Optimal within-patch movement strategies for optimising patch residence time: an agent-based modelling approach

Several optimisation models, like the marginal value theorem (MVT), have been proposed to predict the optimal time foraging animals should remain on patches of resources. These models do not clearly indicate, however, how animals can follow the corresponding predictions. Hence, several proximate patch-leaving decision rules have been proposed. Most if not all of these are based on the animals’ motivation to remain on the patches, but the real behaviours involved in such motivation actually still remain to be identified. Since animals are usually exploiting patches of resources by walking, we developed a model simulating the intra-patch movement decisions of time-limited animals exploiting resources distributed in delimited patches in environments with different resource abundances and distributions. The values of the model parameters were optimised in the different environments by means of a genetic algorithm. Results indicate that simple modifications of the walking pattern of the foraging animals when resources are discovered can lead to patch residence times that appear consistent with the predictions of the MVT. These results provide a more concrete understanding of the optimal patch-leaving decision rules animals should adopt in different environments.     

The value of information for integrated assessment models of climate change

We estimate the value of information (VOI) for three key parameters of climate integrated assessment models (IAMs): marginal damages at low temperature anomalies, marginal damages at high temperature anomalies, and equilibrium climate sensitivity. Most empirical studies of climate damages have examined temperature anomalies up to 3 °C, while some recent theoretical studies emphasize the risks of “climate catastrophes,” which depend on climate sensitivity and on marginal damages at higher temperature anomalies. We use a new IAM to estimate the VOI for each parameter over a range of assumed levels of study precision based on prior probability distributions calibrated using results from previous studies. We measure the VOI as the maximum fixed fraction of consumption that a social planner would be willing to pay to conduct a new study before setting a carbon tax. Our central results suggest that the VOI is greatest for marginal damages at high temperature anomalies.     

Estimating the marginal cost of nature conservation: evidence from Israel

Contrary to many studies regarding the efficient use of resources that measure the marginal cost of nature conservation by looking at a specific objective and asks about efficient way to achieve it, this article tries to estimate the (marginal) cost of nature conservation in a more flexible way. Instead of looking at a specific objective and then not being able to compare different objectives, we take an approach that is based on experts’ valuation of increased satisfaction from nature conservation. We trace the marginal cost of conservation from their answers and use official cost statistics. Officials in the Israeli Nature and Parks Authority (NPA) were surveyed to determine the activities required to increase the level of nature conservation in two districts of the NPA as well as nationwide. We determined the costs of these proposed activities, and subsequently were able to calculate the total cost and marginal cost of conservation efforts. When operating on a limited budget, conservation authorities can use these schedules as an additional tool to help determine the efficiency of different proposed activities both on a regional scale and nationwide, and to ensure the sustainability of the resulting conservation. In addition, our results demonstrate the existence of economies of scale in nature conservation, and the benefit of both bottom-up and top-down decision processes in nature conservation.     

Asymmetric sibling rivalry and nestling growth in red-winged blackbirds (Agelaius phoeniceus)

Many birds hatch their offspring asynchronously, and the adaptive significance of this trait, if any, is controversial. David Lack suggested long ago that by facilitating brood reduction when resources are scarce, hatching asynchrony provides relief from the effects of overcrowding. Some field workers interpret this to mean that the growth and survival of survivors should rise following partial brood loss. Here we show in a 6-year study of red-winged blackbirds (Agelaius phoeniceus) that the presence or absence of marginal offspring in experimentally manipulated broods had virtually no effect upon the growth of core offspring, whereas alterations of the size of core brood had strong and significant effects. Nestling growth was, not surprisingly, slower in broods with partial brood loss. Intriguingly, marginal offspring showed significantly greater variation in mass. Core offspring are less sensitive to, but not exempt from, the inimical effects of resource shortfall than are marginal offspring. The phenotypic handicap appears to marginal offspring a caste of high-variance progeny whose fitness prospects rest upon levels of parental input (stochastic resources) and the size of the core brood (stochastic development). Received: 21 June 1999 / Revised: 5 June 2000 / Accepted: 25 June 2000     

Altruism and environmental risks to health of parents and their children

This paper tests an equilibrium condition from a model that incorporates: (1) altruism of parents toward their young children, and (2) household production of latent health risks. The model demonstrates that an altruistic parent's marginal rate of substitution between an environmental health risk to herself and to her child is equal to the ratio of marginal risk reduction costs. Econometric estimates support this prediction based on data from a stated preference survey involving 488 parents of children aged 3–12 years. This outcome implies that parents reallocate family resources to at least partly offset the effectiveness of public programs that aim to reduce their children's environmental risks.     

The voluntary approach to externality problems: A survey of the critics

The literature critical of the Coase Theorem is synthesized. One conclusion is that bilateral bargaining in a voluntary, frictionless setting results in optimality only by accident, if at all. This is because of the problem of threats and the problem of small numbers bargaining behavior (it is not marginal). The second conclusion is that the placement of liability in general affects the allocation of resources. The exception is when there are no income effects, no transactions costs, and no nonseparabilities. But the existence of externalities implies transaction costs are high, which in turn implies that liability matters.     

Colony choice in birds: models based on temporally invariant site quality

We propose two stochastic models to explain how birds choose colonies. In the resource choice model, birds settle at each site at a rate proportional to the total resources the site contains. In the reduced resource choice model, a smaller cohort of birds enters sites at a rate determined by the total resources at each, and the remaining individuals enter sites at a rate that is linearly proportional to the total number of birds already nesting at each site. Thus, a fraction of birds chooses sites based on the resources present, and the remainder are attracted to a site by the presence of other birds. Colony site quality is assumed not to vary between years. Both models result, on average, in an ideal free distribution of colony sizes if the birds' settlement rate is linearly related to the resources in a site, if resources are distributed equally among individuals within sites, and if individuals with equal resources have equal fitness. We applied these models to long-term data on colony sizes and site usage of cliff swallows in south-western Nebraska. A test of the resource choice model suggested that the swallow population as a whole did not choose sites based strictly on site quality or the total resources contained at each site. However, a test of the reduced resource choice model suggested that a smaller fraction of the individuals in each colony may have based their choice of site on local resource availability, with the remaining birds aggregating at those sites based on the number of birds already settled there. Tests of these models may provide insight into how individuals choose colony sites and why colonies vary in size.     

Substitution between biofuels and fossil fuels: Is there a green paradox?

We show that (i) subsidies for renewable energy policies with the intention of encouraging substitution away from fossil fuels may accentuate climate change damages by hastening fossil fuel extraction, and that (ii) the opposite result holds under some specified conditions. We focus on the case of subsidies for renewable resources produced under increasing marginal costs, and assume that both the renewable resources and the fossil fuels are currently in use. Such subsidies have a direct effect and an indirect effect working in opposite directions. The direct effect is the reduction in demand for fossil fuels at any given price. The indirect effect is the reduction in the current equilibrium price for fossil fuels, which tends to increase the amount of fossil fuels demanded. Whether the sum of the two effects will actually result in an earlier or later date of exhaustion of the stock of fossil fuels depends on the curvature of the demand curve for energy and of the supply curve for the renewable substitute.     

Substitution between biofuels and fossil fuels: Is there a green paradox?

We show that (i) subsidies for renewable energy policies with the intention of encouraging substitution away from fossil fuels may accentuate climate change damages by hastening fossil fuel extraction, and that (ii) the opposite result holds under some specified conditions. We focus on the case of subsidies for renewable resources produced under increasing marginal costs, and assume that both the renewable resources and the fossil fuels are currently in use. Such subsidies have a direct effect and an indirect effect working in opposite directions. The direct effect is the reduction in demand for fossil fuels at any given price. The indirect effect is the reduction in the current equilibrium price for fossil fuels, which tends to increase the amount of fossil fuels demanded. Whether the sum of the two effects will actually result in an earlier or later date of exhaustion of the stock of fossil fuels depends on the curvature of the demand curve for energy and of the supply curve for the renewable substitute.     

Restoring Natural Resources with Destination-Driven Costs

Economics typically assumes that injured natural resources are restored along a fixed path of increasing marginal costs. By contrast, many restoration efforts—such as cleaning a contaminated aquifer or replacing the sand on an oil-tarnished beach—are characterized bydestination-driven costs, which depend mainly on final quality, not the prerestoration quality. Given the resulting nonconvexities in cost, the optimal level of restoration may be a discontinuous and nonmonotonic function of post-injury quality. Regulatory rules should reflect these patterns, as should liability rules, since restoration plans and costs determine the expected cost of putting a resource at risk.     

Demography of central and marginal populations of monkeyflowers (Mimulus cardinalis and M. lewisii)

Every species occupies a limited geographic area, but how spatiotemporal environmental variation affects individual and population fitness to create range limits is not well understood. Because range boundaries arise where, on average, populations are more likely to go extinct than to persist, range limits are an inherently population-level problem for which a demographic framework is useful. In this study, I compare demographic parameters and population dynamics between central and marginal populations of monkeyflowers, Mimulus cardinalis and M. lewisii, along an elevation gradient spanning both species' ranges. Central and marginal populations of both species differed in survival and fecundity. For M. lewisii, these components of fitness were higher in central than in marginal populations, but for M. cardinalis the converse was true. To assess spatiotemporal variation in population dynamics, I used transition matrix models to estimate asymptotic population growth rates (lambda) and found that population growth rates of M. lewisii were highest at the range center and reduced at the range margin. Population growth rates of M. cardinalis were highest at the range margin and greatly reduced at the range center. Life table response analysis decomposed spatiotemporal variation in lambda into contributions from each transition between life stages, finding that transitions from large nonreproductive and reproductive plants to the seed class and stasis in the reproductive class made the largest contributions to spatial differences in lambda. These transitions had only low to moderate sensitivities, indicating that differences in projected population growth rates resulted mainly from observed differences in transition matrix parameters and their underlying vital rates.     

Compositional analysis of overdispersed counts using generalized estimating equations

Multivariate abundance data are commonly collected in ecology, and used to explore questions of “community composition”—how relative abundance of different taxa changes with environmental conditions. In this paper, we propose a log-linear marginal modeling approach for analyzing such compositional count data, via generalized estimating equations. This method exploits the multiplicative nature of log-linear models for counts, by reparameterizing models that describe marginal effects on mean abundance. This allows partitioning into “main effects” and compositional effects, which is appealing for interpretation. We apply the proposed approach to reanalyze compositional counts of benthic invertebrates from Delaware Bay, and data of invertebrate communities inhabiting Acacia plants in eastern Australia. In both cases we resort to a resampling approach to make inferences about regression parameters, because the number of clusters was not large compared to cluster size.     

Transferability of Species Distribution Models: a Functional Habitat Approach for Two Regionally Threatened Butterflies

Abstract:  Numerous models for predicting species distribution have been developed for conservation purposes. Most of them make use of environmental data (e.g., climate, topography, land use) at a coarse grid resolution (often kilometres). Such approaches are useful for conservation policy issues including reserve-network selection. The efficiency of predictive models for species distribution is usually tested on the area for which they were developed. Although highly interesting from the point of view of conservation efficiency, transferability of such models to independent areas is still under debate. We tested the transferability of habitat-based predictive distribution models for two regionally threatened butterflies, the green hairstreak ( Callophrys rubi ) and the grayling ( Hipparchia semele ), within and among three nature reserves in northeastern Belgium. We built predictive models based on spatially detailed maps of area-wide distribution and density of ecological resources. We used resources directly related to ecological functions (host plants, nectar sources, shelter, microclimate) rather than environmental surrogate variables. We obtained models that performed well with few resource variables. All models were transferable—although to different degrees—among the independent areas within the same broad geographical region. We argue that habitat models based on essential functional resources could transfer better in space than models that use indirect environmental variables. Because functional variables can easily be interpreted and even be directly affected by terrain managers, these models can be useful tools to guide species-adapted reserve management.     

Self-reporting of pollution and the firm's behavior under imperfectly enforceable regulations

Motivated by the nature of U.S. laws, a model is developed for a firm that maximizes expected profit and faces imperfectly enforceable pollution standards with imperfectly enforceable reporting requirements. Some previous models of imperfectly enforceable standards and taxes are special cases of this general mode. When the fine for violating the pollution standard is linear in excess pollution, the form will equate the marginal cost of control to the marginal fine rate, and thus actual pollution will be insensitive to enforcement parameters related to under-reporting. The more complex comparative statics that exist when the fine is non-linear are analyzed, and comparisons with other models are made.     

Movement ecology: size-specific behavioral response of an invasive snail to food availability

Immigration, emigration, migration, and redistribution describe processes that involve movement of individuals. These movements are an essential part of contemporary ecological models, and understanding how movement is affected by biotic and abiotic factors is important for effectively modeling ecological processes that depend on movement. We asked how phenotypic heterogeneity (body size) and environmental heterogeneity (food resource level) affect the movement behavior of an aquatic snail (Tarebia granifera), and whether including these phenotypic and environmental effects improves advection-diffusion models of movement. We postulated various elaborations of the basic advection diffusion model as a priori working hypotheses. To test our hypotheses we measured individual snail movements in experimental streams at high- and low-food resource treatments. Using these experimental movement data, we examined the dependency of model selection on resource level and body size using Akaike's Information Criterion (AIC). At low resources, large individuals moved faster than small individuals, producing a platykurtic movement distribution; including size dependency in the model improved model performance. In stark contrast, at high resources, individuals moved upstream together as a wave, and body size differences largely disappeared. The model selection exercise indicated that population heterogeneity is best described by the advection component of movement for this species, because the top-ranked model included size dependency in advection, but not diffusion. Also, all probable models included resource dependency. Thus population and environmental heterogeneities both influence individual movement behaviors and the population-level distribution kernels, and their interaction may drive variation in movement behaviors in terms of both advection rates and diffusion rates. A behaviorally informed modeling framework will integrate the sentient response of individuals in terms of movement and enhance our ability to accurately model ecological processes that depend on animal movement.     

Food quality,spatial deployment,and the intensity of feeding interference in yellow baboons (Papio cynocephalus)

Summary Optimization models lead one to predict that the energy invested in competitive interference with feeding should increase as the quality of the contested food increases. This prediction was tested in a study of feeding interruptions involving juvenile yellow baboons (Papio cynocephalus) in Amboseli National Park, Kenya. For each of the 50 foods eaten by these young primates, 6 measures of food quality (energy content, protein content, yield, yield rate, processing value, and dispersion) and one measure of the spatial deployment of baboons (number of neighbors) were examined for correlations with 4 measures of the frequency and intensity of interruptions (interruption rate, probability of unsuccessful attempts, probability of appropriation, and probability of agonistic behavior). Disperson of food and the proximity of neighboring baboons had little or no effect on the frequency or intensity of interruptions. Food quality had negligible effects on the probabilities of appropriation and agonistic behavior. Yield characteristics were the best predictors of the success of attempted interruptions: attempts were least likely to be successful when processing the food was time-consuming. These results suggest that (1) the interrupter decides whether to interrupt on the basis of increasing its probability of winning the contest and decreasing its cost, and (2) the victim decides whether to resist on the basis of the time that has been and must be invested in harvesting the contested food item.     

Estimating equations for separable spatial-temporal binary data

For binary data with correlation across space and over time, the literature concerning the estimation of fixed effects in marginal models is limited. In this paper, we model the marginal probability of binary responses in terms of parameters of interest by a logistic function. An estimating equation based on the quasi-likelihood concept is developed to estimate parameters. Under separable correlation models, we show that the quasi-likelihood estimate is asymptotically optimal. A series of simulations is conducted to evaluate how the efficiency varies with the regression coefficients. We also compare the relative efficiency with another estimating equation by simulations. The proposed method is applied to an ecological study of forest decline to test independence of two spatial-temporal binary outcomes.     

Regression analysis of forest damage by marginal models for correlated ordinal responses

Studies on forest damage generally cannot be carried out by common regression models, for two main reasons: Firstly, the response variable, damage state of trees, is usually observed in ordered categories. Secondly, responses are often correlated, either serially, as in a longitudinal study, or spatially, as in the application of this paper, where neighbourhood interactions exist between damage states of spruces determined from aerial pictures. Thus so-called marginal regression models for ordinal responses, taking into account dependence among observations, are appropriate for correct inference. To this end we extend the binary models of Liang and Zeger (1986) and develop an ordinal GEEI model, based on parametrizing association by global cross-ratios. The methods are applied to data from a survey conducted in Southern Germany. Due to the survey design, responses must be assumed to be spatially correlated. The results show that the proposed ordinal marginal regression models provide appropriate tools for analysing the influence of covariates, that characterize the stand, on the damage state of spruce.     

Pigou meets Mirrlees: On the irrelevance of tax distortions for the second-best Pigouvian tax

This paper extends the Mirrlees (1971) model of optimal income redistribution with optimal corrective taxes to internalize consumption externalities. Using general utility structures and exploring both linear and non-linear taxes, it is demonstrated that the optimal second-best tax on an externality-generating good should not be corrected for the marginal cost of public funds, since it equals one in the optimal tax system. In the optimum, distortions of income taxes are equal to marginal redistributional gains. If the government does not have access to a non-distortionary marginal source of finance, the marginal cost of public funds can be either larger or smaller than one depending on subjective preferences for income redistribution. The optimal second-best corrective tax is then either higher or lower than the Pigouvian level. The findings in this paper generalize and amend prior results based on representative-agent models, shedding new light on the weak double-dividend hypothesis, and on the welfare gains of recycling revenue from environmental taxes.     

On the extraction of an exhaustible resource by a monopoly

Hotelling's r-percent rule does not hold for monopoly extractors of durable exhaustible resources. An example with a nondurable resource in which the rule also fails to hold is presented. An economy with a fixed average propensity to save is modelled. The monopoly extractor recognizes that resource extraction, by affecting output and hence capital accumulation, affects future demand. The firm exploits this effect by causing the marginal profitability of extraction to grow faster or slower than the rate of interest, depending upon initial conditions. Conditions are developed under which the growth rate will be less than the interest rate.