Rate Of Energy Gain Research Articles

Proportional Control for Daily Energy Regulation in Hummingbirds

Time budgets and food intake of captive hummingbirds (Eugenes fulgens and Lampornis clemenciae) were monitored for several days to estimate net energy exchange and to assess responses to depletion of energy reserves produced by food deprivation. Meal sizes averaged close to values predicted to maximize short-term rates of net energy gain if hummingbirds behaved optimally. Maximization of rate of net energy gain is analogous to an on-off model of control. However, longer-term, daily rates of energy storage were not maximized but generally were proportional to energy reserve depletion. High daily energy storage rates were associated with (1) high frequency feeding (one species, Eugenes), or (2) meal size (one species, Lampornis), and (3) low rates of energy expenditure between meals (both species). Proportional control may represent a compromise between characteristics of on-off controls, with high sensitivity to changes near set points, and integral controls, with low sensitivity to changes near set points.

Optimal Travel Speeds of Animals

Animal travel speeds have been hypothesized to satisfy several possible optimality criteria. These include (1) maximize net rate of energy gain (during foraging), (2) minimize energy cost per unit distance, and (3) minimize rate of energy expenditure. These criteria and others have, however, received little justification. General models of animal travel, coupled with the basic hypothesis that travel speeds are such that fitness is maximized, indicate that animals should sometimes behave in accordance with one of the above criteria. These models also indicate that animals should occasionally travel at their maximum sustainable speeds. In general, however, animals would be expected to travel at speeds that satisfy more complicated optimality criteria that include all the various counteracting factors.

Optimal foraging in hummingbirds: Rule of movement between inflorescences

The movements of hummingbirds between inflorescences of scarlet gilia ( Ipomopsis aggregata) were studied. These movements exhibited the following patterns: (1) Although the hummingbirds appeared to avoid moving to the previous inflorescence, no significant correlation was found between the directions of successive inter-inflorescence movements. (2) The frequency distribution of inter-inflorescence flight distances was found to be leptokurtic. (3) The hummingbirds were more likely to move to an inflorescence the larger and/or closer it was. (4) The hummingbirds moved to inflorescences of greatest apparent size (i.e. ratio of number of flowers available to distance from present inflorescence) more often than they moved to the largest inflorescence, the closest infloresence, or the inflorescence estimated to yield the greatest rate of energy gain. (5) The frequency distribution of moves to the inflorescence having the ith greatest apparent size is well fitted by a geometric distribution. This is consistent with the hummingbrids choosing the inflorescence of greatest apparent size (excluding the previous inflorescence) from within some scanning sector. These movement patterns are consistent with the expectations of optimal foraging theory only if the hummingbirds cannot or do not determine the directions of possible inflorescences relative to the direction of arrival at the present inflorescence and if they cannot assess independently the sizes and distances of possible inflorescences.

Honeyeater foraging: A test of optimal foraging theory

Honeyeaters (Meliphagidae) were observed foraging for nectar from Lambertia formosa inflorescences, each of which has seven flowers. The frequency distribution of numbers of flowers probed per visit to an inflorescence was found to be bimodal, with one peak at two and the other at seven. It is hypothesized that this frequency distribution results from a rule of departure from inflorescences that maximizes the net rate of energy gain. Patterns of nectar distribution were determined for a large sample of inflorescences. In addition the extent to which the honeyeaters re-probe flowers during a visit to an inflorescence was estimated. From these data and from field measurements of the times required by the honeyeaters to perform the various foraging behaviours, computer simulations of honeyeater foraging were constructed. These simulations led in turn to optimal frequency distributions of numbers of flowers probed per inflorescence that were bimodal but had peaks at 1 and 7 instead of 2 and 7. Although the observed and predicted behaviour were consequently similar, the difference between them was nevertheless significant. This difference could have been due to the birds' transient occupancy of the study area.

Beyond Selection: Optimal Ingestion Rate as a Function of Food Value

A simple model based on microphagous feeders (animals which process their food items in bulk with little chance of selecting food items on an individual basis) has been developed to predict how ingestion rate should vary with food quality if the net time rate of gain of some measure of food quality, say energy, is to be maximized. Three variants of the model were considered, in which absorption efficiency (1) was constant, (2) decreased linearly with increased ingestion rate, or (3) decreased exponentially. The optimal ingestion rate, which maximized the net rate of energy gain, depended on food quality and increased on higher quality foods. For certain parameter values, constantly maintaining the maximum ingestion rate resulted in maximal net energy gain. Experimental results from the literature on a variety of animals are not in consistent accord with these predictions. It seems likely that uncontrolled and confounding variables, such as food composition or palatability, may obscure the effects of food quality on ingestion rate.

Why hummingbirds hover and honeyeaters perch

Evidence is presented in support of the suggestion that a hovering bird is able to move between flowers more quickly than one that is perching. This advantage to hovering may be offset, however, by the higher energetic costs of hovering as compared with perching. This trade-off is evaluated in two field situations, one for perching honeyeaters and the other for hovering hummingbirds. In each case it is estimated that the birds employ the foraging mode (hovering versus perching) that results in the greatest net rate of energy gain.

The physics of DT ignition in small fusion targets

Ignition of sub-milligram fusion targets is critically dependent on DT temperature, density, radius, radiation temperature, implosion velocity, and other parameters that characterize the target and its implosion. This paper discusses the interplay of such major physical processes as bremsstrahlung, Compton scattering, DT fusion, hydrodynamics, and thermal conduction during the implosion and especially near turnaround where the potential for ignition or failure most critically depends on the small differences between large rates of energy loss and gain. The phase plane analysis presented here proves to be most advantageous in understanding the DT ignition problem. Four examples are discussed in order to illustrate the interplay of the various physical processes.

On the mechanics and energetics of nectar feeding in butterflies

A mechanistic model describing the mechanics and energetics of nectar-feeding in butterflies is developed. The butterflies Collas eurytheme and Danaus plexippus are used to illustrate the model. Simulation results indicate that there are mechanical limitations upon the range of nectar sugar concentrations and nectar extraction times available to butterflies. There is a unique optimum for net rate of energy gain at 20–25% nectar sugar concentration which is independent of the metabolic rate and of proboscis shape and size over the ranges found in butterflies. The optimal nectar extraction rate depends upon the size and shape of the proboscis. These results are discussed in relation to the design of nectar feeding structures, optimal foraging strategy, and the evolution of insect pollination.

Feeding: Models of Costs and Benefits in Energy Regulation

Models to predict feeding behavior at the level of consumption and use of energy involve either details of internal (physiological) controls or economic principles of regulation based on optimal (evolutionary) foraging theory. These two approaches will ultimately be related, but the former requires more information for specific predictions. The latter can provide predictions based on selected criteria for regulation. Meal sizes and feeding frequencies of hummingbirds are examined relative to two regulatory, criteria: maximizing rate of net energy gain and maximizing efficiency (intakes/expenditures) through a “crop emptying” model that incorporates energy intake from food and energy expenditures for short-term (meal to meal) maintenance and longer-term (overnight) energy storage. Experimental results suggest that the feeding behavior of hummingbirds is differentially sensitive to short-term and daily uses of energy. Changes in overnight energy storage requirements result primarily in changes in meal size, while changes in meal to meal maintenance requirements result primarily in feeding frequency changes. The economic models predict these responses. The feeding behavior of hummingbirds also appears to be sensitive to food quality, time spent flying to and from a food source, and costs associated with the weight of ingested food.

Optimal Foraging in Hummingbirds: Testing the Marginal Value Theorem

To a hummingbird, clusters of flowers on inflorescences represent patches and provide an ideal situation to test prediction of optimal patch-use. The basic question is what decision rule should a hummingbird use to decide whether or not to leave an inflorescence? The hypothesis is that hummingbirds will adopt the decision rule that maximizes their net rate of energy gain while foraging. This hypothesis leads to an analogue of Charnov's marginal value theorem which determines an optimal decision rule. The optimal decision ruleis then used to predict aspects of the hummingbirds' foraging, and these predictions are compared with field data The optimal decision rule is a function of how much information is used by the hummingbirds. Data indicate that a decision to leave an inflorescence is a function of the number of flowers visited, the number of flowers available on the inflorescence, and the amount of nectar obtained at the last flower. The optimal decision rule was calculated assuming no additional information is used.

Optimal Meal Size in Hummingbirds

Optimization theory is applied to hummingbird foraging to explain the observation that birds in the laboratory with access to functionally unlimited food supplies usually do not take as large a meal as they could. Foraging bouts are modeled in terms of time and energy; birds are constrained by the increased energetic costs associated with the added weight of their meal. Predictions of optimal meal size which maximize the rate of net energy gain or which maximize efficiency agree closely with laboratory and limited field data; we presently are unable to discriminate between these two optimality criteria. Predictions which assume optimal use of time or which maximize net energy gain or which neglect weight of the meal all proved unsatisfactory, generally by predicting optimal meal sizes in excess of capacity. Sensitivity analysis revealed that model predictions may be much influenced by parameter values potentially under physiological and/or behavioral control by a hummingbird. While we presently do not understand what governs the values of these parameters, we suggest that this control will eventually prove explicable by an optimality model of bird behavior.

Optimal foraging: Movement patterns of bumblebees between inflorescences

Nectar-collecting bumblebees are hypothesized to employ rules of movement which result in the maximum net rate of energy gain (i.e., are optimal). The optimal movement rules are derived from a mathematical model and are used to generate predicted patterns of movement. The predicted patterns are compared with field observations. These observations support the hypothesis. An important component of the mathematical model is the memory of the foraging animal. The field data have implications concerning the memory capabilities of the bumblebees.

Optimal foraging in bumblebees and coevolution with their plants.

The aims of this paper were to consider the coevolution between bumblebee movement patterns within plants and various properties of the plants such as the spatial distribution of their flowers, and to determine the extent to which the bumblebees and the plants can be considered to be maximally adaptive or optimal. Attention was restricted to plants which have flowers arranged on vertical inflorescences and to the bumblebees which visit these plants.It was found that the bumblebees tend to commence foraging at the bottom of each infloresence, that they tend to move from one flower to the closest vertically higher flower, that they miss flowers as they move upwards and that they tend to leave each inflorescence before reaching the top. It was also found for the four common plant species considered that nectar abundance per flower decreases with flower height on an inflorescence, that the flowers with receptive stigmas are restricted to the bottoms of the inflorescences while the flowers shedding pollen occur above them, and that the flowers are arranged approximately in spirals on the inflorescences.The pattern of movements of the bumblebees and the various properties of the plants appear to represent coevolved adaptations. Furthermore the bumblebees' movement patterns appear to be optimal in the sense that they result in the maximum net rate of energy gain to the bumblebees. Further studies are necessary, however, to determine whether or not the plants can be considered to be optimal.An exception to the above scheme is provided by a plant which is quite uncommon in the study area. This plant also has flowers on vertical inflorescences and appears to be pollinated by bumblebees. However, while the pattern of movements of the bumblebees on this plant species are extremely similar to those on the four common species, this plant species exhibits quite different properties from the other four. Two possible explanations for this exception are presented.

Model of copepod filtering response to changes in size and concentration of food1

Observations indicate that there are three phases in the feeding response of adult females of Calanus pacificus to differences in food concentration. At low concentrations of food, the copepods filter at some reduced rate. As the food supply is increased, the animals increase their filtration rate until some maximum rate is reached. They then maintain this maximum rate until a critical food density is exceeded, at which point the copepods decrease their filtering rate (hold a constant ingestion rate) with further increases in food concentration. A model based on simple arguments concerning the net rate of energy gain to a filter feeder is constructed which predicts functional dependencies of the filtering rate on food concentration for three regions, corresponding to the three phases of feeding behavior observed. The parameters controlling the filtering response in the model are functions of the animal’s characteristic length and the size of the food particles.

Net utilization of roughage and concentrate diets by sheep.

1. Two diets, an all-roughage diet and a high-concentrate diet, were fed at two levels, a low level of estimated 1-5 times maintenance energy requirement and a higher level of estimated two times maintenance energy requirement, to South African Mutton Merino castrated male sheep, aged 13 months and in fairly lean condition at the start of the 93 d experimental period. 2. Body composition and energy retention were determined using the comparative slaughter technique and two series of digestibility and balance studies were done during the course of the experiment. Metabolizability of each diet was estimated and corrected for fermentation heat using the fermentation balance approach. 3. Although there were significantly different rates of energy gain on different diets and feeding levels, fat energy gained (% total energy gained) was similar for the four groups, i.e. 78-80. 4. Regression of energy gain v. corrected metabolizable energy (ME) intake indicated that the maintenance energy requirements of sheep used in this experiment were 310-2 and 302-3 kJ ME/kg body-weight0-75 per d and the values for net utilization of ME for body energy gain were 0-411 and 0-479 with the roughage and concentrate diets respectively. 5. It was concluded that the estimated maintenance energy requirements of sheep obtained in this study are realistic values and that the efficiency of utilization of surplus ME for the two diets did not differ significantly.

The interpretation of transit time magnetic pumping from the point of view of the macroscopic plasma equations

It is shown that the correct macroscopic expression includes dissipation of work done by the pressure forces, and leads to the same value for the local power absorption as the usual microscopic approach, which consists in averaging over the particle distribution function the rate of energy gain by a single particle.

The effects of electrical fields upon electron energy exchanges in flame gases

Rates of electron energy gain from applied electrical fields and rates of energy loss in molecular collisions have been computed. To do this, electron mobilities and rate constants for the excitation of the different molecular energy levels have been computed from electron collisional cross-sections. Gases covered in this way are CO, CO 2, H 2O, H 2O, N 2, and O 2 and these results are applied to the products of combustion of methane-air. Rates of ionization by electron collisions have been calculated for different values of electrical field. Comparisons are made of the different rates at which the separate energy levels of the different chemical species gain energy from the field. The influence of electrical fields on the combustion process is discussed on the basis of such data. An increased chemical rate of reaction may arise from a general ohmic heating of the gas and also from preferential excitation of certain molecular energy levels.

Pecan Shells as a Roughage in Steer Rations and Use of Rib Cut Density in Estimating Energy Gain

One-Hundred-Ten Angus and Hereford steer calves were assigned by stratified randomization to 11 outcome groups of 10 steers each. One of the 11 groups was slaughtered at the outset to facilitate the use of Lofgreen's comparative slaughter technique, with certain modifications, for estimating energy gains during a feeding trial with the other groups. The remaining groups were randomly assigned to five ration treatments designed to compare ground pecan (Carya illinoensis) shells (GPS) with ground hay (GH) as a roughage in a steer ration. The GH and/or GPS were included along with ground shelled corn, soybean oil meal and minerals in the various ration treatments as follows: (1) 20% GH; (2) 20% GPS; (3) 10% GH; (4) 10% GPS; (5) 10% GH+10% GPS. The steers were self fed on their respective rations for either 140 or 161 days. The GPS caused no reduction in feed intake nor the development of any apparent health problems. However, on the basis of rate of live weight gain, rate of energy gain, feed efficiency and various measures of carcass quality, GPS were inferior to GH as a roughage material. The GPS lowered rumen pH. Also, they had a significant influence on certain other measures of rumen fermentation. In this test GPS contributed very little, if any, nutritive value to the ration. GPS were more effective than GH in reducing the incidence of livers condemned due to abscesses, especially at the 10% level of roughage. A rib cut was used effectively as an indicator of carcass density in estimating energy gains of test animals.

The cosmic rays of superhigh energies

The paper considers the generation mechanism of the relativistic particles of superhigh energies (≳1018 eV) in a plasma where the supersonic turbulence and the hydrodynamic shock waves occur. It is found that the conditions necessary for the formation of this turbulence are realized in supernovae shells during the period of the outburst. The estimations of the energy gain rate of the charged particles and comparison with their energy loss rate conditioned by synchrotron radiation and collisions with photons and nuclei show that in the actually determined conditions of shells in Crab and Cassiopeia nebulae, at the early stages of their expansion, acceleration surpasses deceleration. And finally, the estimations of the total number of superhigh energy particles generated during the flare are in agreement with the observed data.

The fermi mechanism and the source spectrum of cosmic ray nuclei

It is shown that the velocity term, occurring in the expression for the rate of energy gain by the Fermi mechanism of acceleration, is to be taken into account in case of acceleration of non-relativistic particles. A spectral form of accelerated particles is derived on this basis and is called the ‘Fermi Spectrum’. At non-relativistic energies this spectral form is significantly different from the currently used forms of power law in total energy per nucleon and in rigidity, and lies about midway between them. It is shown that using this form of source spectrum of cosmic ray nuclei, satisfactory agreement can be obtained between the calculated values and the observed ones of the ratios of H2/He4 and He3/He4, and the energy spectra of protons and helium nuclei near the Earth.