A proposed framework for the development and qualitative evaluation of West Nile virus models and their application to local public health decision-making.

West Nile virus (WNV) is a globally distributed mosquito-borne virus of great public health concern. The number of WNV human cases and mosquito infection patterns vary in space and time. Many statistical models have been developed to understand and predict WNV geographic and temporal dynamics. However, these modeling efforts have been disjointed with little model comparison and inconsistent validation. In this paper, we describe a framework to unify and standardize WNV modeling efforts nationwide. WNV risk, detection, or warning models for this review were solicited from active research groups working in different regions of the United States. A total of 13 models were selected and described. The spatial and temporal scales of each model were compared to guide the timing and the locations for mosquito and virus surveillance, to support mosquito vector control decisions, and to assist in conducting public health outreach campaigns at multiple scales of decision-making. Our overarching goal is to bridge the existing gap between model development, which is usually conducted as an academic exercise, and practical model applications, which occur at state, tribal, local, or territorial public health and mosquito control agency levels. The proposed model assessment and comparison framework helps clarify the value of individual models for decision-making and identifies the appropriate temporal and spatial scope of each model. This qualitative evaluation clearly identifies gaps in linking models to applied decisions and sets the stage for a quantitative comparison of models. Specifically, whereas many coarse-grained models (county resolution or greater) have been developed, the greatest need is for fine-grained, short-term planning models (m-km, days-weeks) that remain scarce. We further recommend quantifying the value of information for each decision to identify decisions that would benefit most from model input.

Using Climate to Explain and Predict West Nile Virus Risk in Nebraska.

We used monthly precipitation and temperature data to give early warning of years with higher West Nile Virus (WNV) risk in Nebraska. We used generalized additive models with a negative binomial distribution and smoothing curves to identify combinations of extremes and timing that had the most influence, experimenting with all combinations of temperature and drought data, lagged by 12, 18, 24, 30, and 36 months. We fit models on data from 2002 through 2011, used Akaike's Information Criterion (AIC) to select the best-fitting model, and used 2012 as out-of-sample data for prediction, and repeated this process for each successive year, ending with fitting models on 2002-2017 data and using 2018 for out-of-sample prediction. We found that warm temperatures and a dry year preceded by a wet year were the strongest predictors of cases of WNV. Our models did significantly better than random chance and better than an annual persistence naïve model at predicting which counties would have cases. Exploring different scenarios, the model predicted that without drought, there would have been 26% fewer cases of WNV in Nebraska through 2018; without warm temperatures, 29% fewer; and with neither drought nor warmth, 45% fewer. This method for assessing the influence of different combinations of extremes at different time intervals is likely applicable to diseases other than West Nile, and to other annual outcome variables such as crop yield.

Time-lagged effects of weather on plant demography: drought and Astragalus scaphoides.

Temperature and precipitation determine the conditions where plant species can occur. Despite their significance, to date, surprisingly few demographic field studies have considered the effects of abiotic drivers. This is problematic because anticipating the effect of global climate change on plant population viability requires understanding how weather variables affect population dynamics. One possible reason for omitting the effect of weather variables in demographic studies is the difficulty in detecting tight associations between vital rates and environmental drivers. In this paper, we applied Functional Linear Models (FLMs) to long-term demographic data of the perennial wildflower, Astragalus scaphoides, and explored sensitivity of the results to reduced amounts of data. We compared models of the effect of average temperature, total precipitation, or an integrated measure of drought intensity (standardized precipitation evapotranspiration index, SPEI), on plant vital rates. We found that transitions to flowering and recruitment in year t were highest if winter/spring of year t was wet (positive effect of SPEI). Counterintuitively, if the preceding spring of year t - 1 was wet, flowering probabilities were decreased (negative effect of SPEI). Survival of vegetative plants from t - 1 to t was also negatively affected by wet weather in the spring of year t - 1 and, for large plants, even wet weather in the spring of t - 2 had a negative effect. We assessed the integrated effect of all vital rates on life history performance by fitting FLMs to the asymptotic growth rate, log(λt). Log(λt) was highest if dry conditions in year t - 1 were followed by wet conditions in the year t. Overall, the positive effects of wet years exceeded their negative effects, suggesting that increasing frequency of drought conditions would reduce population viability of A. scaphoides. The drought signal weakened when reducing the number of monitoring years. Substituting space for time did not recover the weather signal, probably because the weather variables varied little between sites. We detected the SPEI signal when the analysis included data from two sites monitored over 20 yr (2 × 20 observations), but not when analyzing data from four sites monitored over 10 yr (4 × 10 observations).

Pollen-mediated gene flow from glyphosate-resistant common waterhemp (Amaranthus rudis Sauer): consequences for the dispersal of resistance genes.

Gene flow is an important component in evolutionary biology; however, the role of gene flow in dispersal of herbicide-resistant alleles among weed populations is poorly understood. Field experiments were conducted at the University of Nebraska-Lincoln to quantify pollen-mediated gene flow (PMGF) from glyphosate-resistant (GR) to -susceptible (GS) common waterhemp using a concentric donor-receptor design. More than 130,000 common waterhemp plants were screened and 26,199 plants were confirmed resistant to glyphosate. Frequency of gene flow from all distances, directions, and years was estimated with a double exponential decay model using Generalized Nonlinear Model (package gnm) in R. PMGF declined by 50% at <3 m distance from the pollen source, whereas 90% reduction was found at 88 m (maximum) depending on the direction of the pollen-receptor blocks. Amplification of the target site gene, 5-enolpyruvylshikimate-3-phosphate synthase (EPSPS), was identified as the mechanism of glyphosate resistance in parent biotype. The EPSPS gene amplification was heritable in common waterhemp and can be transferred via PMGF, and also correlated with glyphosate resistance in pseudo-F2 progeny. This is the first report of PMGF in GR common waterhemp and the results are critical in explaining the rapid dispersal of GR common waterhemp in Midwestern United States.

Use of opportunistic sightings and expert knowledge to predict and compare Whooping Crane stopover habitat.

Predicting a species' distribution can be helpful for evaluating management actions such as critical habitat designations under the U.S. Endangered Species Act or habitat acquisition and rehabilitation. Whooping Cranes (Grus americana) are one of the rarest birds in the world, and conservation and management of habitat is required to ensure their survival. We developed a species distribution model (SDM) that could be used to inform habitat management actions for Whooping Cranes within the state of Nebraska (U.S.A.). We collated 407 opportunistic Whooping Crane group records reported from 1988 to 2012. Most records of Whooping Cranes were contributed by the public; therefore, developing an SDM that accounted for sampling bias was essential because observations at some migration stopover locations may be under represented. An auxiliary data set, required to explore the influence of sampling bias, was derived with expert elicitation. Using our SDM, we compared an intensively managed area in the Central Platte River Valley with the Niobrara National Scenic River in northern Nebraska. Our results suggest, during the peak of migration, Whooping Crane abundance was 262.2 (90% CI 40.2-3144.2) times higher per unit area in the Central Platte River Valley relative to the Niobrara National Scenic River. Although we compared only 2 areas, our model could be used to evaluate any region within the state of Nebraska. Furthermore, our expert-informed modeling approach could be applied to opportunistic presence-only data when sampling bias is a concern and expert knowledge is available.

Nondetection sampling bias in marked presence-only data.

Species distribution models (SDM) are tools used to determine environmental features that influence the geographic distribution of species' abundance and have been used to analyze presence-only records. Analysis of presence-only records may require correction for nondetection sampling bias to yield reliable conclusions. In addition, individuals of some species of animals may be highly aggregated and standard SDMs ignore environmental features that may influence aggregation behavior.We contend that nondetection sampling bias can be treated as missing data. Statistical theory and corrective methods are well developed for missing data, but have been ignored in the literature on SDMs. We developed a marked inhomogeneous Poisson point process model that accounted for nondetection and aggregation behavior in animals and tested our methods on simulated data.Correcting for nondetection sampling bias requires estimates of the probability of detection which must be obtained from auxiliary data, as presence-only data do not contain information about the detection mechanism. Weighted likelihood methods can be used to correct for nondetection if estimates of the probability of detection are available. We used an inhomogeneous Poisson point process model to model group abundance, a zero-truncated generalized linear model to model group size, and combined these two models to describe the distribution of abundance. Our methods performed well on simulated data when nondetection was accounted for and poorly when detection was ignored.We recommend researchers consider the effects of nondetection sampling bias when modeling species distributions using presence-only data. If information about the detection process is available, we recommend researchers explore the effects of nondetection and, when warranted, correct the bias using our methods. We developed our methods to analyze opportunistic presence-only records of whooping cranes (Grus americana), but expect that our methods will be useful to ecologists analyzing opportunistic presence-only records of other species of animals.

Integrating info-gap decision theory with robust population management: a case study using the Mountain Plover.

Wildlife managers often make decisions under considerable uncertainty. In the most extreme case, a complete lack of data leads to uncertainty that is unquantifiable. Information-gap decision theory deals with assessing management decisions under extreme uncertainty, but it is not widely used in wildlife management. So too, robust population management methods were developed to deal with uncertainties in multiple-model parameters. However, the two methods have not, as yet, been used in tandem to assess population management decisions. We provide a novel combination of the robust population management approach for matrix models with the information-gap decision theory framework for making conservation decisions under extreme uncertainty. We applied our model to the problem of nest survival management in an endangered bird species, the Mountain Plover (Charadrius montanus). Our results showed that matrix sensitivities suggest that nest management is unlikely to have a strong effect on population growth rate, confirming previous analyses. However, given the amount of uncertainty about adult and juvenile survival, our analysis suggested that maximizing nest marking effort was a more robust decision to maintain a stable population. Focusing on the twin concepts of opportunity and robustness in an information-gap model provides a useful method of assessing conservation decisions under extreme uncertainty.

Confronting socially generated uncertainty in adaptive management.

As more and more organizations with responsibility for natural resource management adopt adaptive management as the rubric in which they wish to operate, it becomes increasingly important to consider the sources of uncertainty inherent in their endeavors. Without recognizing that uncertainty originates both in the natural world and in human undertakings, efforts to manage adaptively at the least will prove frustrating and at the worst will prove damaging to the very natural resources that are the management targets. There will be more surprises and those surprises potentially may prove at the very least unwanted and at the worst devastating. We illustrate how acknowledging uncertainty associated with the natural world is necessary but not sufficient to avoid surprise using case studies of efforts to manage three wildlife species; Hector's Dolphins, American Alligators and Pallid Sturgeon. Three characteristics of indeterminism are salient to all of them; non-stationarity, irreducibility and an inability to define objective probabilities. As an antidote, we recommend employing a holistic treatment of indeterminism, that includes recognizing that uncertainty originates in ecological systems and in how people perceive, interact and decide about the natural world of which they are integral players.

Evaluating the efficacy of adaptive management approaches: is there a formula for success?

Within the field of natural-resources management, the application of adaptive management is appropriate for complex problems high in uncertainty. Adaptive management is becoming an increasingly popular management-decision tool within the scientific community and has developed into two primary schools of thought: the Resilience-Experimentalist School (with high emphasis on stakeholder involvement, resilience, and highly complex models) and the Decision-Theoretic School (which results in relatively simple models through emphasizing stakeholder involvement for identifying management objectives). Because of these differences, adaptive management plans implemented under each of these schools may yield varying levels of success. We evaluated peer-reviewed literature focused on incorporation of adaptive management to identify components of successful adaptive management plans. Our evaluation included adaptive management elements such as stakeholder involvement, definitions of management objectives and actions, use and complexity of predictive models, and the sequence in which these elements were applied. We also defined a scale of degrees of success to make comparisons between the two adaptive management schools of thought. Our results include the relationship between the adaptive management process documented in the reviewed literature and our defined continuum of successful outcomes. Our data suggest an increase in the number of published articles with substantive discussion of adaptive management from 2000 to 2009 at a mean rate of annual change of 0.92 (r² = 0.56). Additionally, our examination of data for temporal patterns related to each school resulted in an increase in acknowledgement of the Decision-Theoretic School of thought at a mean annual rate of change of 0.02 (r² = 0.6679) and a stable acknowledgement for the Resilience-Experimentalist School of thought (r² = 0.0042; slope = 0.0013). Identifying the elements of successful adaptive management will be advantageous to natural-resources managers considering adaptive management as a decision tool.

Resource selection by elk in an agro-forested landscape of northwestern Nebraska.

In recent years, elk have begun recolonizing areas east of the Rocky Mountains that are largely agro-forested ecosystems composed of privately owned land where management of elk is an increasing concern due to crop and forage depredation and interspecific disease transmission. We used a Geographic Information System, elk use locations (n = 5013), random locations (n = 25,065), discrete-choice models, and information-theoretic methods to test hypotheses about elk resource selection in an agro-forested landscape located in the Pine Ridge region of northwestern Nebraska, USA. Our objectives were to determine landscape characteristics selected by female elk and identify publicly owned land within the Pine Ridge for potential redistribution of elk. We found distance to edge of cover influenced selection of resources by female elk most and that in areas with light hunting pressure, such as ours, this selection was not driven by an avoidance of roads. Female elk selected resources positioned near ponderosa pine cover types during all seasons, exhibited a slight avoidance of roads during spring and fall, selected areas with increased slope during winter and spring, and selected north- and east-facing aspects over flat areas and areas with south-facing slopes during winter months. We used our models to identified a potential elk redistribution area that had a higher proportion of landcover with characteristics selected by elk in our study area than the current herd areas and more landcover that was publicly owned. With appropriate management plans, we believe elk within the Potential Elk Redistribution Area would predominantly occupy publicly owned land, which would help minimize crop and forage damage on privately owned lands.

Model complexity affects transient population dynamics following a dispersal event: a case study with pea aphids.

Stage-structured population models predict transient population dynamics if the population deviates from the stable stage distribution. Ecologists' interest in transient dynamics is growing because populations regularly deviate from the stable stage distribution, which can lead to transient dynamics that differ significantly from the stable stage dynamics. Because the structure of a population matrix (i.e., the number of life-history stages) can influence the predicted scale of the deviation, we explored the effect of matrix size on predicted transient dynamics and the resulting amplification of population size. First, we experimentally measured the transition rates between the different life-history stages and the adult fecundity and survival of the aphid, Acythosiphon pisum. Second, we used these data to parameterize models with different numbers of stages. Third, we compared model predictions with empirically measured transient population growth following the introduction of a single adult aphid. We find that the models with the largest number of life-history stages predicted the largest transient population growth rates, but in all models there was a considerable discrepancy between predicted and empirically measured transient peaks and a dramatic underestimation of final population sizes. For instance, the mean population size after 20 days was 2394 aphids compared to the highest predicted population size of 531 aphids; the predicted asymptotic growth rate (lamdamax) was consistent with the experiments. Possible explanations for this discrepancy are discussed.

Plant reproductive allocation predicts herbivore dynamics across spatial and temporal scales.

Life-history theory suggests that iteroparous plants should be flexible in their allocation of resources toward growth and reproduction. Such plasticity could have consequences for herbivores that prefer or specialize on vegetative versus reproductive structures. To test this prediction, we studied the response of the cactus bug (Narnia pallidicornis) to meristem allocation by tree cholla cactus (Opuntia imbricata). We evaluated the explanatory power of demographic models that incorporated variation in cactus relative reproductive effort (RRE; the proportion of meristems allocated toward reproduction). Field data provided strong support for a single model that defined herbivore fecundity as a time-varying, increasing function of host RRE. High-RRE plants were predicted to support larger insect populations, and this effect was strongest late in the season. Independent field data provided strong support for these qualitative predictions and suggested that plant allocation effects extend across temporal and spatial scales. Specifically, late-season insect abundance was positively associated with interannual changes in cactus RRE over 3 years. Spatial variation in insect abundance was correlated with variation in RRE among five cactus populations across New Mexico. We conclude that plant allocation can be a critical component of resource quality for insect herbivores and, thus, an important mechanism underlying variation in herbivore abundance across time and space.

Zero tolerance ecology: improving ecological inference by modelling the source of zero observations.

A common feature of ecological data sets is their tendency to contain many zero values. Statistical inference based on such data are likely to be inefficient or wrong unless careful thought is given to how these zeros arose and how best to model them. In this paper, we propose a framework for understanding how zero-inflated data sets originate and deciding how best to model them. We define and classify the different kinds of zeros that occur in ecological data and describe how they arise: either from 'true zero' or 'false zero' observations. After reviewing recent developments in modelling zero-inflated data sets, we use practical examples to demonstrate how failing to account for the source of zero inflation can reduce our ability to detect relationships in ecological data and at worst lead to incorrect inference. The adoption of methods that explicitly model the sources of zero observations will sharpen insights and improve the robustness of ecological analyses.