Endogenous growth,asymmetric trade and resource dependence

The aggregate income of oil-exporting countries relative to that of oil-poor countries has been remarkably constant in recent decades, despite the existence of structural gaps in productivity growth rates. This stylized fact is rationalized in an endogenous growth model of asymmetric trade where resource-poor and resource-rich economies display productivity differences but stable income shares due to terms-of-trade dynamics. The model yields two testable predictions that deserve empirical scrutiny: (i) the asymmetric impact, between exporters and importers, of national taxes on resource use on income shares and (ii) the inverse relation between terms-of-trade dynamics and total factor productivity growth.     

Endogenous growth,asymmetric trade and resource dependence

The aggregate income of oil-exporting countries relative to that of oil-poor countries has been remarkably constant in recent decades, despite the existence of structural gaps in productivity growth rates. This stylized fact is rationalized in an endogenous growth model of asymmetric trade where resource-poor and resource-rich economies display productivity differences but stable income shares due to terms-of-trade dynamics. The model yields two testable predictions that deserve empirical scrutiny: (i) the asymmetric impact, between exporters and importers, of national taxes on resource use on income shares and (ii) the inverse relation between terms-of-trade dynamics and total factor productivity growth.     

A resource-based approach to modelling the dynamics of interacting populations

The procedure for modelling the growth of single-species populations [Sakanoue, S., 2007. Extended logistic model for growth of single-species populations. Ecol. Model. 205, 159–168] is improved to be applicable to the study of the dynamics of interacting populations. The improved procedure is based on three assumptions: resource availability changes with population size as a variable, resource supply to populations and population demand for resources are defined as functions of resource availability and population size, and the variables of resource availability and population size shift in the supply function attracted to the demand function. These assumptions are organized into three equations. The equations can generate the dynamics models of plant, herbivore, and detritivore populations, and their own resources. The models can be used to describe prey–predator dynamics. They naturally contain nonlinear terms for the predator’s numerical and functional responses. Depending on the terms, the fluctuations in resource availability and population size stabilize. The three equations can also generate the dynamics models of different populations consuming the same resources. The analysis of zero isoclines of the models shows that a superior population can be simply defined as one with a higher intrinsic rate of natural increase, that a stable coexistence may be realized with the intraspecific interference or the interspecific facilitation of superiors, and that the interspecific interference or the intraspecific facilitation of inferiors may make the coexistence unstable and the inferiors winners depending on their initial population size.     

Testing model feasibility and sufficiency through laboratory simulation: A case study

Complex computer simulations of ecological models often fail to have much impact on later stages of applied research and management. We believe that this reflects a methodological gap. We present a case study where we try to bridge this gap. A recently published general model for insect outbreak has not yet been tested adequately in the field because of the complexity, size, and time involved in real-world insect pest outbreaks. However, a modified version of the model can be used to predict complex dynamics for a laboratory managed population of vinegar flies (Drosophila melanogaster).A comparison of the dynamics of the laboratory system with the simulation predictions allowed us to conclude that the model is “feasible”, i.e. under certain circumstances the model can predict the dynamics of some real system. These results were obtained despite considerable environmental and biological variability, indicating the robustness of the model. The factors chosen for the model appear to be “sufficient” to describe the real system's essential dynamics. Testing for feasibility and sufficiency should, in our opinion, always precede the much more expensive stages of field testing.     

Local Population Dynamics in Metapopulation Models: Implications for Conservation

Abstract: Habitat fragmentation and the division of populations into spatially separated units have led to the increasing use of metapopulation models to characterize these populations. One prominent model that has served as a heuristic tool was introduced by Levins and is based on a collection of simplifying assumptions that exclude information on the dynamics and spatial distribution of local populations. Levins's and similar models predict the proportion of occupied habitat patches at equilibrium and the conditions needed to avoid total extinction. There are many obvious concerns about using such models, including how realistic alterations might change the predictions and whether occupancy has any relationship to population-level processes. Although many of the assumptions of these simple models are known to be unrealistic, we do not know how the assumptions affect model predictions. We simulated a metapopulation, and our results show that assumptions such as homogeneity of habitat patches, random migration among patches, equivalent extinction probabilities in all patches, and a large number of patches can lead to large overestimations of habitat occupancy. But when we explicitly modeled the underlying population dynamics within each patch, we found (1) that there was a strong correlation between proportion of occupied patches and total metapopulation size and (2) that the distribution of individuals among patches was relatively insensitive to model assumptions. Thus, our results show that although realistic modifications will change model predictions for occupancy, occupancy and population trends will be correlated. These correlations between occupancy and population size suggest that occupancy models may have some utility in conservation applications.     

Enchytraeid population dynamics: Resource limitation and size-dependent mortality

Enchytraeids are regarded as keystone soil organisms in forest ecosystems. Their abundance and biomass fluctuate widely. Predicting the consequences of anthropogenic disturbances requires an understanding of the mechanisms underlying enchytraeid population dynamics. Here I develop a simple model, which predicts that the type of dynamics is controlled by resource input rate. If fungal resource input is a discrete event once a year, an exponential growth phase is followed by starvation and sharp decline of enchytraeid abundance. Model simulations with three different forcing functions were compared to field data. Initial parameter values were obtained from various independent sources, and parameters were estimated by minimizing the residual sum of squares. The best fitting model with resource addition once a year explained 39% of the variation in enchytraeid biomass over an 8-year study period. Further, variation in rainfall explained 59% of the variation in R² of the exponential phase models, which is also an index of the stability of population size-structure. The results emphasize the importance of resource limitation for enchytraeid population dynamics and support the hypothesis that the mortality during the decline phase is size-dependent.     

Impact of minimum winter temperatures on the population dynamics of Dendroctonus frontalis.

Predicting population dynamics is a fundamental problem in applied ecology. Temperature is a potential driver of short-term population dynamics, and temperature data are widely available, but we generally lack validated models to predict dynamics based upon temperatures. A generalized approach involves estimating the temperatures experienced by a population, characterizing the demographic consequences of physiological responses to temperature, and testing for predicted effects on abundance. We employed this approach to test whether minimum winter temperatures are a meaningful driver of pestilence from Dendroctonus frontalis (the southern pine beetle) across the southeastern United States. A distance-weighted interpolation model provided good, spatially explicit, predictions of minimum winter air temperatures (a putative driver of beetle survival). A Newtonian heat transfer model with empirical cooling constants indicated that beetles within host trees are buffered from the lowest air temperatures by approximately 1-4 degrees C (depending on tree diameter and duration of cold bout). The life stage structure of beetles in the most northerly outbreak in recent times (New Jersey) were dominated by prepupae, which were more cold tolerant (by >3 degrees C) than other life stages. Analyses of beetle abundance data from 1987 to 2005 showed that minimum winter air temperature only explained 1.5% of the variance in interannual growth rates of beetle populations, indicating that it is but a weak driver of population dynamics in the southeastern United States as a whole. However, average population growth rate matched theoretical predictions of a process-based model of winter mortality from low temperatures; apparently our knowledge of population effects from winter temperatures is satisfactory, and may help to predict dynamics of northern populations, even while adding little to population predictions in southern forests. Recent episodes of D. frontalis outbreaks in northern forests may have been allowed by a warming trend from 1960 to 2004 of 3.3 degrees C in minimum winter air temperatures in the southeastern United States. Studies that combine climatic analyses, physiological experiments, and spatially replicated time series of population abundance can improve population predictions, contribute to a synthesis of population and physiological ecology, and aid in assessing the ecological consequences of climatic trends.     

Effect of sheep grazing and fire on sage grouse populations in southeastern Idaho

This paper describes the development, evaluation, and use of a model that simulates the effect of grazing and fire on temporal and spatial aspects of sagebrush community vegetation and sage grouse population dynamics. The model is represented mathematically as a discrete-time, stochastic compartment model based on difference equations with a time interval of 1 week. In the model, sheep graze through sage grouse breeding habitat during spring and fall, and different portions of the area can burn at different frequencies, creating a habitat mosaic of burned and unburned areas.The model was evaluated by examining predictions of (1) growth of sagebrush canopy cover after fire, (2) seasonal dynamics of grass and forb biomass under historical environmental conditions, and (3) sage grouse population dynamics associated with selected sagebrush canopy covers. Simulated changes in sagebrush canopy cover following fire correspond well with qualitative reports of long-term trends, simulated seasonal dynamics of herbaceous biomass correspond well with field data, and simulated responses of sage grouse population size and age structure to changing sagebrush canopy cover correspond well to qualitative field observations.Simulation results suggest that large fires occurring at high frequencies may lead to the extinction of sage grouse populations, whereas fires occurring at low frequencies may benefit sage grouse if burned areas are small and sheep grazing is absent. Sheep grazing may contribute to sage grouse population decline, but is unlikely to cause extinction under fire regimes that are favorable to sage grouse.     

Integrating intraseasonal grassland dynamics in cross-scale distribution modeling to support waterbird recovery plans

Despite much discussion about the utility of remote sensing for effective conservation, the inclusion of these technologies in species recovery plans remains largely anecdotal. We developed a modeling approach for the integration of local, spatially measured ecosystem functional dynamics into a species distribution modeling (SDM) framework in which other ecologically relevant factors are modeled separately at broad scales. To illustrate the approach, we incorporated intraseasonal water-vegetation dynamics into a cross-scale SDM for the Common Snipe (Gallinago gallinago), which is highly dependent on water and vegetation dynamics. The Common Snipe is an Iberian grassland waterbird characteristic of European agricultural meadows and a member of one of the most threatened bird guilds. The intraseasonal dynamics of water content of vegetation were measured using the standard deviation of the normalized difference water index time series computed from bimonthly images of the Sentinel-2 satellite. The recovery plan for the Common Snipe in Galicia (northwestern Iberian Peninsula) provided an opportunity to apply our modeling framework. Model accuracy in predicting the species’ distribution at a regional scale (resulting from integration of downscaled climate projections with regional habitat–topographic suitability models) was very high (area under the curve [AUC] of 0.981 and Boyce's index of 0.971). Local water-vegetation dynamic models, based exclusively on Sentinel-2 imagery, were good predictors (AUC of 0.849 and Boyce's index of 0.976). The predictive power improved (AUC of 0.92 and Boyce's index of 0.98) when local model predictions were restricted to areas identified by the continental and regional models as priorities for conservation. Our models also performed well (AUC of 0.90 and Boyce's index of 0.93) when projected to updated water-vegetation conditions. Our modeling framework enabled incorporation of key ecosystem processes closely related to water and carbon cycles while accounting for other factors ecologically relevant to endangered grassland waterbirds across different scales, allowed identification of priority areas for conservation, and provided an opportunity for cost-effective recovery planning by monitoring management effectiveness from space.     

Effects of an Invasive Plant on Population Dynamics in Toads

When populations decline in response to unfavorable environmental change, the dynamics of their population growth shift. In populations that normally exhibit high levels of variation in recruitment and abundance, as do many amphibians, declines may be difficult to identify from natural fluctuations in abundance. However, the onset of declines may be evident from changes in population growth rate in sufficiently long time series of population data. With data from 23 years of study of a population of Fowler's toad (Anaxyrus [ = Bufo] fowleri) at Long Point, Ontario (1989–2011), we sought to identify such a shift in dynamics. We tested for trends in abundance to detect a change point in population dynamics and then tested among competing population models to identify associated intrinsic and extrinsic factors. The most informative models of population growth included terms for toad abundance and the extent of an invasive marsh plant, the common reed (Phragmites australis), throughout the toads’ marshland breeding areas. Our results showed density‐dependent growth in the toad population from 1989 through 2002. After 2002, however, we found progressive population decline in the toads associated with the spread of common reeds and consequent loss of toad breeding habitat. This resulted in reduced recruitment and population growth despite the lack of significant loss of adult habitat. Our results underscore the value of using long‐term time series to identify shifts in population dynamics coincident with the advent of population decline. Efectos de una Planta Invasora sobre las Dinámica Poblacional de Sapos     

Allee Effect and the Uncertainty of Population Recovery

Recovery of depleted populations is fundamentally important for conservation biology and sustainable resource harvesting. At low abundance, population growth rate, a primary determinant of population recovery, is generally assumed to be relatively fast because competition is low (i.e., negative density dependence). But population growth can be limited in small populations by an Allee effect. This is particularly relevant for collapsed populations or species that have not recovered despite large reductions in, or elimination of, threats. We investigated how an Allee effect can influence the dynamics of recovery. We used Atlantic cod (Gadus morhua) as the study organism and an empirically quantified Allee effect for the species to parameterize our simulations. We simulated recovery through an individual‐based mechanistic simulation model and then compared recovery among scenarios incorporating an Allee effect, negative density dependence, and an intermediate scenario. Although an Allee effect significantly slowed recovery, such that population increase could be negligible even after 100 years or more, it also made the time required for biomass rebuilding much less predictable. Our finding that an Allee effect greatly increased the uncertainty in recovery time frames provides an empirically based explanation for why the removal of threat does not always result in the recovery of depleted populations or species. El Efecto Allee y la Incertidumbre de la Recuperación de Poblaciones     

Pre-encounter versus post-encounter inducible defenses in predator–prey model systems

It has been reported that, in order to reduce mortality, prey are able to change their phenotype in response to cues released from predators. These short-time responses constitute effective antipredator strategies in variable environments, and involve changes in morphology, behavior, physiology or life-history traits of prey individuals belonging to a wide spectrum of taxa. Defenses can be classified into pre-encounter and post-encounter, depending on the phase of the predation process in which they take place. Also, inducible defenses should be costly.Despite the current knowledge of inducible defenses at the individual level, our understanding of their dynamic consequences at the population and community level is limited. In this work we construct and analyze numerically a predator–prey system, parameterized from published experimental data, in which prey exhibit inducible defenses of the type pre-encounter (affecting attack rate) or post-encounter (affecting handling time) and entailing either metabolic or feeding costs. The above assumptions were analyzed over a gradient of resource availability.Our results indicated that both types of cost have a similar effect on the dynamics of the model system, but we expect that different costs will produce different outcomes in a more complex model community. Conversely, pre-encounter and post-encounter IDs define domains of attraction with different size and shape within the studied sections of the multidimensional parameter space. Roughly speaking, post-encounter IDs determine a more rich dynamics when plausible parameter values are chosen, and the effect of resource density is different if the ID is handling-time based or attack-rate based. In agreement with previous works, our analyses indicate that IDs can damp population oscillations and prevent the paradox of enrichment.     

Uncertainty analysis of transient population dynamics

Two types of demographic analyses, perturbation analysis and uncertainty analysis, can be conducted to gain insights about matrix population models and guide population management. Perturbation analysis studies how the perturbation of demographic parameters (survival, growth, and reproduction parameters) may affect the population projection, while uncertainty analysis evaluates how much uncertainty there is in population dynamic predictions and where the uncertainty comes from. Previously, both perturbation analysis and uncertainty analysis were conducted on the long-term population growth rate. However, the population may not reach its equilibrium state, especially when there is management by harvesting or hunting. Recently, there has been an increased interest in short-term transient dynamics, which can differ from asymptotic long-term dynamics. There are currently techniques to conduct perturbation analyses of short-term transient dynamics, but no techniques have been proposed for uncertainty analysis of such dynamics. In this study, we introduced an uncertainty analysis technique, the general Fourier Amplitude Sensitivity Test (FAST), to study uncertainties in transient population dynamics. The general FAST is able to identify the amount of uncertainty in transient dynamics and contributions by different demographic parameters. We applied the general FAST to a mountain goat (Oreamnos americanus) matrix population model to give a clear illustration of how uncertainty analysis can be conducted for transient dynamics arising from matrix population models.     

Effects of Social Structure and Prey Dynamics on Extinction Risk in Gray Wolves

Extinction models based on diffusion theory generally fail to incorporate two important aspects of population biology—social structure and prey dynamics. We include these aspects in an individual-based extinction model for small, isolated populations of the gray wolf (Canis lupus). Our model predicts mean times to extinction significantly longer than those predicted by more general (diffusion) models. According to our model, an isolated population of 50 wolves has a 95% chance of surviving just 9 years and only a 30% chance of surviving beyond 100 years. Reflecting the influence of social structure, a wolf population initially comprising 50 individuals is expected to persist only a few years longer, on average (71 years), than is a population initially comprising just a single reproductive pair (62 years). In contrast, substantially greater average prey abundance leads to dramatically longer expected persistence times. Autocorrelated prey dynamics result in a more complex distribution of extinction times than predicted by many extinction models. We contend that demographic stochasticity may pose the greatest threat to small, isolated wolf populations, although environmental stochasticity and genetic effects may compound this threat. Our work highlights the importance of considering social structure and resource dynamics in the development of population viability analyses.     

An individual based model of bearded pig abundance

We develop an individual based model of bearded pig abundance which predicts population dynamics based on the processes of energy accumulation and expenditure, reproduction and mortality of individual pigs. Because fatness is a key indicator of condition and reproductive potential in bearded pigs, processes are represented in terms of a fatness index variable. Only a small number of parameters are used in this simple model; these were chosen on the basis of fatness index data and qualitative observations of bearded pig population dynamics. The model was found to be accurate in predicting the timing of observed pig eruptions, and robust in that model results were unaffected by moderate variation in parameter values. There was insufficient quantitative data to obtain precise predictions of fatness and abundance, but qualitative insights about the effects of the size and timing of fruiting events on pig abundance were obtained. The results showed that a single fruiting peak will not produce a bearded pig eruption, no matter how large the fruiting event is, because the duration of the fruiting is too short to allow exponential growth of the population. Consecutive masting events are necessary for an eruption, because if events are separated by more than 1 year, the population will decline to its minimum fatness and abundance levels. It is also necessary for at least one of the fruiting events in a consecutive sequence to be a large event, as consecutive small fruiting events do not increase the fatness enough to cause an eruption. These insights help to explain and predict the effects of changes in mast fruiting patterns on bearded pig populations, such as the predicted increase in frequency and reduction in size of masting fruiting events as a result of climate change.     

Introducing effects of temperature and CO2 elevation on tree growth into a statistical growth and yield model

Impacts of elevated temperature and CO₂ on tree growth were introduced into a statistical growth and yield model for Finnish conditions based on corresponding predictions obtained from a physiological growth model. This one-way link between models was made by means of species-specific transfer functions describing the increase in stem volume growth of trees as a function of elevated temperature and CO₂, stand density and the tree's competition status in a stand of Scots pine (Pinus sylvestris), silver birch (Betula pendula) and Norway spruce (Picea abies). This method allows the inner dynamics of the statistical model to be followed when the impacts of temperature and CO₂ elevation on tree growth are introduced into the calculation of volume growth and further allocated between diameter and height growth. In this way compatibility with previous predictions of tree growth by means of statistical models and related model systems under current climatic conditions could be retained.The performance of the statistical model with species-specific transfer functions was evaluated by comparing its predictions with corresponding predictions given by a physiological model under conditions of elevated temperature and CO₂. These calculations revealed that the growth response of individual trees to elevated temperature and CO₂ can be introduced into the statistical model from a physiological growth model with an outcome that results in fairly satisfactory growth responses at the stand level as well.     

Coexistence of intraguild predators and prey in resource-rich environments

The prevalence of intraguild predation (IGP) in productive environments has long puzzled ecologists. Theory predicts the exclusion of intraguild prey from such environments, but data consistently defy this expectation. This suggests that coexistence mechanisms at high resource productivity may differ from those at lower productivity. Here I present a mathematical model that investigates multiple coexistence mechanisms. I incorporate two biological features widely observed in IGP communities: intraspecific interference via cannibalism or superparasitism, and temporal refuges arising from differential sensitivities to abiotic variation. I develop predictions based on three aspects of the IG prey-IG predator interaction: mutual invasibility, transient dynamics, and long-term abundances. These predictions specify the conditions under which coexistence mechanisms reinforce vs. deter one another: when a competition-IGP trade-off allows coexistence at intermediate productivity a temporal refuge for the intraguild prey always allows coexistence at high productivity, but intraspecific interference does so only at a net fitness cost to the intraguild predator. Intraspecific interference that benefits the intraguild predator not only reduces tradeoff-mediated coexistence at intermediate productivity, but also undermines the refuge's coexistence-enhancing effect at high productivity. Different mechanism combinations yield characteristic signatures in time series data during transient dynamics. By judicious measurement of parameters and examining time series for critical signatures, one can elucidate the mechanisms that allow IGP to prevail in resource-rich environments.     

Nonlinear relationships between vital rates and state variables in demographic models

To accurately estimate population dynamics and viability, structured population models account for among-individual differences in demographic parameters that are related to individual state. In the widely used matrix models, such differences are incorporated in terms of discrete state categories, whereas integral projection models (IPMs) use continuous state variables to avoid artificial classes. In IPMs, and sometimes also in matrix models, parameterization is based on regressions that do not always model nonlinear relationships between demographic parameters and state variables. We stress the importance of testing for nonlinearity and propose using restricted cubic splines in order to allow for a wide variety of relationships in regressions and demographic models. For the plant Borderea pyrenaica, we found that vital rate relationships with size and age were nonlinear and that the parameterization method had large effects on predicted population growth rates, X (linear IPM, 0.95; nonlinear IPMs, 1.00; matrix model, 0.96). Our results suggest that restricted cubic spline models are more reliable than linear or polynomial models. Because even weak nonlinearity in relationships between vital rates and state variables can have large effects on model predictions, we suggest that restricted cubic regression splines should be considered for parameterizing models of population dynamics whenever linearity cannot be assumed.     

Models of withdrawing renewable and non-renewable resources based on Odum's energy systems theory and Daly's quasi-sustainability principle

This paper presents a theoretical model of withdrawing resources based on Odum's energy systems diagrams. According to the theory of a general pulsing principle, withdrawing resources changes in time shifting from the initial phases of growth and maturity to the phases of descent and low energy restoration. A simulation was performed in order to hypothesize potential future trends of withdrawing renewable and non-renewable resources and to show some aspects of their sustainability–unsustainability, respectively. According to Odum's theory, after the rapid growth of the last century, our civilization is living in a climax transition phase and it is now approaching a descent phase. A “way down” will be necessary due to the exhaustion of non-renewable and to the limited use of renewable resources. An integrated “renew–non-renew” model was developed by Odum to show how a “business as usual” trend will bring us to a drastic transition to a world that uses scarce renewable resources. Nevertheless, a different choice is possible, based on Daly's concept of quasi-sustainability that can inspire a new model. The latter argued that the exploitation of a non-renewable resource must be paired with a compensating investment in a renewable substitute. Our model shows that we can use non-renewable resources better to considerably improve our capacity of capturing renewable resources in the future. We present this as a necessary condition to address a sustainable environmental policy.     

A Behaviorally Explicit Demographic Model Integrating Habitat Selection and Population Dynamics in California Sea Lions

Abstract: Although there has been a call for the integration of behavioral ecology and conservation biology, there are few tools currently available to achieve this integration. Explicitly including information about behavioral strategies in population viability analyses may enhance the ability of conservation biologists to understand and estimate patterns of extinction risk. Nevertheless, most behavioral‐based PVA approaches require detailed individual‐based data that are rarely available for imperiled species. We present a mechanistic approach that incorporates spatial and demographic consequences of behavioral strategies into population models used for conservation. We developed a stage‐structured matrix model that includes the costs and benefits of movement associated with 2 habitat‐selection strategies (philopatry and direct assessment). Using a life table for California sea lions (Zalophus californianus), we explored the sensitivity of model predictions to the inclusion of these behavioral parameters. Including behavioral information dramatically changed predicted population sizes, model dynamics, and the expected distribution of individuals among sites. Estimated population sizes projected in 100 years diverged up to 1 order of magnitude among scenarios that assumed different movement behavior. Scenarios also exhibited different model dynamics that ranged from stable equilibria to cycles or extinction. These results suggest that inclusion of behavioral data in viability models may improve estimates of extinction risk for imperiled species. Our approach provides a simple method for incorporating spatial and demographic consequences of behavioral strategies into population models and may be easily extended to other species and behaviors to understand the mechanisms of population dynamics for imperiled populations.