A qualitative characterization of the competitive nonrenewable resource extracting firm

Using variational differential equations, a systematic qualitative analysis is carried out for the competitive nonrenewable resource extracting firm. The parameters of interest are the output price, variable input price, discount rate, lease length, initial resource stock, and various tax rates. The effects of changes in these parameters on the entire optimal time paths of the current shadow value of the stock, the resource stock, and the extraction rate are characterized in the perturbed phase plane.     

Hartwick's rule and maximin paths when the exhaustible resource has an amenity value

This paper studies the maximin paths of the canonical Dasgupta–Heal–Solow model when the stock of natural capital is a direct argument of well-being, besides consumption. Hartwick's rule then appears as an efficient tool to characterize solutions in a variety of settings. We start with the case without technical progress. We obtain an explicit solution of the maximin problem in the case where production and utility are Cobb–Douglas. When the utility function is CES with a low elasticity of substitution between consumption and natural capital, we show that it is optimal to preserve forever a critical level of natural capital, determined endogeneously. We then study how technical progress affects the optimal maximin paths, in the Cobb–Douglas utility case. On the long run path of the economy capital, production and consumption grow at a common constant rate, while the resource stock decreases at a constant rate and is therefore completely depleted in the very long run. A higher amenity value of the resource stock leads to faster economic growth, but to a lower long run rate of depletion. We then develop a complete analysis of the dynamics of the maximin problem when the sole source of well-being is consumption, and provide a numerical resolution of the model with resource amenity. The economy consumes, produces and invests less in the short run if the resource has an amenity value than if it does not, whereas it is the contrary in the medium and long runs. However, and without surprise, the resource stock remains for ever higher with resource amenity than without.     

Optimal management with potential regime shifts

We analyze how the threat of a potential future regime shift affects optimal management. We use a simple general growth model to analyze four cases that involve combinations of stock collapse versus changes in system dynamics, and exogenous versus endogenous probabilities of regime shift. Prior work in economics has focused on stock collapse with endogenous probabilities and reaches ambiguous conclusions on whether the potential for regime shift will increase or decrease intensity of resource use and level of resource stock. We show that all other cases yield unambiguous results. In particular, with endogenous probability of regime shift that affects system dynamics the potential for regime shift causes optimal management to become precautionary in the sense of maintaining higher resource stock levels.     

Predicting Extinction Risk of Brazilian Atlantic Forest Angiosperms

Understanding how plant life history affects species vulnerability to anthropogenic disturbances and environmental change is a major ecological challenge. We examined how vegetation type, growth form, and geographic range size relate to extinction risk throughout the Brazilian Atlantic Forest domain. We used a database containing species‐level information of 6,929 angiosperms within 112 families and a molecular‐based working phylogeny. We used decision trees, standard regression, and phylogenetic regression to explore the relationships between species attributes and extinction risk. We found a significant phylogenetic signal in extinction risk. Vegetation type, growth form, and geographic range size were related to species extinction risk, but the effect of growth form was not evident after phylogeny was controlled for. Species restricted to either rocky outcrops or scrub vegetation on sandy coastal plains exhibited the highest extinction risk among vegetation types, a finding that supports the hypothesis that species adapted to resource‐limited environments are more vulnerable to extinction. Among growth forms, epiphytes were associated with the highest extinction risk in non‐phylogenetic regression models, followed by trees, whereas shrubs and climbers were associated with lower extinction risk. However, the higher extinction risk of epiphytes was not significant after correcting for phylogenetic relatedness. Our findings provide new indicators of extinction risk and insights into the mechanisms governing plant vulnerability to extinction in a highly diverse flora where human disturbances are both frequent and widespread. Predicción del Riesgo de Extinción de Angiospermas del Bosque Atlántico Brasileño     

Control theory applied to natural and environmental resources an exposition

Four control theory models of natural and environmental resource use, drawn from the existing literature, are developed in a manner to emphasize their technical and decentralized interpretive similarity. Renewable, nonrenewable, and amenity resource use are treated as closely related problems of optimal (biological, earth material, ecological, or environmental) capital allocation over time. Thus nonrenewable resources, and the problem of exhaustion, are just limiting (zero growth) cases of renewable resources, and the problem of species extinction. Just as exhaustion can be optimal, extinction can be optimal. Waste recycling is treated as part of the problem of optimal regeneration of “sclean” environmental capital; wilderness use as a problem of managing the regeneration of ecological capital.     

Growth rates, seed size, and physiology: do small-seeded species really grow faster?

Relative growth rate (RGR) is currently the most commonly used method for measuring and comparing species' intrinsic growth potential. Comparative studies have, for example, revealed that small-seeded species have higher RGR, leading to the common belief that small-seeded species possess physiological adaptations for rapid growth that would allow them to outgrow large-seeded species, given sufficient time. We show that, because RGR declines as individual plants grow, it is heavily biased by initial size and does not measure the size-corrected growth potential that determines the outcome of competition in the long-term. We develop a daily growth model that includes a simple mechanistic representation of aboveground and belowground growth and its dependency on plant size and environmental factors. Intrinsic growth potential is encapsulated by the size-independent growth coefficient, G. We parameterized the model using repeated-harvest data from 1724 plants of nine species growing in contrasting nutrient and temperature regimes. Using information-theoretic criteria, we found evidence for interspecific differences in only three of nine model parameters: G, aboveground allocation, and frost damage. With other parameters shared between species, the model accurately reproduced above- and belowground biomass trajectories for all nine species in each set of environmental conditions. In contrast to conventional wisdom, the relationship between G and seed size was positive, despite a strong negative correlation between seed size and average RGR, meaning that large-seeded rather than small-seeded species have higher size-corrected growth potential. Further, we found a significant positive correlation between G and frost damage that, according to simulations, causes rank reversals in final biomass under daily temperature changes of +/- 5 degrees C. We recommend the wider use of this new kind of plant growth analysis as a better way of understanding underlying differences in species' physiology; but we recognize that RGR is still a useful metric if considering the potential rate of population increase in empty habitats.     

Bigger is not always better: offspring size does not predict growth or survival for seven ascidian species

The presumed trade-off between offspring size and quality predicted by life history theory is often invoked to explain the wide range of propagule sizes observed in animals and plants. This trade-off is broadly supported by intraspecific studies but has been difficult to test in an interspecific context, particularly in animals. We tested the fitness consequences of offspring size both intra- and interspecifically for seven species of ascidians (sessile, suspension-feeding, marine invertebrates) whose offspring volumes varied over three orders of magnitude. We measured two major components of fitness, juvenile growth rates and survival, in laboratory and field experiments encompassing several food conditions. Contrary to the predictions of life history theory, larger offspring size did not result in higher rates of growth or survival, and large offspring did not perform better under nutritional stress, either intraspecifically or interspecifically. In fact, two of the four species with small offspring grew rapidly enough to catch up in size to the species with large offspring in as little as eight weeks, under wild-type food conditions. Trade-offs between growth potential and defense may overwhelm and obscure any trade-offs between offspring size and survival or growth rate. While large initial size may still confer a competitive advantage, we failed to detect any consequences of interspecific variation in initial size. This implies that larger offspring in these species, far from being inherently superior in growth or survival, require compensation in other aspects of life history if reproductive effort is to be efficient. Our results suggest that the importance of initial offspring size is context dependent and often overestimated relative to other life history traits.     

Predicting the Risk of Extinction through Hybridization

Abstract: Natural hybridization threatens a substantial number of plant and animal species with extinction, but extinction risk has been difficult to evaluate in the absence of a quantitative assessment of risk factors. We investigated a number of ecological parameters likely to affect extinction risk, through an individual-based model simulating the life cycle of two hybridizing annual plant species. All parameters tested, ranging from population size to variance in pollen-tube growth rates, affected extinction risk. The sensitivity of each parameter varied dramatically across parameter sets, but, overall, the competitive ability, initial frequency, and selfing rate of the native taxon had the strongest effect on extinction. In addition, prezygotic reproductive barriers had a stronger influence on extinction rates than did postzygotic barriers. A stable hybrid zone was possible only when habitat differentiation was included in the model. When there was no habitat differentiation, either one of the parental species or the hybrids eventually displaced the other two taxa. The simulations demonstrated that hybridization is perhaps the most rapidly acting genetic threat to endangered species, with extinction often taking place in less than five generations. The simulation model was also applied to naturally hybridizing species pairs for which considerable genetic and ecological information is available. The predictions from these "worked examples" are in close agreement with observed outcomes and further suggest that an endemic cordgrass species is threatened by hybridization. These simulations provide guidance concerning the kinds of data required to evaluate extinction risk and possible conservation strategies.     

Extinction of Mammal Populations in Western North American National Parks

Patterns of local extinction of mammal populations in western North American parks were examined in relation to current biogeographic and population lifetime models. The analysis was based on species sighting records as of 1989. While western North American parks are obviously not true isolates, patterns of mammal extinction in them are nonetheless consistent with two predictions of the land-bridge island hypothesis. First, the number of extinctions has exceeded the number of colonizations since park establishment, and, second, the rate of extinction is inversely related to park area. Factors influencing the lifetime of mammal populations were evaluated using a stepwise multivariate survival analysis procedure for censored data. Survival time for mammal populations was positively related to estimated initial population size. After accounting for population size, species within the order Lagomorpha were particularly prone to extinction. Finally, after controlling for population size and taxon variation, survival time was positively related to age of maturity, indicating that species with longer generation times—age of maturity and generation time are highly correlated in mammals—persist longer in absolute time.     

Interspecific Patterns of Genetic Diversity in Birds: Correlations with Extinction Risk

Abstract:  Birds are frequently used as indicators of ecosystem health and are the most comprehensively studied class in the animal kingdom. Nevertheless, a comprehensive, interspecific assessment of the correlates of avian genetic diversity is lacking, even though indices of genetic diversity are of considerable interest in the conservation of threatened species. We used published data on variation at microsatellite loci from 194 bird species to examine correlates of diversity, particularly with respect to conservation status and population size. We found a significant decline in mean heterozygosity with increasing extinction risk, and showed, by excluding species whose heterozygosity values were calculated with heterospecific primers, that this relationship was not dependent on ascertainment bias. Results of subsequent regression analyses suggested that smaller population sizes of threatened species were largely responsible for this relationship. Thus, bird species at risk of extinction are relatively depauperate in terms of neutral genetic diversity, which is expected to make population recovery more difficult if it reflects adaptive genetic variation. Conservation policy will need to minimize further loss of diversity if the chances of saving threatened species are to be maximized.     

Body Size and Risk of Extinction in Australian Mammals

Abstract: The link between body size and risk of extinction has been the focus of much recent attention. For Australian terrestrial mammals this link is of particular interest because it is widely believed that species in the intermediate size range of 35–5500 g (the "critical weight range") have been the most prone to recent extinction. But the relationship between body size and extinction risk in Australian mammals has never been subject to a robust statistical analysis. Using a combination of randomization tests and phylogenetic comparative analyses, we found that Australian mammal extinctions and declines have been nonrandom with respect to body size, but we reject the hypothesis of a critical weight range at intermediate sizes. Small species appear to be the least prone to extinction, but extinctions have not been significantly clustered around intermediate sizes. Our results suggest that hypotheses linking intermediate body size with high risk of extinction in Australian mammals are misguided and that the focus of future research should shift to explaining why the smallest species are the most resistant to extinction.     

Optimal monitoring and control under state uncertainty: Application to lionfish management

State variables in many renewable resource management problems, such as the abundance of a fish stock, are imperfectly observed over time. In systems characterized by state uncertainty, decision makers often invest in monitoring to learn about the level of a stock. We develop a stochastic bioeconomic model of marine invasive species management under state uncertainty. The decision maker in our model simultaneously evaluates optimal investment in monitoring and population control. Using a recently-devised method for solving continuous-state Partially Observable Markov Decision Processes (POMDPs), we find that the ability to learn through monitoring can alter the role of population control in the optimal policy function, for example by reducing control intensity in favor of monitoring. Optimal monitoring depends on the management context, including in our application lionfish population structure. The rich transient dynamics of our model depend critically on the relationship between the initial conditions for information and invader abundance.     

Private aquaculture and commercial fisheries: Bioeconomics of salmon ranching

This paper shows that common property problems associated with open access salmon ranching in the absence of a commercial fishery result in inefficiency characterized by overstocking. The presence of an open access fishery presents additional common property problems which will inhibit the development of fish ranching. At prices where salmon ranching does occur, the open access commercial fishery will tend to overexploit the natural fish stock to a greater extent than if there were no salmon ranching. It is shown that there exists a range of prices where both fish stocks can coexist with open access. However, there is a limit price above which the natural stock will be driven to extinction through overfishing stimulated by stock from salmon ranchers. The range of prices under which both species can coexist can be increased through either restrictions of fishery effort or reducing the catchability of aquacultured stock. Cooperative management of both aquaculture and commercial fishing results in profits from both activities and will not cause extinction of the natural fish stock.     

Geographic range size and extinction risk assessment in nomadic species

Geographic range size is often conceptualized as a fixed attribute of a species and treated as such for the purposes of quantification of extinction risk; species occupying smaller geographic ranges are assumed to have a higher risk of extinction, all else being equal. However many species are mobile, and their movements range from relatively predictable to‐and‐fro migrations to complex irregular movements shown by nomadic species. These movements can lead to substantial temporary expansion and contraction of geographic ranges, potentially to levels which may pose an extinction risk. By linking occurrence data with environmental conditions at the time of observations of nomadic species, we modeled the dynamic distributions of 43 arid‐zone nomadic bird species across the Australian continent for each month over 11 years and calculated minimum range size and extent of fluctuation in geographic range size from these models. There was enormous variability in predicted spatial distribution over time; 10 species varied in estimated geographic range size by more than an order of magnitude, and 2 species varied by >2 orders of magnitude. During times of poor environmental conditions, several species not currently classified as globally threatened contracted their ranges to very small areas, despite their normally large geographic range size. This finding raises questions about the adequacy of conventional assessments of extinction risk based on static geographic range size (e.g., IUCN Red Listing). Climate change is predicted to affect the pattern of resource fluctuations across much of the southern hemisphere, where nomadism is the dominant form of animal movement, so it is critical we begin to understand the consequences of this for accurate threat assessment of nomadic species. Our approach provides a tool for discovering spatial dynamics in highly mobile species and can be used to unlock valuable information for improved extinction risk assessment and conservation planning.     

Optimal pollution in the presence of adjustment costs

This paper explores optimal pollution control when pollution is considered a stock and costs of treating pollution are a function both of the level and rate of change of pollution control. It is shown that even if the long run optimum stock of pollution is below the initial level adjustment costs may imply an optimally increasing stock of pollution in the short run. The results obtained are contrasted with those which emerge when adjustment costs are absent and when damages are taken to be a function of the flow of pollution; the appropriate tax rates of polluting discharges are examined.     

Habitat Change and Plant Demography: Assessing the Extinction Risk of a Formerly Common Grassland Perennial

Abstract:  An important aim of conservation biology is to understand how habitat change affects the dynamics and extinction risk of populations. We used matrix models to analyze the effect of habitat degradation on the demography of the declining perennial plant Trifolium montanum in 9 calcareous grasslands in Germany over 4 years and experimentally tested the effect of grassland management. Finite population growth rates (λ) decreased with light competition, measured as leaf-area index above T. montanum plants. At unmanaged sites λ was <1 due to lower recruitment and lower survival and flowering probability of large plants. Nevertheless, in stochastic simulations, extinction of unmanaged populations of 100 flowering plants was delayed for several decades. Clipping as a management technique rapidly increased population growth because of higher survival and flowering probability of large plants in managed than in unmanaged plots. Transition-matrix simulations from these plots indicated grazing or mowing every second year would be sufficient to ensure a growth rate ≥1 if conditions stayed the same. At frequently grazed sites, the finite growth rate was approximately 1 in most populations of T. montanum . In stochastic simulations, the extinction risk of even relatively small grazed populations was low, but about half the extant populations of T. montanum in central Germany are smaller than would be sufficient for a probability of survival of >95% over 100 years. We conclude that habitat change after cessation of management strongly reduces recruitment and survival of established individuals of this perennial plant. Nevertheless, our results suggest extinction processes may take a long time in perennial plants, resulting in an extinction debt. Even if management is frequent, many remnant populations of T. montanum may be at risk because of their small size, but even a slight increase in size could considerably reduce their extinction risk.     

Determining When to Change Course in Management Actions

Time is of the essence in conservation biology. To secure the persistence of a species, we need to understand how to balance time spent among different management actions. A new and simple method to test the efficacy of a range of conservation actions is required. Thus, we devised a general theoretical framework to help determine whether to test a new action and when to cease a trial and revert to an existing action if the new action did not perform well. The framework involves constructing a general population model under the different management actions and specifying a management objective. By maximizing the management objective, we could generate an analytical solution that identifies the optimal timing of when to change management action. We applied the analytical solution to the case of the Christmas Island pipistrelle bat (Pipistrelle murrayi), a species for which captive breeding might have prevented its extinction. For this case, we used our model to determine whether to start a captive breeding program and when to stop a captive breeding program and revert to managing the species in the wild, given that the management goal is to maximize the chance of reaching a target wild population size. For the pipistrelle bat, captive breeding was to start immediately and it was desirable to place the species in captivity for the entire management period. The optimal time to revert to managing the species in the wild was driven by several key parameters, including the management goal, management time frame, and the growth rates of the population under different management actions. Knowing when to change management actions can help conservation managers’ act in a timely fashion to avoid species extinction. Determinar Cuándo Cambiar el Rumbo en las Acciones de Manejo     

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.     

Fitting probability models to population dynamics data

Methods for modeling population dynamics in probability using the generalized point process approach are developed. The life history of these populations is such that seasonal reproduction occurs during a short time. Several models are developed and analyzed. Data about two species: colonial spiders (Stegodyphus dumicola) and a migratory bird (wood thrush, Hylocichla mustelina) are used to estimate model parameters with appropriate log maximum likelihood functions. For the spiders, the model is fitted to provide evolutionary feasible colony size based on maximum likelihood estimates of fecundity and survival data. For the migratory bird species, a maximum likelihood estimates are derived for the fecundity and survival rates of young and adult birds and immigration rate. The presented approach allows computation of quantities of interest such as probability of extinction and average time to extinction.     

Extinction Rate Estimates for Plant Populations in Revisitation Studies: Importance of Detectability

Abstract:  Many researchers have obtained extinction-rate estimates for plant populations by comparing historical and current records of occurrence. A population that is no longer found is assumed to have gone extinct. Extinction can then be related to characteristics of these populations, such as habitat type, size, or species, to test ideas about what factors may affect extinction. Such studies neglect the fact that a population may be overlooked, however, which may bias estimates of extinction rates upward. In addition, if populations are unequally detectable across groups to be compared, such as habitat type or population size, comparisons become distorted to an unknown degree. To illustrate the problem, I simulated two data sets, assuming a constant extinction rate, in which populations occurred in different habitats or habitats of different size and these factors affected their detectability. The conventional analysis implicitly assumed that detectability equalled 1 and used logistic regression to estimate extinction rates. It wrongly identified habitat and population size as factors affecting extinction risk. In contrast, with capture-recapture methods, unbiased estimates of extinction rates were recovered. I argue that capture-recapture methods should be considered more often in estimations of demographic parameters in plant populations and communities.