Invasion and eradication of a competitively superior species in heterogeneous landscapes

The effect of heterogeneous environments upon the dynamics of invasion and the eradication or control of invasive species is poorly understood, although it is a major challenge for biodiversity conservation. Here, we first investigate how the probability and time for invasion are affected by spatial heterogeneity. Then, we study the effect of control program strategies (e.g. species specificity, spatial scale of action, detection and eradication efficiency) on the success and time of eradication. We find that heterogeneity increases both the invasion probability and the time to invasion. Heterogeneity also reduces the probability of eradication but does not change the time taken for successful eradication. We confirm that early detection of invasive species reduces the time until eradication, but we also demonstrate that this is true only if the local control action is sufficiently efficient. The criterion of removal efficiency is even more important for an eradication program than simply ensuring control effort when the invasive species is not abundant.     

Quantifying Eradication Success: the Removal of Feral Pigs from Santa Cruz Island, California

Abstract:  A major challenge facing pest-eradication efforts is determining when eradication has been achieved. When the pest can no longer be detected, managers have to decide whether the pest has actually been eliminated and hence to decide when to terminate the eradication program. For most eradication programs, this decision entails considerable risk and is the largest single issue facing managers of such programs. We addressed this issue for an eradication program of feral pigs ( Sus scrofa ) from Santa Cruz Island, California. Using a Bayesian approach, we estimated the degree of confidence in the success of the eradication program at the point when monitoring failed to detect any more pigs. Catch-effort modeling of the hunting effort required to dispatch pigs during the eradication program was used to determine the relationship between detection probability and searching effort for different hunting methods. We then used these relationships to estimate the amount of monitoring effort required to declare eradication successful with criteria that either set a threshold for the probability that pigs remained undetected (type I error) or minimized the net expected costs of the eradication program (cost of type I and II errors). For aerial and ground-based monitoring techniques, the amount of search effort required to declare eradication successful on the basis of either criterion was highly dependent on the prior belief in the success of the program unless monitoring intensities exceeded 30 km of searching effort per square kilometer of search area for aerial monitoring and, equivalently, 38 km for ground monitoring. Calculation of these criteria to gauge the success of eradication should form an essential component of any eradication program as it allows for a transparent assessment of the risks inherent in the decision to terminate the program.     

Evaluation of potential responses to invasive non-native species with structured decision making

In managing invasions and colonizations of non-native species, eradication or control efforts must proceed quickly. There are 2 challenges in taking such quick action. First, managers frequently have to choose among complex and often competing environmental, social, and economic objectives. Second, the effects are highly uncertain. We applied participatory structured decision making (SDM) to develop a response plan for the recent invasion of non-native myrtle rust (Uredo rangelii) in Australia. Structured decision making breaks a complex decision process into 5 steps: identify problems (i.e., decisions to be made), formulate objectives, develop management alternatives, estimate consequences of implementing those alternatives, and select preferred alternatives by evaluating trade-offs among alternatives. To determine the preferred mid- to long-term alternatives to managing the rust, we conducted 2 participatory workshops and 18 interviews with individuals to elicit stakeholders' key concerns and convert them into 5 objectives (minimize management cost, minimize economic cost to industry, minimize effects on natural ecosystems and landscape amenities, and minimize environmental effects associated with use of fungicide) and to identify the 5 management alternatives (full eradication, partial eradication, slow spread, live with it [i.e., major effort invested in mitigation of effects], and do nothing). We also developed decision trees to graphically represent the essence of the decision by displaying the relations between uncertainties and decision points. In the short term or before local expansion of myrtle rust, the do-nothing alternative was not preferred, but an eradication alternative was only recommended if the probability of eradication exceeded about 40%. After the expansion of myrtle rust, the slow-the-spread alternative was preferred regardless of which of the short-term management alternatives was selected at an earlier stage. The participatory SDM approach effectively resulted in informed and transparent response plans that incorporated multiple objectives in decision-making processes under high uncertainty.     

Bayesian Decision Analysis for Evaluating Management Options to Promote Recovery of a Depleted Salmon Population

Abstract:  The endangered population of sockeye salmon (Oncorhynchus nerka) in Cultus Lake, British Columbia, Canada, migrates through commercial fishing areas along with other, much more abundant sockeye salmon populations, but it is not feasible to selectively harvest only the latter, abundant populations. This situation creates controversial trade-offs between recovery actions and economic revenue. We conducted a Bayesian decision analysis to evaluate options for recovery of Cultus Lake sockeye salmon. We used a stochastic population model that included 2 sources of uncertainty that are often omitted from such analyses: structural uncertainty in the magnitude of a potential Allee effect and implementation uncertainty (the deviation between targets and actual outcomes of management actions). Numerous state-dependent, time-independent management actions meet recovery objectives. These actions prescribe limitations on commercial harvest rates as a function of abundance of Cultus Lake sockeye salmon. We also quantified how much reduction in economic value of commercial harvests of the more abundant sockeye salmon populations would be expected for a given increase in the probability of recovery of the Cultus population. Such results illustrate how Bayesian decision analysis can rank options for dealing with conservation risks and can help inform trade-off discussions among decision makers and among groups that have competing objectives.     

Incorporating Uncertainty of Management Costs in Sensitivity Analyses of Matrix Population Models

The importance of accounting for economic costs when making environmental‐management decisions subject to resource constraints has been increasingly recognized in recent years. In contrast, uncertainty associated with such costs has often been ignored. We developed a method, on the basis of economic theory, that accounts for the uncertainty in population‐management decisions. We considered the case where, rather than taking fixed values, model parameters are random variables that represent the situation when parameters are not precisely known. Hence, the outcome is not precisely known either. Instead of maximizing the expected outcome, we maximized the probability of obtaining an outcome above a threshold of acceptability. We derived explicit analytical expressions for the optimal allocation and its associated probability, as a function of the threshold of acceptability, where the model parameters were distributed according to normal and uniform distributions. To illustrate our approach we revisited a previous study that incorporated cost‐efficiency analyses in management decisions that were based on perturbation analyses of matrix population models. Incorporating derivations from this study into our framework, we extended the model to address potential uncertainties. We then applied these results to 2 case studies: management of a Koala (Phascolarctos cinereus) population and conservation of an olive ridley sea turtle (Lepidochelys olivacea) population. For low aspirations, that is, when the threshold of acceptability is relatively low, the optimal strategy was obtained by diversifying the allocation of funds. Conversely, for high aspirations, the budget was directed toward management actions with the highest potential effect on the population. The exact optimal allocation was sensitive to the choice of uncertainty model. Our results highlight the importance of accounting for uncertainty when making decisions and suggest that more effort should be placed on understanding the distributional characteristics of such uncertainty. Our approach provides a tool to improve decision making.     

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     

Invasive cordgrass modifies wetland trophic function

Vascular plants strongly control belowground environments in most ecosystems. Invasion by vascular plants in coastal wetlands, and by cordgrasses (Spartina spp.) in particular, are increasing in incidence globally, with dramatic ecosystem-level consequences. We examined the trophic consequences of invasion by a Spartina hybrid (S. alterniflora x S. foliosa) in San Francisco Bay (USA) by documenting differences in biomass and trophic structure of benthic communities between sediments invaded by Spartina and uninvaded sediments. We found the invaded system shifted from an algae-based to a detritus-based food web. We then tested for a relationship between diet and tolerance to invasion, hypothesizing that species that consume Spartina detritus are more likely to inhabit invaded sediments than those that consume surface algae. Infaunal diets were initially examined with natural abundance stable isotope analyses and application of mixing models, but these yielded an ambiguous picture of food sources. Therefore, we conducted isotopic enrichment experiments by providing 15N-labeled Spartina detritus both on and below the sediment surface in areas that either contained Spartina or were unvegetated. Capitellid and nereid polychaetes, and oligochaetes, groups shown to persist following Spartina invasion of San Francisco Bay tidal flats, took up 15N from labeled native and invasive Spartina detritus. In contrast, we found that amphipods, bivalves, and other taxa less tolerant to invasion consumed primarily surficial algae, based on 13C enrichment experiments. Habitat (Spartina vs. unvegetated patches) and location of detritus (on or within sediments) did not affect 15N uptake from detritus. Our investigations support a "trophic shift" model for ecosystem response to wetland plant invasion and preview loss of key trophic support for fishes and migratory birds by shifting dominance to species not widely consumed by species at higher trophic levels.     

Cost-Effective Suppression and Eradication of Invasive Predators

Abstract: Introduced predators can have pronounced effects on naïve prey species; thus, predator control is often essential for conservation of threatened native species. Complete eradication of the predator, although desirable, may be elusive in budget‐limited situations, whereas predator suppression is more feasible and may still achieve conservation goals. We used a stochastic predator–prey model based on a Lotka‐Volterra system to investigate the cost‐effectiveness of predator control to achieve prey conservation. We compared five control strategies: immediate eradication, removal of a constant number of predators (fixed‐number control), removal of a constant proportion of predators (fixed‐rate control), removal of predators that exceed a predetermined threshold (upper‐trigger harvest), and removal of predators whenever their population falls below a lower predetermined threshold (lower‐trigger harvest). We looked at the performance of these strategies when managers could always remove the full number of predators targeted by each strategy, subject to budget availability. Under this assumption immediate eradication reduced the threat to the prey population the most. We then examined the effect of reduced management success in meeting removal targets, assuming removal is more difficult at low predator densities. In this case there was a pronounced reduction in performance of the immediate eradication, fixed‐number, and lower‐trigger strategies. Although immediate eradication still yielded the highest expected minimum prey population size, upper‐trigger harvest yielded the lowest probability of prey extinction and the greatest return on investment (as measured by improvement in expected minimum population size per amount spent). Upper‐trigger harvest was relatively successful because it operated when predator density was highest, which is when predator removal targets can be more easily met and the effect of predators on the prey is most damaging. This suggests that controlling predators only when they are most abundant is the “best” strategy when financial resources are limited and eradication is unlikely.     

Interactions between mangroves and exotic Spartina in an anthropogenically disturbed estuary in southern China

Cordgrass (Spartina alterniflora) was introduced to China in 1979 from the United States for reducing coastal erosion. It grows vigorously in China and has spread over much of the Chinese coast, from Leizhou Peninsula to Liaoning, a range of more than 19 degrees of latitude. On the southern coast of China, S. alterniflora has invaded mangrove-dominated habitats during the last two decades, but little is known about interactions between native mangroves and invasive S. alterniflora. We studied the distribution and competitive interactions between native mangroves and S. alterniflora in the Zhangjiang Estuary at four tidal sites along a salinity gradient: oligohaline upstream, mesohaline, polyhaline, and euhaline downstream. S. alterniflora occurred at all four sites, and several mangrove species occurred at all but the downstream euhaline site. S. alterniflora has invaded the estuary widely and has spread to the lower tidal margins of mangroves. It has not invaded mangrove areas with a closed canopy but has established in the mangrove zone where the canopy was opened by human disturbance. Ramets of S. alterniflora transplanted into the understory of mangrove stands with closed canopies died within 10 weeks, but 37.5% survived and grew well on open mud flats. S. alterniflora had virtually no competitive effect on mangrove seedlings planted at the upstream oligohaline site. However, S. alterniflora competitively reduced biomass of mangrove seedlings to 33% over a period of 14 weeks at the mesohaline and polyhaline sites where human disturbance has opened the mangrove canopy. In contrast, S. alterniflora marginally facilitated growth and survival of experimental seedlings at the downstream euhaline site. In China, mangroves occur along the coastline south of Whenzhou, but they have been severely disturbed and removed widely, mainly by mariculture activities. Natural vegetation patterns and our experimental results suggest that, without intervention, S. alterniflora could gradually replace these mangroves in mid-salinity regions of Chinese estuaries.     

Monitoring,imperfect detection,and risk optimization of a Tasmanian devil insurance population

Most species are imperfectly detected during biological surveys, which creates uncertainty around their abundance or presence at a given location. Decision makers managing threatened or pest species are regularly faced with this uncertainty. Wildlife diseases can drive species to extinction; thus, managing species with disease is an important part of conservation. Devil facial tumor disease (DFTD) is one such disease that led to the listing of the Tasmanian devil (Sarcophilus harrisii) as endangered. Managers aim to maintain devils in the wild by establishing disease‐free insurance populations at isolated sites. Often a resident DFTD‐affected population must first be removed. In a successful collaboration between decision scientists and wildlife managers, we used an accessible population model to inform monitoring decisions and facilitate the establishment of an insurance population of devils on Forestier Peninsula. We used a Bayesian catch‐effort model to estimate population size of a diseased population from removal and camera trap data. We also analyzed the costs and benefits of declaring the area disease‐free prior to reintroduction and establishment of a healthy insurance population. After the monitoring session in May–June 2015, the probability that all devils had been successfully removed was close to 1, even when we accounted for a possible introduction of a devil to the site. Given this high probability and the baseline cost of declaring population absence prematurely, we found it was not cost‐effective to carry out any additional monitoring before introducing the insurance population. Considering these results within the broader context of Tasmanian devil management, managers ultimately decided to implement an additional monitoring session before the introduction. This was a conservative decision that accounted for uncertainty in model estimates and for the broader nonmonetary costs of mistakenly declaring the area disease‐free.     

Cost‐effective conservation of an endangered frog under uncertainty

How should managers choose among conservation options when resources are scarce and there is uncertainty regarding the effectiveness of actions? Well‐developed tools exist for prioritizing areas for one‐time and binary actions (e.g., protect vs. not protect), but methods for prioritizing incremental or ongoing actions (such as habitat creation and maintenance) remain uncommon. We devised an approach that combines metapopulation viability and cost‐effectiveness analyses to select among alternative conservation actions while accounting for uncertainty. In our study, cost‐effectiveness is the ratio between the benefit of an action and its economic cost, where benefit is the change in metapopulation viability. We applied the approach to the case of the endangered growling grass frog (Litoria raniformis), which is threatened by urban development. We extended a Bayesian model to predict metapopulation viability under 9 urbanization and management scenarios and incorporated the full probability distribution of possible outcomes for each scenario into the cost‐effectiveness analysis. This allowed us to discern between cost‐effective alternatives that were robust to uncertainty and those with a relatively high risk of failure. We found a relatively high risk of extinction following urbanization if the only action was reservation of core habitat; habitat creation actions performed better than enhancement actions; and cost‐effectiveness ranking changed depending on the consideration of uncertainty. Our results suggest that creation and maintenance of wetlands dedicated to L. raniformis is the only cost‐effective action likely to result in a sufficiently low risk of extinction. To our knowledge we are the first study to use Bayesian metapopulation viability analysis to explicitly incorporate parametric and demographic uncertainty into a cost‐effective evaluation of conservation actions. The approach offers guidance to decision makers aiming to achieve cost‐effective conservation under uncertainty.     

Using the functional response of a consumer to predict biotic resistance to invasive prey

Predators sometimes provide biotic resistance against invasions by nonnative prey. Understanding and predicting the strength of biotic resistance remains a key challenge in invasion biology. A predator's functional response to nonnative prey may predict whether a predator can provide biotic resistance against nonnative prey at different prey densities. Surprisingly, functional responses have not been used to make quantitative predictions about biotic resistance. We parameterized the functional response of signal crayfish (Pacifastacus leniusculus) to invasive New Zealand mud snails (Potamopyrgus antipodarum; NZMS) and used this functional response and a simple model of NZMS population growth to predict the probability of biotic resistance at different predator and prey densities. Signal crayfish were effective predators of NZMS, consuming more than 900 NZMS per predator in a 12-h period, and Bayesian model fitting indicated their consumption rate followed a type 3 functional response to NZMS density. Based on this functional response and associated parameter uncertainty, we predict that NZMS will be able to invade new systems at low crayfish densities (< 0.2 crayfish/m2) regardless of NZMS density. At intermediate to high crayfish densities (> 0.2 crayfish/m2), we predict that low densities of NZMS will be able to establish in new communities; however, once NZMS reach a threshold density of -2000 NZMS/m2, predation by crayfish will drive negative NZMS population growth. Further, at very high densities, NZMS overwhelm predation by crayfish and invade. Thus, interacting thresholds of propagule pressure and predator densities define the probability of biotic resistance. Quantifying the shape and uncertainty of predator functional responses to nonnative prey may help predict the outcomes of invasions.     

Smoothing of land use maps for trend and change detection in urbanization

Urban sprawl and its evolution over relatively short periods of time demands that we develop statistical tools to make best use of the routinely produced land use data from satellites. An efficient smoothing framework to estimate spatial patterns in binary raster maps derived from land use datasets is developed and presented in this paper. The framework is motivated by the need to model urbanization, specifically urban sprawl, and also its temporal evolution. We frame the problem as estimation of a probability of urbanization surface and use Bayesian P-splines as the tool of choice. Once such a probability map is produced, with associated uncertainty, we develop exploratory tools to identify regions of significant change across space and time. The proposal is used to study urbanisation and its development around the city of Bologna, Emilia Romagna, Italy, using land use data from the Cartography Archive of Emilia Romagna Region for the period 1976–2008.     

Choosing ecosystem service investments that are robust to uncertainty across multiple parameters

Info-gap decision theory facilitates decision making for problems in which uncertainty is large and probability distributions of uncertain variables are unknown. The info-gap framework allows the decision maker to maximize robustness to failure in the presence of uncertainty, where uncertainty is in the parameters of the model and failure is defined as the model output falling below some minimally acceptable performance threshold. Info-gap theory has found particular application to problems in conservation biology and ecological economics. In this study, we applied info-gap theory to an ecosystem services tradeoff case study in which a decision maker aiming to maximize ecosystem service investment returns must choose between two alternative land uses: native vegetation conservation or the establishment of an exotic timber plantation. The uncertain variables are the carbon price and the water price. With a "no-information" uncertainty model that assumes equal relative uncertainty across both variables, info-gap theory identifies a minimally acceptable reward threshold above which conservation is preferred, but below which plantation establishment is preferred. However, with an uncertainty model that allows the carbon price to be substantially more uncertain than the water price, conservation of native vegetation becomes an economically more robust investment option than establishing alien pine plantations. We explored the sensitivity of the results to the use of alternative uncertainty models, including asymmetric uncertainty in individual variables. We emphasize the general finding that the results of info-gap analyses can be sensitive to the choice of uncertainty model and that, therefore, future applications to ecological problems should be careful to incorporate all available qualitative and quantitative information relating to uncertainties or should at least justify the no-information uncertainty model.     

Assessing model structure uncertainty through an analysis of system feedback and Bayesian networks.

Ecological predictions and management strategies are sensitive to variability in model parameters as well as uncertainty in model structure. Systematic analysis of the effect of alternative model structures, however, is often beyond the resources typically available to ecologists, ecological risk practitioners, and natural resource managers. Many of these practitioners are also using Bayesian belief networks based on expert opinion to fill gaps in empirical information. The practical application of this approach can be limited by the need to populate large conditional probability tables and the complexity associated with ecological feedback cycles. In this paper, we describe a modeling approach that helps solve these problems by embedding a qualitative analysis of sign directed graphs into the probabilistic framework of a Bayesian belief network. Our approach incorporates the effects of feedback on the model's response to a sustained change in one or more of its parameters, provides an efficient means to explore the effect of alternative model structures, mitigates the cognitive bias in expert opinion, and is amenable to stakeholder input. We demonstrate our approach by examining two published case studies: a host-parasitoid community centered on a nonnative, agricultural pest of citrus cultivars and the response of an experimental lake mesocosm to nutrient input. Observations drawn from these case studies are used to diagnose alternative model structures and to predict the system's response following management intervention.     

Modulation of predator-prey interactions by the Allee effect

An Allee effect arising from density-dependent mating success can have significant impacts at the ecosystem level when considered in the context of predator-prey interactions. These are captured by a mathematical model for the exchange of biomass between a structured predator population (continuous weight distribution) and a resource. Because the predator’s mating success affects the amount of resources required for the production of offsprings and their future growth into mature organisms, it influences the flux of biomass between trophic levels. Under simple assumptions, the equations can be reduced to an equivalent unstructured predator-prey model in which the Allee effect modulates the predation rate: the mating probability multiplies the rate of predator growth as well as the rate of resource depletion. Implications of the Allee effect for the bifurcation structure and equilibrium densities are examined. The model is compared to a modified version in which the Allee effect instead modulates the assimilation efficiency, hence the mating probability does not appear in the dynamical equation for the resource density. Both models exhibit qualitatively similar dynamics. However, compared to the model in which the Allee effect modulates predation, the model in which the Allee effect modulates assimilation efficiency predicts (i) unrealistically inefficient resource assimilation when predator density is low, (ii) a higher risk of catastrophic extinction resulting from a change in the parameter controlling the strength of the Allee effect, and (iii) no possibility of an increase in population size when the density dependence is enhanced.     

Nitrogen inputs promote the spread of an invasive marsh grass.

Excess nutrient loading and large-scale invasion by nonnatives are two of the most pervasive and damaging threats to the biotic and economic integrity of our estuaries. Individually, these are potent forces, but it is important to consider their interactive impacts as well. In this study we investigated the potential limitation of a nonnative intertidal grass, Spartina alterniflora, by nitrogen (N) in estuaries of the western United States. Nitrogen fertilization experiments were conducted in three mud-flat habitats invaded by S. alterniflora in Willapa Bay, Washington, USA, that differed in sediment N. We carried out parallel experiments in San Francisco Bay, California, USA, in three habitats invaded by hybrid Spartina (S. alterniflora x S. foliosa), in previously unvegetated mud flat, and in native S. foliosa or Salicornia virginica marshes. We found similar aboveground biomass and growth rates between habitats and estuaries, but end-of-season belowground biomass was nearly five times greater in San Francisco Bay than in Willapa Bay. In Willapa Bay, aboveground biomass was significantly correlated with sediment N content. Addition of N significantly increased aboveground biomass, stem density, and the rate of spread into uninvaded habitat (as new stems per day) in virtually all habitats in both estuaries. Belowground biomass increased in Willapa Bay only, suggesting that belowground biomass is not N limited in San Francisco Bay due to species differences, N availability, or a latitudinal difference in the response of Spartina to N additions. The relative impact of added N was greater in Willapa Bay, the estuary with lower N inputs from the watershed, than in San Francisco Bay, a highly eutrophic estuary. Nitrogen fertilization also altered the competitive interaction between hybrid Spartina and Salicornia virginica in San Francisco Bay by increasing the density and biomass of the invader and decreasing the density of the native. There was no significant effect of N on the native, Spartina foliosa. Our results indicate that excess N loading to these ecosystems enhances the vulnerability of intertidal habitats to rapid invasion by nonnative Spartina sp.     

The Use of Bayesian Model Averaging to Better Represent Uncertainty in Ecological Models

Abstract:   In conservation biology, uncertainty about the choice of a statistical model is rarely considered. Model-selection uncertainty occurs whenever one model is chosen over plausible alternative models to represent understanding about a process and to make predictions about future observations. The standard approach to representing prediction uncertainty involves the calculation of prediction (or confidence) intervals that incorporate uncertainty about parameter estimates contingent on the choice of a "best" model chosen to represent truth. However, this approach to prediction based on statistical models tends to ignore model-selection uncertainty, resulting in overconfident predictions. Bayesian model averaging (BMA) has been promoted in a range of disciplines as a simple means of incorporating model-selection uncertainty into statistical inference and prediction. Bayesian model averaging also provides a formal framework for incorporating prior knowledge about the process being modeled. We provide an example of the application of BMA in modeling and predicting the spatial distribution of an arboreal marsupial in the Eden region of southeastern Australia. Other approaches to estimating prediction uncertainty are discussed.     

Effects of Harvesting Flowers from Shrubs on the Persistence and Abundance of Wild Shrub Populations at Multiple Spatial Extents

Abstract: Wildflower harvesting is an economically important activity of which the ecological effects are poorly understood. We assessed how harvesting of flowers affects shrub persistence and abundance at multiple spatial extents. To this end, we built a process‐based model to examine the mean persistence and abundance of wild shrubs whose flowers are subject to harvest (serotinous Proteaceae in the South African Cape Floristic Region). First, we conducted a general sensitivity analysis of how harvesting affects persistence and abundance at nested spatial extents. For most spatial extents and combinations of demographic parameters, persistence and abundance of flowering shrubs decreased abruptly once harvesting rate exceeded a certain threshold. At larger extents, metapopulations supported higher harvesting rates before their persistence and abundance decreased, but persistence and abundance also decreased more abruptly due to harvesting than at smaller extents. This threshold rate of harvest varied with species’ dispersal ability, maximum reproductive rate, adult mortality, probability of extirpation or local extinction, strength of Allee effects, and carrying capacity. Moreover, spatial extent interacted with Allee effects and probability of extirpation because both these demographic properties affected the response of local populations to harvesting more strongly than they affected the response of metapopulations. Subsequently, we simulated the effects of harvesting on three Cape Floristic Region Proteaceae species and found that these species reacted differently to harvesting, but their persistence and abundance decreased at low rates of harvest. Our estimates of harvesting rates at maximum sustainable yield differed from those of previous investigations, perhaps because researchers used different estimates of demographic parameters, models of population dynamics, and spatial extent than we did. Good demographic knowledge and careful identification of the spatial extent of interest increases confidence in assessments and monitoring of the effects of harvesting. Our general sensitivity analysis improved understanding of harvesting effects on metapopulation dynamics and allowed qualitative assessment of the probability of extirpation of poorly studied species.     

Model weights and the foundations of multimodel inference

Statistical thinking in wildlife biology and ecology has been profoundly influenced by the introduction of AIC (Akaike's information criterion) as a tool for model selection and as a basis for model averaging. In this paper, we advocate the Bayesian paradigm as a broader framework for multimodel inference, one in which model averaging and model selection are naturally linked, and in which the performance of AIC-based tools is naturally evaluated. Prior model weights implicitly associated with the use of AIC are seen to highly favor complex models: in some cases, all but the most highly parameterized models in the model set are virtually ignored a priori. We suggest the usefulness of the weighted BIC (Bayesian information criterion) as a computationally simple alternative to AIC, based on explicit selection of prior model probabilities rather than acceptance of default priors associated with AIC. We note, however, that both procedures are only approximate to the use of exact Bayes factors. We discuss and illustrate technical difficulties associated with Bayes factors, and suggest approaches to avoiding these difficulties in the context of model selection for a logistic regression. Our example highlights the predisposition of AIC weighting to favor complex models and suggests a need for caution in using the BIC for computing approximate posterior model weights.