Eric L. Charnov

Optimal foraging, the marginal value theorem

There has been much recent work on foraging that derives hypotheses from the assumption that animals are in some way optimizing in their foraging activities. Useful reviews may be found in Krebs (1973) or Schoener (1971). The problems considered usually relate to breadth of diet (Schoener, 1969, 1971; Emlen 1966; MacArthur, 1972; MacArthur and Painka, 1966; Marten, 1973; Pulliam, 1974; Werner, 1974; Werner and Hall, 1974; Timmins, 1973; Pearson, 1974; Rapport, 1971; Charnov, 1973,1976; Eggers, 1975), strategies of movement (Cody, 1971; Pyke, 1974; Smith, 1974a, b; Ware, 1975), or use of a patchy environment (Royama, 1970; MacArthur and Pianka, 1966; Pulliam, 1974; Smith and Dawkins, 1971; Tullock, 1970; Emlen, 1973; Krebs, 1973; Krebs, Ryan, and Charnov, 1974; Charnov, Orians, and Hyatt, 1976). The above list of references is provided as a beginning to this fast expanding literature and is far from exhaustive. This paper will develop a model for the use of a “patchy habitat” by an optimal predator. The general problem may be stated as fohows. Food is found in clumps or patches. The predator encounters food items within a patch but spends time in traveling between patches. This is schematically shown in Fig. 1. The predator must make decisions as to which patch types it will visit and when it will leave the patch it is presently in. This paper will focus on the second question. An important assumption of the model is that while the predator is in a patch, its food intake rate for that patch decreases with time spent there. The predator depresses (Charnov, Orians, and Hyatt, 1976) the availability of food to itself so that the amount of food gained for T time spent in a patch of type i is hi(T), where the function rises to an asymptote. A hypothetical example is shown in Fig. 2. While it is not necessary that the first derivative of hi(T) be decreasing for all T (it might be increasing at first if the predator scares up prey upon arrival in a new patch), I will limit discussion to this case since more

Effects of size and temperature on developmental time

Body size and temperature are the two most important variables affecting nearly all biological rates and times. The relationship of size and temperature to development is of particular interest, because during ontogeny size changes and temperature often varies. Here we derive a general model, based on first principles of allometry and biochemical kinetics, that predicts the time of ontogenetic development as a function of body mass and temperature. The model fits embryonic development times spanning a wide range of egg sizes and incubation temperatures for birds and aquatic ectotherms (fish, amphibians, aquatic insects and zooplankton). The model also describes nearly 75% of the variation in post-embryonic development among a diverse sample of zooplankton. The remaining variation is partially explained by stoichiometry, specifically the whole-body carbon to phosphorus ratio. Development in other animals at other life stages is also described by this model. These results suggest a general definition of biological time that is approximately invariant and common to all organisms.

Effects of Body Size and Temperature on Population Growth

For at least 200 years, since the time of Malthus, population growth has been recognized as providing a critical link between the performance of individual organisms and the ecology and evolution of species. We present a theory that shows how the intrinsic rate of exponential population growth, \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\encodingdefault{OT2} \normalfont \selectfont} \DeclareTextFontCommand{\textcyr}{\cyr} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \landscape

Hunting by expectation or optimal foraging: A study of patch use by chickadees

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Optimal foraging: Some simple stochastic models.

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Reaction norms for age and size at maturity in response to temperature: A puzzle for life historians.

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