Multiple-pattern parameter identification and uncertainty analysis approach for water quality modeling

This paper presents a multiple-pattern parameter identification and uncertainty analysis approach for robust water quality modeling using a neural network (NN) embedded genetic algorithm (GA). The modeling approach uses an adaptive NN–GA framework to inversely solve the governing equations in a water quality model for multiple parameter patterns, along with an alternating fitness method to maintain solution diversity. The procedure was demonstrated through a coupled 2D hydrodynamic and eutrophication model for Loch Raven Reservoir in Maryland. The inverse problem was formulated as a nonlinear optimization problem minimizing the degree of misfit (DOM) between model results and observed data. A set of NN models was developed to approximate the input-output response relationship of the Loch Raven Reservoir model and was incorporated into a GA framework in an adaptive fashion to search for near-optimal solutions minimizing the DOM. The numerical example showed that the adaptive NN–GA approach is capable of identifying multiple parameter patterns that reproduce the observed data equally well. The resulting parameter patterns were incorporated into the numerical model, and a multiple-pattern robust water quality modeling analysis, along with a compound margin of safety (CMOS) method, was proposed and applied to analyze the parameter pattern uncertainty.     

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.     

Hierarchical spatial modeling for estimation of population size

Estimation of population size has traditionally been viewed from a finite population sampling perspective. Typically, the objective is to obtain an estimate of the total population count of individuals within some region. Often, some stratification scheme is used to estimate counts on subregions, whereby the total count is obtained by aggregation with weights, say, proportional to the areas of the subregions. We offer an alternative to the finite population sampling approach for estimating population size. The method does not require that the subregions on which counts are available form a complete partition of the region of interest. In fact, we envision counts coming from areal units that are small relative to the entire study region and that the total area sampled is a very small proportion of the total study area. In extrapolating to the entire region, we might benefit from assuming that there is spatial structure to the counts. We implement this by modeling the intensity surface as a realization from a spatially correlated random process. In the case of multiple population or species counts, we use the linear model of coregionalization to specify a multivariate process which provides associated intensity surfaces hence association between counts within and across areal units. We illustrate the method of population size estimation with simulated data and with tree counts from a Southwestern pinyon-juniper woodland data set.     

Including model uncertainty in estimating variances in multiple capture studies

We present bootstrap-based methods which incorporate model uncertainty in estimating variances in multiple capture studies. Each of our three methods has a specific set of properties, and we discuss when each method should be used. Our first method can be used in any multiple capture setting, but it gives an estimate of the variance conditional on the number of observed animals. Our other two methods yield estimates of the unconditional variance; they require good estimates of part or all of the specific probability model, respectively. Smoothed estimated cell probabilities are utilized by the latter method. We contrast the three methods on a real-life data set, and then conduct simulations for a simple setting. Finally, we detail the use of our methodology for specific settings and discuss adaptations for tag-return studies.     

An approach to uncertainty estimation in determining polycyclic aromatic hydrocarbons in fuel-contaminated soils

An estimation of uncertainty contribution in the entire set of the analytical data of polycyclic aromatic hydrocarbons (PAHs) in soil during a full year is presented. The analyses were performed as part of a project devoted to the assessment of the natural attenuation of selected PAHs in agricultural soil contaminated by a fuel spill. In particular, we investigated the effect of natural attenuation on the PAH dissipation rate in plots of two types of scenarios in agricultural soils. One of them was previously affected by an accidental fuel spill 10 years ago, and the other one was non-affected. The major components for estimating uncertainty contributions have been evaluated based on intermediate precision from different levels of PAH mass fraction, sample locations, and long term data set. An analysis of variance (ANOVA) test was applied to the mass fractions of clean or blank soil sub-samples versus contaminated soil sub-samples for grouping comparable data. Variables of influence in this study were site, month, and lysimeter of sampling (referring to a stainless steel box, with side lengths of 50 cm). Study sites or the spatial arrangement of lysimeter showed a clear effect in sub-sample results with the lowest mass fraction levels for heavier PAH, while monthly sampling was the variable of most significant influence for the more strongly contaminated sub-sample results.

Finally, the results of the PAH mass fractions in contaminated soil sub-samples indicated a monthly variation for which lighter, volatile PAHs rapidly decreased while the less volatile did not change.     

Can modeling improve estimation of desert tortoise population densities?

The federally listed desert tortoise (Gopherus agassizii) is currently monitored using distance sampling to estimate population densities. Distance sampling, as with many other techniques for estimating population density, assumes that it is possible to quantify the proportion of animals available to be counted in any census. Because desert tortoises spend much of their life in burrows, and the proportion of tortoises in burrows at any time can be extremely variable, this assumption is difficult to meet. This proportion of animals available to be counted is used as a correction factor (g0) in distance sampling and has been estimated from daily censuses of small populations of tortoises (6-12 individuals). These censuses are costly and produce imprecise estimates of go due to small sample sizes. We used data on tortoise activity from a large (N = 150) experimental population to model activity as a function of the biophysical attributes of the environment, but these models did not improve the precision of estimates from the focal populations. Thus, to evaluate how much of the variance in tortoise activity is apparently not predictable, we assessed whether activity on any particular day can predict activity on subsequent days with essentially identical environmental conditions. Tortoise activity was only weakly correlated on consecutive days, indicating that behavior was not repeatable or consistent among days with similar physical environments.     

Risk aversion and CO2 regulatory uncertainty in power generation investment: Policy and modeling implications

We consider a simulation of risk-averse producers when making investment decisions in a competitive energy market, who face uncertainty about future regulation of carbon dioxide emissions. Investments are made under regulatory uncertainty; then the regulatory state is revealed and producers realize returns. We consider anticipated taxes, grandfathered permits and auctioned permits and show that some anticipated policies increase investment in the relatively dirty technology. Beliefs about the policy instrument that will be used to price carbon may be as important as certainty that carbon will be priced. More generally, a failure to consider risk aversion may bias policy analysis for the power sector.     

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.     

Making conservation decisions under uncertainty for the persistence of multiple species.

Population models for multiple species provide one of the few means of assessing the impact of alternative management options on the persistence of biodiversity, but they are inevitably uncertain. Is it possible to use population models in multiple-species conservation planning given the associated uncertainties? We use information-gap decision theory to explore the impact of parameter uncertainty on the conservation decision when planning for the persistence of multiple species. An information-gap approach seeks robust outcomes that are most immune from error. We assess the impact of uncertainty in key model parameters for three species, whose extinction risks under four alternative management scenarios are estimated using a metapopulation model. Three methods are described for making conservation decisions across the species, taking into account uncertainty. We find that decisions based on single species are relatively robust to uncertainty in parameters, although the estimates of extinction risk increase rapidly with uncertainty. When identifying the best conservation decision for the persistence of all species, the methods that rely on the rankings of the management options by each species result in decisions that are similarly robust to uncertainty. Methods that depend on absolute values of extinction risk are sensitive to uncertainty, as small changes in extinction risk can alter the ranking of the alternative scenarios. We discover that it is possible to make robust conservation decisions even when the uncertainties of the multiple-species problem appear overwhelming. However, the decision most robust to uncertainty is likely to differ from the best decision when uncertainty is ignored, illustrating the importance of incorporating uncertainty into the decision-making process.     

Static modeling of dynamic recreation behavior: Implications for prediction and welfare estimation

This paper examines the consequences of using a static model of recreation trip-taking behavior when the underlying decision problem is dynamic. Specifically we examine the implications for trip forecasting and welfare estimation using a panel dataset of Lake Michigan salmon anglers for the 1996 and 1997 fishing seasons. We derive and estimate both a structural dynamic model using Bellman's equation, and a reduced-form static model with trip probability expressions mimicking those of the dynamic model. We illustrate an inherent identification problem in the reduced-form model that creates biased welfare estimates, and we discuss the general implications of this for the interpretation of preference parameters in static models. We then use both models to simulate trip taking behavior and show that although their in-sample trip forecasts are similar, their welfare estimates and out-of-sample forecasts are quite different.     

Static modeling of dynamic recreation behavior: Implications for prediction and welfare estimation

This paper examines the consequences of using a static model of recreation trip-taking behavior when the underlying decision problem is dynamic. Specifically we examine the implications for trip forecasting and welfare estimation using a panel dataset of Lake Michigan salmon anglers for the 1996 and 1997 fishing seasons. We derive and estimate both a structural dynamic model using Bellman's equation, and a reduced-form static model with trip probability expressions mimicking those of the dynamic model. We illustrate an inherent identification problem in the reduced-form model that creates biased welfare estimates, and we discuss the general implications of this for the interpretation of preference parameters in static models. We then use both models to simulate trip taking behavior and show that although their in-sample trip forecasts are similar, their welfare estimates and out-of-sample forecasts are quite different.     

Perturbations alter community convergence, divergence, and formation of multiple community states

Environmental perturbations (e.g., disturbance, fertilization) commonly shift communities to a new mean state, but much less is known about their effects on the variability (dispersion) of communities around the mean, particularly when perturbations are combined. Community dispersion may increase or decrease (representing a divergence or convergence among communities) if changing environmental conditions alter species interactions or magnify small initial differences that develop during community assembly. We used data from an experimental study of disturbance and fertilization in a low-productivity grassland to test how these two perturbations affect patterns of species composition and abundance. We found that a one-time biomass reduction decreased community dispersion, which persisted over four growing seasons. Conversely, continuous fertilization increased community dispersion and, when combined with disturbance, led to the formation of three distinct community states. These results illustrate that perturbations can have differing effects on community dispersion. Attention to the variance in community responses to perturbations lends insight into how ecological interactions determine community structure, which may be missed when focusing only on mean responses. Furthermore, multiple perturbations may have complex effects on community dispersion, yielding convergence or divergence patterns that are difficult to predict based on analysis of single factors.     

Reserve and land prices with exploration under uncertainty

Arrow and Chang (J. Econom. Environ. Manag.9, 1–10 (1982) analyze an exploration-extraction model with uncertainty about the distribution of deposits. Reserve prices do not exhibit any rising trend when the unexplored land area is big but, in order to know what happens when the unexplored area is smaller, “a probabilistic analysis not yet performed” (ibid. p. 10) is required. Their conjecture of a rising trend at less than the discount rate is confirmed. However, land prices can be expected to grow faster than reserve prices, which helps discriminate between Arrow and Chang's, and other rationalizations of the failure of resource prices to rise at the discount rate.     

On the latent state estimation of nonlinear population dynamics using Bayesian and non-Bayesian state-space models

Nonlinear state-space models have been increasingly applied to study population dynamics and data assimilation in environmental sciences. State-space models can account for process error and measurement error simultaneously to correct for the bias in the estimates of system state and model parameters. However, few studies have compared the performance of different nonlinear state-space models for reconstructing the state of population dynamics from noisy time series. This study compared the performance of the extended Kalman filter (EKF), unscented Kalman filter (UKF) and Bayesian nonlinear state-space models (BNSSM) through simulations. Synthetic population time series were generated using the theta logistic model with known parameters, and normally distributed process and measurement errors were introduced using the Monte Carlo simulations. At higher levels of nonlinearity, the UKF and BNSSM had lower root mean square error (RMSE) than the EKF. The BNSSM performed reliably across all levels of nonlinearity, whereas increased levels of nonlinearity resulted in higher RMSE of the EKF. The Metropolis–Hastings algorithm within the Gibbs algorithm was used to fit the theta logistic model to synthetic time series to estimate model parameters. The estimated posterior distribution of the parameter θ indicated that the 95% credible intervals included the true values of θ (=0.5 and 1.5), but did not include 1.0 and 0.0. Future studies need to incorporate the adaptive Metropolis algorithm to estimate unknown model parameters for broad applications of Bayesian nonlinear state-space models in ecological studies.     

Rapid Increases and Time‐Lagged Declines in Amphibian Occupancy after Wildfire

Climate change is expected to increase the frequency and severity of drought and wildfire. Aquatic and moisture‐sensitive species, such as amphibians, may be particularly vulnerable to these modified disturbance regimes because large wildfires often occur during extended droughts and thus may compound environmental threats. However, understanding of the effects of wildfires on amphibians in forests with long fire‐return intervals is limited. Numerous stand‐replacing wildfires have occurred since 1988 in Glacier National Park (Montana, U.S.A.), where we have conducted long‐term monitoring of amphibians. We measured responses of 3 amphibian species to fires of different sizes, severity, and age in a small geographic area with uniform management. We used data from wetlands associated with 6 wildfires that burned between 1988 and 2003 to evaluate whether burn extent and severity and interactions between wildfire and wetland isolation affected the distribution of breeding populations. We measured responses with models that accounted for imperfect detection to estimate occupancy during prefire (0–4 years) and different postfire recovery periods. For the long‐toed salamander (Ambystoma macrodactylum) and Columbia spotted frog (Rana luteiventris), occupancy was not affected for 6 years after wildfire. But 7–21 years after wildfire, occupancy for both species decreased ≥25% in areas where >50% of the forest within 500 m of wetlands burned. In contrast, occupancy of the boreal toad (Anaxyrus boreas) tripled in the 3 years after low‐elevation forests burned. This increase in occupancy was followed by a gradual decline. Our results show that accounting for magnitude of change and time lags is critical to understanding population dynamics of amphibians after large disturbances. Our results also inform understanding of the potential threat of increases in wildfire frequency or severity to amphibians in the region. Incrementos Rápidos y Declinaciones Desfasadas en la Ocupación de Anfibios Después de un Incendio     

Price uncertainty and the exhaustive firm

In the presence of a resource constraint the risk-averse exhaustive firm reacts to price uncertainty in a manner different than its competitive counterpart. In particular: (i) some results are independent of attitudes toward risk; (ii) comparative statics results differ from the no resource constraint case; and (iii) results depend upon the relative magnitudes of the discount rate and quasi-fixed costs. An assumption crucial to the relevance of risk-aversion in an intertemporal setting is the presence of imperfections in capital markets (i.e., the absence of complete contingent commodity markets).     

Relation between Occupancy and Abundance for a Territorial Species,the California Spotted Owl

Land and resource managers often use detection–nondetection surveys to monitor the populations of species that may be affected by factors such as habitat alteration, climate change, and biological invasions. Relative to mark‐recapture studies, using detection–nondetection surveys is more cost‐effective, and recent advances in statistical analyses allow the incorporation of detection probability, covariates, and multiple seasons. We examined the efficacy of using detection–nondetection data (relative to mark‐recapture data) for monitoring population trends of a territorial species, the California Spotted Owl (Strix occidentalis occidentalis). We estimated and compared the finite annual rates of population change (λ_t) and the resulting realized population change (Δ_t) from both occupancy and mark‐recapture data collected over 18 years (1993–2010). We used multiseason, robust‐design occupancy models to estimate that territory occupancy declined during our study (Δ_t = 0.702, 95% CI 0.552–0.852) due to increasing territory extinction rates ( = 0.019 [SE 0.012]; = 0.134 [SE 0.043]) and decreasing colonization rates ( = 0.323 [SE 0.124]; = 0.242 [SE 0.058]). We used Pradel's temporal‐symmetry model for mark‐recapture data to estimate that the population trajectory closely matched the trends in territory occupancy (Δ_t = 0.725, 95% CI 0.445–1.004). Individual survival was constant during our study ( = 0.816 [SE 0.020]; = 0.815 [SE 0.019]), whereas recruitment declined slightly ( = 0.195 [SE 0.032]; = 0.160 [SE 0.023]). Thus, we concluded that detection–nondetection data can provide reliable inferences on population trends, especially when funds preclude more intensive mark‐recapture studies. Relación entre Ocupación y Abundancia en una Especie Territorial, el Búho Moteado de California     

Use of Multispecies Occupancy Models to Evaluate the Response of Bird Communities to Forest Degradation Associated with Logging

Forest degradation is arguably the greatest threat to biodiversity, ecosystem services, and rural livelihoods. Therefore, increasing understanding of how organisms respond to degradation is essential for management and conservation planning. We were motivated by the need for rapid and practical analytical tools to assess the influence of management and degradation on biodiversity and system state in areas subject to rapid environmental change. We compared bird community composition and size in managed (ejido, i.e., communally owned lands) and unmanaged (national park) forests in the Sierra Tarahumara region, Mexico, using multispecies occupancy models and data from a 2‐year breeding bird survey. Unmanaged sites had on average higher species occupancy and richness than managed sites. Most species were present in low numbers as indicated by lower values of detection and occupancy associated with logging‐induced degradation. Less than 10% of species had occupancy probabilities >0.5, and degradation had no positive effects on occupancy. The estimated metacommunity size of 125 exceeded previous estimates for the region, and sites with mature trees and uneven‐aged forest stand characteristics contained the highest species richness. Higher estimation uncertainty and decreases in richness and occupancy for all species, including habitat generalists, were associated with degraded young, even‐aged stands. Our findings show that multispecies occupancy methods provide tractable measures of biodiversity and system state and valuable decision support for landholders and managers. These techniques can be used to rapidly address gaps in biodiversity information, threats to biodiversity, and vulnerabilities of species of interest on a landscape level, even in degraded or fast‐changing environments. Moreover, such tools may be particularly relevant in the assessment of species richness and distribution in a wide array of habitats. Uso de Modelos de Ocupación para Múltiples Especies para Evaluar la Respuesta de las Comunidades de Aves a la Degradación de Bosques Asociada con la Tala     

A general model for tagging on multiple component fisheries: an integration of age-dependent reporting rates and mortality estimation

A major objective of analyzing multiple year tag return data in fisheries is to estimate fishing and natural mortality rates which may vary by age class and calendar year. To do this one needs to be able to estimate the reporting rates for the tags recovered. Some fisheries such as that for Southern Bluefin Tuna (Thunnus maccoyii) have multiple components with potentially different reporting rates for the tag returns. In this paper we develop a general model for multi-cohort, multi-year tag return analyses where there are multiple components to the fishery with potentially different reporting rates. We require the assumption that one component has a reporting rate of 100% (i.e., this could be the component of a boat based fishery where scientific observers are present). We show further how it is possible to partition the overall likelihood developed into two conditionally independent components. The first component of the likelihood is the standard multinomial likelihood that allows estimation of fishing and natural mortality rates. It uses the tag return matrix summed over all the components of the fishery. It requires an average reporting rate for the tag returns (where the average reporting rate is a weighted average of the individual reporting rates of the different components). The second component is also multinomial for the individual component tag returns and allows us to estimate individual component reporting rates. However, this requires that we augment our second component tag return likelihood with a catch data likelihood for the corresponding components. The methodology is illustrated on some Southern Bluefin Tuna tagging and catch data. We also discuss important model assumptions and give suggestions for future research including the integration of tag-return and catch at age data analyses.