacking (Rapport & Turner 1977), very likely because most of the other papers’ authors did not know much, if anything, about it. This is despite the appearance of such phrases as “the economics of consumer choice” (MacArthur 1972), “marginal value theorem” (Charnov 1976b), or “currency” (Schoener 1971). It is hard to verify the ignorance in most cases, but speaking for myself, I can confirmits near totality. For example Joel Cohen pointed out to me that a graphical model in Schoener (1969b) is a “production function,” and Rapport and Turner (1977) say that the tradeoff between time and energy in Schoener (1971) is a rediscovery of the economist’s notion of marginal costs. Pianka (personal communication) also notes the ignorance for himself, and probably, for MacArthur: “I recall telling a Princeton economics grad student our theory and having him say it was ‘old hat’!” One striking exception to the generalizationexists, however: Belovsky received his undergraduate degree in economics.

Not only have nearly all ecologists been chronically ignorant of economic analyses, but to go a step farther, it seems that when the latter were directly appropriated, they were less influential. […] Hence had economics never been invented, optimal foraging concepts would likely exist virtually unchanged, albeit with more biological terminology.” (Schoener 1987, 35f)

While the ignorance of economics by Schoener and Pianka is thus certified by their own testimony,2 Schoener’s conclusions about other peers must be taken with a grain of salt. First, even if all ecologists were ignorant about economics, this does not mean that no influence existed. The case of Geoffrey A. Parker illustrates an unnoticed influence via an informal communication with his father, Dr. Alan Parker (see section 9). Second, Eric L. Charnov graduated in fisheries and resource management; he took several pure economics classes and many classes that dealt with economic arguments in a context of fisheries and resource management; he even took a class in forest management and learned about timber harvesting; and he called his model the Marginal Value Theorem as a tribute to the many economic theorems he learned about (Charnov, pers. comm.). Indeed, economic textbooks are cluttered with theorems (e.g., Baumol 1961).

7 Explicit import of the marginal utility model Rapport (1971; 1980; 1981; Rapport and Turner 1977) took big chunks of marginal utility theory and introduced them to an ecological context, keeping economic terms like indifference curve, welfare etc. Just like consumers should choose a combination of different goods yielding the optimal utility, so generalist predators should switch between different prey species yielding the optimal food gain. He only dropped the consumption curve through the optimal ratios ci (cf. fig. 1) and plotted a concave time budget line assuming that the search-time required to catch a prey item increases as the predator becomes more specialized (see fig 2. in Rapport 1971). Rapport (1971, 585) mentioned a textbook on microeconomics as a particular source of inspiration: “The model here derives from consideration of models found useful in microeconomic analysis (Watson 1963).”

2 Unfortunately, the correspondence of Robert MacArthur archived at the Yale University library is sealed until 2035.

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The techniques required for modeling indifference curves and optimal consumer choice could readily be taken from this textbook for students and applied to other situations. Whereas Rapport (1971) was purely theoretical, Rapport (1980; 1981) used the model as a frame of interpretation for experiments manipulating the combinations of food items offered to a protozoon.

Covich (1972; 1974) independently applied the same theory to the food choice of mice species and later to pollinator insect. The introduction of the theory by Covich (1972) is more comprehensive than in Rapport (1971) and so are his references to relevant publications of economics. He even mentions “F. Y. Edgeworth in 1881” and “I. Fisher in 1892” (Fishers thesis published by Yale University Press) in the main text though not in the reference list. Covich (1972) manipulated the availability of food items (pumpkin and sunflower seeds) for deer and beech mice, in order to construe the model from the observed change in feeding behavior resulting. That is, the utility in energy gain of the food items remained implicit and the behavior informed the model builder about the indifference relations of the food items. The model was the theoretical framework for interpreting the behavior. Later, Covich (1974) use this theoretical framework in order to interpret findings of his peers about pollinator behavior.

Both Rapport and Covich used the model, in order to gain insights about the value of different food items for their consumer species. But they could not predict the feeding preferences from the model. And that means they could not test their model in the hypothetico-deductive way.

Fig. 7.1: Animal preference map for the optimal choice of food items X and Y. Three different kinds of budget lines are illustrated: B1 is concave to the origin, B2 straight, and B3 convex. As usual, the indifference curves Ii are convex to the origin. The optimal ratios of food items are at the points Ei (from Covich 1972, 73)

8 Marginalist economics as a college to graduate fromEven without conscious application of economic theory, knowledge could diffuse to behavioral ecology in less visible ways. The case of Geoffrey A. Parker (see below) illustrates an unnoticed influence. Between the explicit use of economic tools and the unconscious influence along obscure routes, however, there is the alma mater type of influence that can be strong but invisible in publications. Naturally, graduate research applies knowledge from undergraduate training but the lecturers and textbooks are usually not cited because their knowledge can be taken for granted in thepeers. For example, modern genetics research papers are full of terms and concepts like gene, DNA,mutation, linkage disequilibrium without even once giving a reference to the originators (except for deep reviews, papers dealing with particularly recalcitrant issues, or indeed historical analyses). Each time and place has its common knowledge that can be taken for granted and needs no references. This does not exclude the possibility of misjudgments of the peers’ knowledge.

Eric Charnov graduated in fisheries and resource management including classes in economics and operations research (pers. comm.). Calling his optimal foraging theory the marginal

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value theorem (Charnov 1976b) was a conscious reminiscence to the many marginalist economics he had learned of as an undergraduate, but he did not mean to refer to the marginal utility theory described in section 4 in particular (Charnov, pers. comm.). Apparently, Charnov had taken a knowledge of economics as evinced by Rapport or Covich as a matter of course. However, Charnov(1976b, 132) did cite a book on operations research by Taha (1971) on “the second derivative conditions for a multidimensional optimization problem to be an optimum” (Charnov, pers. comm.),which was definitely more than he could take for granted in peers. That is, Charnov did not actively sanitize his article from all traces of its provenance before publication. On the contrary, he named the marginal value theorem in honor of the marginalist economists of whom he had learned as an undergraduate and dropped a citation concerning an arcanum of operations research.

Fig. 9.1: Graphical model by Charnov (1976b, 132). Unlike Wicksell (1893; 1935), he did not draw out the tangent to meet the x-axis but, like Fisher (1907, 1930), he used a rate (slope) instead.

9 Fortuitous benefit from economics jetsamNon-public communication is an obscure route for the diffusion of knowledge. Here, non-public means any communication that does not reach beyond the direct participants, like private conversations or lectures that do not get recorded and published. Unlike Charnov, Parker ran through the classical zoology curriculum with no training on economics whatever (Parker 2001). The crucial tip for solving the problem of optimal persistence of males with females (Parker 1974) came from his father, Dr. Alan Parker, who was an industrial chemist and microbiologist working on antibiotics production and knew this method from his job.

“I talked over the problem with my father, and he saw a parallel in industrial economics. Thesituation resembled a process where there was a fixed “setting up” time before the process could begin, and where the cumulative yield showed diminishing returns with the time that the process ran. To maximize the yield rate, the optimal run time was given graphically by a tangent drawn to the curve of cumulative yield with time, the tangent starting from a point on the time axis to the left of the origin a distance equal to the setting up time.” (Parker 2001, 14; see also Parker 1974, 164 and 2010, 443)

As the tip to draw the tangent intersecting the x-axis at -S (negative value of the average time spent searching for a female) reached Parker via the private communication with his father, who knew it from his job in the biochemical industry. Unfortunately, the source of Alan Parker remains unknown (Geoffrey Parker, pers. comm.). The resulting model of optimal mating time (fig. 9.1), however, is strikingly similar to that of Wicksell (fig. 3.1).

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When Geoffrey Parker wanted to analyze this optimization problem more generally, he recruited the electrical engineer Robert A. Stuart. They applied their model to the yellow dung fly, Scathophaga stercoraria. (Parker & Stuart 1976). Around oviposition sites, dung pats, the males either search for females, copulate with a female or guard it after copulation, while the female is laying eggs. Hence the feeding, cleaning, resting and other behaviors could conveniently be ignored. The guarding prevents any other male from mating after him, who would otherwise displace his sperm and reduce his fertilization success from over 80 to under 20% of the next batch.

Fig. 9.1: The emblematic graphical model of the marginal value theorem. Although Charnov (1976b) is usually credited for the marginal value theorem, the graph of Parker (1974; Parker & Stuart 1976) became notorious.

Parker and Stuart apportioned the three behavioral patterns of male dung flies that could be observed on dung pats to the two sides of their trade-off as follows:

“However, extra time invested in copulation means missed opportunities to capture new females. The mean search cost S for a new female is approximately 140 min (Parker 1970b),to which must be added the 16.5 min guarding time during oviposition.” (Parker & Stuart 1976, 1060)

That is, they ignored resting, cleaning, feeding and other behaviors, because it took place away from the dung pats. But their reason for adding the guarding to the searching time was their assumption that both were mandatory expenditures (Parker, pers. comm.) and that none of the three patterns could simply be dropped from the trade-off. While this reflects the economic convention ofdividing the full costs into fixed costs on the one hand and variable costs on the other, such economic reasoning did not inform their choice (Parker, pers. comm.).

However, a comparison with other approaches can highlight the analogy with economics. Take the biological functions, for example. Searching is for finding a mate, copula for transferring sperm and guarding for ensuring the fertilization success of that sperm. Reasoning about biological functions, the three patterns either form one unit as opposed to resting, feeding cleaning and the like, or the copula and guarding form a sub-unit with closely related functions in fertilization—the copula for transferring sperm and the guarding for ensuring the fertilization success of that sperm. Reasoning from biological functions, then, would have suggested to trade copulating duration plus guarding time off against searching time, but this would have destroyed the model fit.

Other forms of modeling do also suggest other choices. For example, genetic models often assume that drift or recombination would make no difference and therefore ignore them, no matter whether they are fixed or variable. In game theory, the fixed costs that all players need to pay anyway do not even enter the payoff matrix. As Parker and Stuart assumed that mate guarding was

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mandatory and invariable, they could as well have dropped it from their trade-off.3 This would have turned the good into a nearly perfect fit of their model-prediction with copula duration observed in the field.4 That is, they have not chosen the apportioning that would have yielded the best model fit. The apportioning of Parker and Stuart is isomorphic to conventions in economics, even if this was not the conscious reason for their choice.

DiscussionMy historical issue was twofold. On the one hand, an explanation was needed for the apparent contradiction between researchers that explicitly denied any input from economics into foraging ecology (MacArthur & Pianka 1966; Schoener 1987, 35f) and others explicitly crediting economics as a source of inspiration for foraging ecology (e.g., Rapport 1971; Covich 1972). The explanation is that two different kinds of diet model existed and only one was imported from economics. The import suffered from the impossibility to determine indifference curves in advance. Hence, it could not be used as a tool for predicting behavior, but only as a framework for interpreting it a posteriori.That rendered it less successful than the homegrown diet model. The relative success of these models was only contingently related to their provenance and not due to chauvinism by ecologists.

The second issue was the rather subtle and difficult one to show that knowledge transfer alsooccurs through private and unpublished communication, but can sometimes be tracked down despite the lack of citations of published sources. This has been successful and the importance of these informal routes of knowledge transfer cannot be denied given the above evidence on the patchmodel of foraging ecology. At the same time, such knowledge transfer does not imply cognition of the ultimate sources or plagiarism at all. The pupil who calculates or writes correctly is not charged with plagiarizing his teachers, and teachers who do not bother their pupils with ultimate sources are neither. Researchers who apply the lessons of their student years properly without citing their erstwhile textbooks are not plagiarizing either.

Acknowledgments. Thanks to Geoffrey Parker, Eric Charnov and Alan Covich for patiently answering questions via e-mail.

3 By the way, mate-guarding is neither mandatory nor invariable in the yellow dung fly, as studies of their mating behavior at sites other than cow-dung showed (e.g., Pitnick et al. 2009).

4 Three behaviors can be apportioned to the sides of a trade-off in six different ways: A+B vs C, A vs B+C, A+C vs B, A vs B, A vs C, B vs C. Parker and Stuart (1976) chose A+C vs B (searching+guarding vs copulating), while A vs B would have yielded the best model fit.

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References [for ease of writing, will be deleted later]Alchian, Armen A. 1950. Uncertainty, evolution and economic theory. Journal of Political

Economy 58: 211-222.Baumol, William J. 1961. Economic theory and operations analysis. Englewood Cliffs, NJ:

Prentice-Hall. [https://archive.org/details/in.ernet.dli.2015.124487]Becker, Gary S. 1962. Irrational behavior and economic theory. Journal of Political Economy 70: 1-

13.Becker, Gary S. 1974. A theory of social interactions. Journal of Political Economy 82: 1032-1093.Becker, Gary S. 1976a. Altruism, egoism, and genetic fitness: economics and sociobiology. Journal

of Economic Literature 14: 817-826.Becker, Gary S. 1976b. The economic approach to human behavior. University of Chicago Press.Bierman, Harold Jr. 1968. The growth period decision. Management Science 14(6): B302-B309.Boulding, Kenneth E. 1966 (first edition in 1941). Economics Analysis, vol. I, Microeconomics.

New York: Harper and Row. Boulding, Kenneth E. 1986. What went wrong with economics? The American Economist 30: 5-12.Charnov, Eric L. 1976a. Optimal foraging. Attack strategy of a mantid. American Naturalist 110:

141-151.Charnov, Eric L. 1976b. Optimal foraging, the marginal value theorem. Theoretical Population

Biology 9: 129-136.Charnov, Eric L., and Gordon H. Orians. 1973. Optimal foraging: some theoretical explorations.

Lobo Vault, University of New Mexico. http://hdl.handle.net/1928/1649. Accessed 26 January 2017.

Charnov Eric L., and John R. Krebs. 1974. On clutch size and fitness. Ibis 116: 217-219.Committee for the Prize in Economic Sciences in Memory of Alfred Nobel. 2017. Richard H.

Thaler: integrating economics with psychology. Royal Swedish Academy of Sciences, 9 October 2017. Accessed 23 Oct 2017: http://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2017/advanced-economicsciences2017.pdf.

Covich, Alan P. 1972. Ecological economics of seed consumption by Peromyscus: a graphical model of resource substitution. Transactions of the Connecticut Academy of Arts and Sciences 44: 71-93.

Covich, Alan P. 1974. Ecological economics of foraging among coevolving animals and plants. Annals of the Missouri Botanical Garden 61: 794-805.

Covich, Alan P. 1976. Analysing shapes of foraging areas: some ecological and economic theories. Annual Review of Ecology and Systematics 7: 235-257.

Dorfman, Robert. 1995. Austrian and American capital theories: a contrast of cultures. Journal of the History of Economic Thought 17: 21-34.

Edgeworth, Francis Ysidoro. 1881. Mathematical psychics: an essay on the application of mathematics to the moral sciences. London: C. Kegan Paul & Co. [https://archive.org/details/mathematicalpsyc00edgeuoft]

Enke, Stephen. 1951. On maximizing profits: a distinction between Chamberlin and Robinson. The American Economic Review 41: 566-578.

Etzioni, Amitai. 2011. Behavioral economics: toward a new paradigm. American Behavioral Scientist 55(8): 1099-1119.

16

625

630

635

640

645

650

655

http://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2017/advanced-economicsciences2017.pdfhttp://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2017/advanced-economicsciences2017.pdfhttp://hdl.handle.net/1928/1649https://archive.org/details/mathematicalpsyc00edgeuofthttps://archive.org/details/in.ernet.dli.2015.124487

Fisher, Irving. 1892 (reprinted in 1926). Mathematical investigations in the theory of value and price. New Haven: Yale University Press. [https://archive.org/details/in.ernet.dli.2015.84061]

Fisher, Irving. 1907. The Rate of Interest. The Macmillan Company, New York. [https://archive.org/stream/rateinterestits03fishgoog#page/n51/mode/1up]

Fisher, Irving 1913. The impatience theory of interest. American Economic Review 3(3): 610-618.Fisher, Irving. 1930. The Theory of Interest. The Macmillan Company, New York.

[http://files.libertyfund.org/files/1416/Fisher_0219.pdf]Friedman, Milton. 1953. Essays in positive economics. Chicago University Press.Gossen, Hermann H. 1854. Entwicklung der Gesetze des menschlichen Verkehrs und der daraus

fließenden Regeln für menschliches Handeln. Friedrich Vieweg und Sohn, Braunschweig. https://books.google.de/books?id=BzFGAAAAYAAJ. Accessed 20 January 2017

Hall, R. L. & C. J. Hitch. 1939. Price theory and business behaviour. Oxford Economic Papers 2: 12-45.

Heilbroner, Robert. 1991. Economics as universal science. Social Research 58(2): 457-474.Hirshleifer, Jack. 1958. On the theory of optimal investment decision. Journa of Political Economy

66: 198-209.Hirshleifer, Jack. 1967. A note on the Bohm-Bawerk/Wicksell Theory of interest. The Review of

Economic Studies 34(2): 191-199.Hirshleifer, Jack. 1970. Investment, interest and capital. New York: Prentice-Hall. Hirshleifer, Jack. 1977. Shakespeare vs. Becker on altruism: the importance of having the last word.

Journal of Economic Literature 15: 500-502.Hirshleifer, Jack. 1985. The expanding domain of economics. American Economic Review 75: 53-

68.Huneman, Philippe, and Johannes Martens. 2017. The behavioural ecology of irrational behaviours.

History and Philosophy of the Life Sciences 39: 23. doi: 10/1007/s40656-017-0150-5.Kahnemean, Daniel. 2003. Maps of bounded rationality: psychology for behavioral economics.

American Economics Review 93: 1449-1475.Krebs, John R. 2010. Luck, chance and choice. In Animal Behaviour: The Second Generation, eds.,

Lee C. Drickamer, and Donald A. Dewsbury, 375-404. Cambridge Univ Press.Krebs, John R., and Nicholas B. Davies. 1978. Behavioural ecology: an evolutionary approach.

Oxford: Blackwell Scientific Publications.Krebs, John R., and Nicholas B. Davies. 1997. Behavioural ecology: an evolutionary approach.

Fourth edition. Oxford: Blackwell Science.MacArthur Robert H., and Eric R. Pianka. 1966. On optimal use of a patchy environment.

American Naturalist 100: 603-609.MacArthur, Robert H. 1972. Geographical ecology: Patterns in the distribution of species.

Princeton University Press.Meyers, Albert Leonard. 1948. Elements of modern economics. Third edition. Yew York: Prentice-

Hall.Mongin, Philippe. 1997. The marginalist controversy. In Handbook of economic methodology, eds.,

J. Davis, W. Hands & U. Maki, 558-562, London Edward Elgar.Pareto, Vilfredo. 1919. Manuale di economia politica con una introduzione alla scienza sociale.

Milano: Società Editrice Libraria. https://archive.org/details/manualedieconomi00pareuoft. Accessed 21 January 2017.

17

660

665

670

675

680

685

690

695

700

https://archive.org/details/manualedieconomi00pareuofthttps://books.google.de/books?id=BzFGAAAAYAAJhttps://books.google.de/books?id=BzFGAAAAYAAJhttp://files.libertyfund.org/files/1416/Fisher_0219.pdfhttps://archive.org/stream/rateinterestits03fishgoog#page/n51/mode/1uphttps://archive.org/stream/rateinterestits03fishgoog#page/n51/mode/1uphttps://archive.org/details/in.ernet.dli.2015.84061

Parker, Geoffrey A. 1974. Courtship persistence and female-guarding as male time investment strategies. Behaviour 48: 157-184.

Parker, Geoffrey A. 2001. Golden flies, sunlit meadows: a tribute to the yellow dungfly. In Model Systems in Behavioral Ecology, ed., Lee A. Dugatkin, 3-26. NJ: Princeton Univ Press.

Parker, Geoffrey A. 2010. Reflections before dusk. In Leaders in Animal Behaviour: The Second Generation, eds., Lee C. Drickamer, and Donald A. Dewsbury, 429-464. Cambridge Univ Press.

Parker, Geoffrey A., and Robert A. Stuart. 1976. Animal behavior as a strategy optimizer: evolution of resource assessment strategies and optimal emigration thresholds. American Naturalist 110: 1055-1077.

Pitnick, Scott, Kali R. H. Henn, Stephen D. Maheux et al. 2009. Size-dependent alternative male mating tactics in the yellow dung fly, Scathophaga stercoraria. Proceedings of the Royal Societyof London B 276: 3229-3237.

Rapport, David J. 1971. An optimization model for food selection. American Naturalist 105: 575-587.

Rapport, David J. 1980. Optimal foraging for complementary diets. American Naturalist 116: 324-346.

Rapport, David J. 1981. Foraging behavior of Stentor coeruleus: a microeconomic interpretation.. In Mforaging behavior, eds., Alan C. Kamil & Theodore D. Sargent, 77-93. New York: Garland Publishing.

Rapport, David J., and James E. Turner. 1977. Economic models in ecology. Science 195: 367-373.Robinson, Joan. 1953-54. The production function and the theory of capital. Review of Economic

Studies 21(2): 81-106.Robinson, Joan. 1956. The accumulation of capital. Homewood, IL: Richard D. Irwin.Schoener, Thomas W. 1969. Optimal size and specialization in constant and fluctuating

environments: an energy-time approach. Brookhaven Symposia in Biology 22: 103-114.Schoener, Thomas W. 1987. A brief history of optimal foraging ecology. In Foraging Behavior,

eds., Alan C. Kamil, John R. Krebs, and H. Ronald Pulliam, 5-67. New York: Plenum Press.Screpanti, Ernesto, and Stefano Zamagni. 2005. An outline of the history of economic thought.

Second edition. Oxford University Press.Seager, Henry R. 1912. The impatience theory of interest. American Economic Review 2(4): 834-

851.Seager, Henry R. 1913. Comment. American Economic Review 3(3): 618.Simon, Herbert A. 1955. A behavioral model of rational choice. Quarterly Journal of Economics

69(1): 99-118.Simon, Herbert A. 1979. Information processing models of cognition. Annual Review of Psychology

30: 363-396.Simon, Herbert A. 1986. The failure of armchair economics. Challenge 29(5): 18-25.Smith, Christopher C., and Stephe D. Fretwell. 1974. The optimal balance between size and number

of offspring. American Naturalist 108: 409-506. Stephens, David W., and John R. Krebs. 1986. Foraging theory. Princeton University Press.Stigler, George J. (1941). Production and distribution theories. The formative period. New York:

Macmillan Company. [https://archive.org/details/in.ernet.dli.2015.264085]Taha, Hamdy A. 1971. Operations research. An introduction. New York: Macmillan.

18

705

710

715

720

725

730

735

740

https://archive.org/details/in.ernet.dli.2015.264085

Tintner, Gerhard. 1941a. The theory of choice under subjective risk and uncertainty. Econometrica 9: 298-304.

Tintner, Gerhard. 1941b. The pure theory of production under technological risk and uncertainty. Econometrica 9: 305-311.

Tomo, Shigeki. 1995. Beyond Roscher or not? A reappraisal of Menger’s and Böhm-Bawerk’s contributions to the theory of interest. Journal of Economic Studies 22: 127-133.

Tomo, Shegeki. 1997. On the development of Böhm-Bawerk’s interest theory from ‘Fisherian’ to ‘Wicksellian.’ History of Economics Review 26(1): 1-10.

Tullock, Gordon. 1970. Switching in general predators. Bulletin of the Ecological Society of America 51: 21-23.

Tullock, Gordon. 1971a. The coal tit as a careful shopper. American Naturalist 105: 77-80.Tullock, Gordon. 1971b. Biological externalities. Journal of Theoretical Biology 33: 565-576.Uhr, Carl G. 1962. Economic doctrines of Knut Wicksell. Berkeley: University of California Press.Vromen, Jack. 2011. Allusions to evolution: edifying evolutionary biology rather than economic

theory. In Building Chicago economics. New perspectives on the history of America’s most powerful economics program, eds., Robert van Horn, Philip Mirowski, and Thomas A. Stapleford, 208-236. Cambridge University Press.

Watson, Donald S. 1972[1963]. Price theory and its uses. Third edition. Boston: Houghton Mifflin Company. [https://archive.org/stream/pricetheoryitsu000wats#page/n8/mode/1up]

Wicksell, Knut. 1893. Über Wert, Kapital und Rente nach der neueren nationalökonomischen Theorie. Jena: G. Fischer.

Wicksell, Knut. 1900. Finanztheoretische Untersuchungen nebst Darstellung und Kritik des Steuerwesens Schwedens. Jena: Gustav Fischer.

Wicksell, Knut. 1935. Lectures on political economy, vol. 1. Translated from the Swedish by E. Classen. London: George Routledge and Sons. https://archive.org/details/in.ernet.dli.2015.54610,accessed 21 June 2017

Wicksell, Knut. 1954, reprinted in 1970. Value, Capital and Rent. Translated by S. H. Frowein. NewYork: Augustus M. Kelley Publishers. https://mises.org/library/value-capital-and-rent-0. Accessed 25 January 2017

Ydenberg, Ronald C., Joel S. Brown, and David W. Stephens. 2007. Foraging: an overview. In Foraging: behavior and ecology, eds., D.W. Stephens, J.S. Brown, and R.C. Ydenberg, 1-28. University of Chicago Press.

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775

https://mises.org/library/value-capital-and-rent-0https://archive.org/details/in.ernet.dli.2015.54610https://archive.org/stream/pricetheoryitsu000wats#page/n8/mode/1up