State dependent behavior and the Marginal Value Theorem

The Marginal Value Theorem (MVT) is the dominant paradigm inpredicting patch use and numerous tests support its qualitativepredictions. Quantitative tests under complex foraging situationscould be expected to be more variable in their support becausethe MVT assumes behavior maximizes only net energy-intake rate.However across a survey of 26 studies, foragers rather consistently"erred" in staying too long in patches. Such a consistent directionto the errors suggests that the simplifying assumptions ofthe MVT introduce a systematic bias rather than just imprecision. Therefore, I simulated patch use as a state-dependent responseto physiological state, travel cost, predation risk, prey densities,and fitness currencies other than net-rate maximization (e.g.,maximizing survival, reproductive investment, or mating opportunities).State-dependent behavior consistently results in longer patchresidence times than predicted by the MVT or another foragingmodel, the minimize µ/g rule, and these rules fail to closely approximate the best behavioral strategy over a widerange of conditions. Because patch residence times increasewith state-dependent behavior, this also predicts mass regulationbelow maximum energy capacities without direct mass-specificcosts. Finally, qualitative behavioral predictions from theMVT about giving-up densities in patches and the effects oftravel costs are often inconsistent with state-dependent behavior.Thus in order to accurately predict patch exploitation patterns,the model highlights the need to: (1) consider predator behavior(sit-and-wait versus actively foraging); (2) identify activitiesthat can occur simultaneously to foraging (i.e., mate searchor parental care); and (3) specify the range of nutritional states likely in foraging animals. Future predictive modelsof patch use should explicitly consider these parameters.     

Optimal size of storage for recovery after unpredictable disturbances

Terrestrial plants often live in environments in which above-ground photosynthetic organs (production parts) are suddenly removed by unpredictable disturbances, such as fire, frost, desiccation, pathogen attack, breakage by wind and trampling, or herbivory by insects and mammals. We study the optimal growth schedule for a plant having a below-ground storage organ that is used for recovery (or regrowth) of photosynthetic organs after disturbances. We assume the following: (1) the daily production rate increases with the production part size, but saturates for large size due to shading and local resource depletion, (2) disturbances occur randomly and remove all the aerial parts, (3) plants are finally killed by fatal disturbances that also occur randomly and (4) the plant chooses the pattern of growth, reproduction, storage and recovery after disturbances by reallocation of stored material to maximize the total lifetime reproductive success. The model is analysed by stochastic dynamic programming. The results are as follows: (1) the ratio of storage size to production part size (S/F ratio) is large if the longevity is large and if the disturbance rate is large but a little smaller than the productivity coefficient, (2) the S/F ratio is larger for mature plants than for small immature plants, (3) after disturbances, the above-ground production part recovers relatively quickly, but reproductive activity is depressed until storage size recovers and (4) the variations over time and between habitats differing in disturbance frequency are larger for storage size and for reproductive activity than for production part size. These tendencies are more pronounced for a linear production function (with initial linear increase followed by a sudden stop), but less so for a hyperbolic production function (with a gradually decreasing slope). We also discuss the growth and regrowth behaviour of plants adapted to a disturbance frequency growing under one different disturbance frequency.     

On compromise in foraging and an experiment by Krebs et al. (1977)

A vectorized version of the method of stochastic dynamic programming is used to demonstrate that behaviour observed in Parus major by Krebs et al. (1977) is more consistent with the hypothesis that animals compromise between time and energy in foraging than with the hypothesis that they maximize their rate of energy gain.     

The influence of predation risk on diet selectivity: A theoretical analysis

Studies that have examined the effect of experimental increases in predation risk on diet selectivity have shown both decreased and increased diet selectivity. A possible explanation for these disparate results emerges from an examination of the prey sets used in these studies, which differed in the relationship between the values of risk components associated with the capture of different prey types (‘danger’) and their profitabilities. When less profitable prey were more dangerous, selectivity increased with predation risk. When prey were equally dangerous, selectivity did not change. Finally, when the more profitable prey were also more dangerous, selectivity decreased with risk. Here, we examine theoretically the influence of a forager's estimate of the probability that a predator is present (φ) on the selection of diets from prey sets with varying danger–profitability relationships. A dynamic programming model is used to determine the maximum attack time (or distance) for each of two types of prey, differing in their energetic content, for a range of forager energy state and φ levels. The diets which would result if foragers attacked prey according to the rules provided by the dynamic model are then determined. The model results indicate that the prey danger–profitability relationship determines the diet selectivity response to φ, confirming that variation in this relationship could be responsible for the range of experimental results. This revised version was published online in July 2006 with corrections to the Cover Date.     

The formulation of the control of an expression pattern in a gene network by propositional calculus

In this study we model a gene network as a continuous-time switching network. In this model, each gene has a binary state which indicates if the gene expresses or not. We propose a method to control a sequence of expression patterns in the gene network model by adding another continuous-time switching network. By using propositional calculus, we will show that the control problem can be formulated as a mixed-integer linear programming problem with linear constraints.     

Adult cardiorenal benefits from postnatal fish oil supplement in rat offspring of low-protein pregnancies

We investigated the effect of fish oil (FO) treatment on cardiorenal structure of adult offspring from low-protein pregnancies. Three month old offspring were assigned to eight groups (four male groups and four female groups, n=8 each) (NP=normal-protein diet, LP=low-protein diet): NP, LP, NP plus FO, and LP plus FO. Left ventricle and kidney were analyzed with light microscopy and stereology. The both sexes of LP offspring showed 30% lower birth weights than the respective NP offspring and high blood pressure (BP) levels in adulthood which was efficiently reduced by FO treatment. In the heart, FO treated the cardiomyocyte hypertrophy, the vascularization impairment, and decreased the cardiomyocyte loss usually observed in adult LP offspring. In the kidney, FO treated, in the male, the imbalance of the cortex-to-medulla ratio observed in both sexes of LP offspring, and reduced the glomeruli loss in the LP offspring. The positive correlation between the number of cardiomyocyte nuclei later in life and the body mass (BM) at birth was significant only in both sexes of LP offspring and this correlation disappeared in LP plus fish oil offspring. The positive correlation between the number of glomeruli later in life and the BM at birth was significant in NP male offspring and in both sexes of LP offspring. In conclusion, FO supplement, which is a rich source of n-3 fatty acids (DHA and EPA), has beneficial effects on BP control and cardiac and renal adverse remodeling usually seen in offspring of the LP pregnancies.