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USGS2014

Accounting for imperfect detection in Hill numbers for biodiversity studies

Hill numbers unify biodiversity metrics by combining several into one expression. For example, species richness, Shannon's diversity index and the Gini–Simpson index are a few of the most used diversity measures, and they can be expressed as Hill numbers. Traditionally, Hill numbers have been calculated from relative abundance data, but the expression has been modified to use incidence data as well. We demonstrate an approach for estimating Hill numbers using an occupancy modelling framework that accounts for imperfect detection. We alter the Hill numbers formula to use occupancy probabilities as opposed to the incidence probabilities that have been used previously and to calculate its summations from the modelled species richness. After introducing the occupancy-based Hill numbers, we demonstrate the differences between them and the incidence-based Hill numbers previously used through a simulation study and two applications. In the simulation study and the two examples using real data, the occupancy-based Hill numbers were larger than the incidence-based Hill numbers, although species richness was estimated similarly using both methods. The occupancy-based Hill number estimators are always at their asymptotic values (i.e. as if an infinite number of samples have been taken for the study region), therefore making it easy to compare biodiversity between different assemblages. In addition, the Hill numbers are computed as derived quantities within a Bayesian hierarchical model, allowing for straightforward inference.

Methods in Ecology and Evolution↗

USGS2014

Modelling non-Euclidean movement and landscape connectivity in highly structured ecological networks

Movement is influenced by landscape structure, configuration and geometry, but measuring distance as perceived by animals poses technical and logistical challenges. Instead, movement is typically measured using Euclidean distance, irrespective of location or landscape structure, or is based on arbitrary cost surfaces. A recently proposed extension of spatial capture-recapture (SCR) models resolves this issue using spatial encounter histories of individuals to calculate least-cost paths (ecological distance: Ecology , 94 , 2013, 287) thereby relaxing the Euclidean assumption. We evaluate the consequences of not accounting for movement heterogeneity when estimating abundance in highly structured landscapes, and demonstrate the value of this approach for estimating biologically realistic space-use patterns and landscape connectivity. We simulated SCR data in a riparian habitat network, using the ecological distance model under a range of scenarios where space-use in and around the landscape was increasingly associated with water (i.e. increasingly less Euclidean). To assess the influence of miscalculating distance on estimates of population size, we compared the results from the ecological and Euclidean distance based models. We then demonstrate that the ecological distance model can be used to estimate home range geometry when space use is not symmetrical. Finally, we provide a method for calculating landscape connectivity based on modelled species-landscape interactions generated from capture-recapture data. Using ecological distance always produced unbiased estimates of abundance. Explicitly modelling the strength of the species-landscape interaction provided a direct measure of landscape connectivity and better characterised true home range geometry. Abundance under the Euclidean distance model was increasingly (negatively) biased as space use was more strongly associated with water and, because home ranges are assumed to be symmetrical, produced poor characterisations of home range geometry and no information about landscape connectivity. The ecological distance SCR model uses spatially indexed capture-recapture data to estimate how activity patterns are influenced by landscape structure. As well as reducing bias in estimates of abundance, this approach provides biologically realistic representations of home range geometry, and direct information about species-landscape interactions. The incorporation of both structural (landscape) and functional (movement) components of connectivity provides a direct measure of species-specific landscape connectivity.

Methods in Ecology and Evolution↗

USGS2015

On the existence of maximum likelihood estimates for presence-only data

Presence-only data can be used to determine resource selection and estimate a species’ distribution. Maximum likelihood is a common parameter estimation method used for species distribution models. Maximum likelihood estimates, however, do not always exist for a commonly used species distribution model – the Poisson point process. We demonstrate the issue with conventional maximum likelihood mathematically, using a data example, and a simulation experiment and show alternative estimation methods. We found that when habitat preferences are strong or the number of presence-only locations is small, by chance, maximum likelihood coefficient estimates for the Poisson point process model may not exist. We found that several alternative estimation methods can produce reliable estimates, but results will depend on the chosen method. It is important to identify conditions for which maximum likelihood estimates are unlikely to be identifiable from presence-only data. In data sets where the maximum likelihood estimates do not exist, penalized likelihood and Bayesian methods will produce coefficient estimates, but these are sensitive to the choice of estimation procedure and prior or penalty term. When sample size is small or it is thought that habitat preferences are strong, we propose a suite of estimation procedures researchers can consider using.

Methods in Ecology and Evolution↗

USGS2015

Performance of species occurrence estimators when basic assumptions are not met: a test using field data where true occupancy status is known

Populations are rarely censused. Instead, observations are subject to incomplete detection, misclassification and detection heterogeneity that result from human and environmental constraints. Though numerous methods have been developed to deal with observational uncertainty, validation under field conditions is rare because truth is rarely known in these cases. We present the most comprehensive test of occupancy estimation methods to date, using more than 33 000 auditory call observations collected under standard field conditions and where the true occupancy status of sites was known. Basic occupancy estimation approaches were biased when two key assumptions were not met: that no false positives occur and that no unexplained heterogeneity in detection parameters occurs. The greatest bias occurred for dynamic parameters (i.e. local colonization and extinction), and in many cases, the degree of inaccuracy would render results largely useless. We examined three approaches to increase adherence or relax these assumptions: modifying the sampling design, employing estimators that account for false-positive detections and using covariates to account for site-level heterogeneity in both false-negative and false-positive detection probabilities. We demonstrate that bias can be substantially reduced by modifications to sampling methods and by using estimators that simultaneously account for false-positive detections and site-level covariates to explain heterogeneity. Our results demonstrate that even small probabilities of misidentification and among-site detection heterogeneity can have severe effects on estimator reliability if ignored. We challenge researchers to place greater attention on both heterogeneity and false positives when designing and analysing occupancy studies. We provide 9 specific recommendations for the design, implementation and analysis of occupancy studies to better meet this challenge.

Methods in Ecology and Evolution↗

USGS2015

Testing hypotheses on distribution shifts and changes in phenology of imperfectly detectable species

With ongoing climate change, many species are expected to shift their spatial and temporal distributions. To document changes in species distribution and phenology, detection/non-detection data have proven very useful. Occupancy models provide a robust way to analyse such data, but inference is usually focused on species spatial distribution, not phenology. We present a multi-season extension of the staggered-entry occupancy model of Kendall et al . (2013, Ecology , 94, 610), which permits inference about the within-season patterns of species arrival and departure at sampling sites. The new model presented here allows investigation of species phenology and spatial distribution across years, as well as site extinction/colonization dynamics. We illustrate the model with two data sets on European migratory passerines and one data set on North American treefrogs. We show how to derive several additional phenological parameters, such as annual mean arrival and departure dates, from estimated arrival and departure probabilities. Given the extent of detection/non-detection data that are available, we believe that this modelling approach will prove very useful to further understand and predict species responses to climate change.

Methods in Ecology and Evolution↗

USGS2015

When do we need more data? A primer on calculating the value of information for applied ecologists

Applied ecologists continually advocate further research, under the assumption that obtaining more information will lead to better decisions. Value of information (VoI) analysis can be used to quantify how additional information may improve management outcomes: despite its potential, this method is still underused in environmental decision-making. We provide a primer on how to calculate the VoI and assess whether reducing uncertainty will change a decision. Our aim is to facilitate the application of VoI by managers who are not familiar with decision-analytic principles and notation, by increasing the technical accessibility of the tool. Calculating the VoI requires explicit formulation of management objectives and actions. Uncertainty must be clearly structured and its effects on management outcomes evaluated. We present two measures of the VoI. The expected value of perfect information is a calculation of the expected improvement in management outcomes that would result from access to perfect knowledge. The expected value of sample information calculates the improvement in outcomes expected by collecting a given sample of new data. We guide readers through the calculation of VoI using two case studies: (i) testing for disease when managing a frog species and (ii) learning about demographic rates for the reintroduction of an endangered turtle. We illustrate the use of Bayesian updating to incorporate new information. The VoI depends on our current knowledge, the quality of the information collected and the expected outcomes of the available management actions. Collecting information can require significant investments of resources; VoI analysis assists managers in deciding whether these investments are justified.

Methods in Ecology and Evolution↗

USGS2015

A quantitative framework for estimating risk of collision between marine mammals and boats

Speed regulations of watercraft in protected areas are designed to reduce lethal collisions with wildlife but can have economic consequences. We present a quantitative framework for investigating the risk of deadly collisions between boats and wildlife. We apply encounter rate theory to demonstrate how marine mammal-boat encounter rate can be used to predict the expected number of deaths associated with management scenarios. We illustrate our approach with management scenarios for two endangered species: the Florida manatee Trichechus manatus latirostris and the North Atlantic right whale Eubalaena glacialis . We used a Monte Carlo simulation approach to demonstrate the uncertainty that is associated with our estimate of relative mortality. We show that encounter rate increased with vessel speed but that the expected number of encounters varies depending on the boating activities considered. For instance, in a scenario involving manatees and boating activities such as water skiing, the expected number of encounters in a given area (in a fixed time interval) increased with vessel speed. In another scenario in which a vessel made a transit of fixed length the expected number of encounters decreases slightly with boat speed. In both cases the expected number of encounters increased with distanced travelled by the boat. For whales, we found a slight reduction (~0.1%) in the number of encounters under a scenario where speed is unregulated; this reduction, however, is negligible, and overall expected relative mortality was ~30% lower under the scenario with speed regulation. The probability of avoidance by the animal or vessel was set to 0 because of lack of data, but we explored the importance of this parameter on the model predictions. In fact, expected relative mortality under speed regulations decreases even further when the probability of avoidance is a decreasing function of vessel speed. By applying encounter rate theory to the case of boat collisions with marine mammals, we gained new insights about encounter processes between wildlife and watercraft. Our work emphasizes the importance of considering uncertainty when estimating wildlife mortality. Finally, our findings are relevant to other systems and ecological processes involving the encounter between moving agents.

Methods in Ecology and Evolution↗

USGS2015

Assessing the robustness of quantitative fatty acid signature analysis to assumption violations

Knowledge of animal diets can provide important insights into life history and ecology, relationships among species in a community and potential response to ecosystem change or perturbation. Quantitative fatty acid signature analysis (QFASA) is a method of estimating diets from data on the composition, or signature, of fatty acids stored in adipose tissue. Given data on signatures of potential prey, a predator diet is estimated by minimizing the distance between its signature and a mixture of prey signatures. Calibration coefficients, constants derived from feeding trials, are used to account for differential metabolism of individual fatty acids. QFASA has been widely applied since its introduction and several variants of the original estimator have appeared in the literature. However, work to compare the statistical properties of QFASA estimators has been limited. One important characteristic of an estimator is its robustness to violations of model assumptions. The primary assumptions of QFASA are that prey signature data contain representatives of all prey types consumed and the calibration coefficients are known without error. We investigated the robustness of two QFASA estimators to a range of violations of these assumptions using computer simulation and recorded the resulting bias in diet estimates. We found that the Aitchison distance measure was most robust to errors in the calibration coefficients. Conversely, the Kullback–Leibler distance measure was most robust to the consumption of prey without representation in the prey signature data. In most QFASA applications, investigators will generally have some knowledge of the prey available to predators and be able to assess the completeness of prey signature data and sample additional prey as necessary. Conversely, because calibration coefficients are derived from feeding trials with captive animals and their values may be sensitive to consumer physiology and nutritional status, their applicability to free-ranging animals is difficult to establish. We therefore recommend that investigators first make any improvements to the prey signature data that seem warranted and then base estimation on the Aitchison distance measure, as it appears to minimize risk from violations of the assumption that is most difficult to verify.

Methods in Ecology and Evolution↗

USGS2015

A functional model for characterizing long-distance movement behaviour

Advancements in wildlife telemetry techniques have made it possible to collect large data sets of highly accurate animal locations at a fine temporal resolution. These data sets have prompted the development of a number of statistical methodologies for modelling animal movement. Telemetry data sets are often collected for purposes other than fine-scale movement analysis. These data sets may differ substantially from those that are collected with technologies suitable for fine-scale movement modelling and may consist of locations that are irregular in time, are temporally coarse or have large measurement error. These data sets are time-consuming and costly to collect but may still provide valuable information about movement behaviour. We developed a Bayesian movement model that accounts for error from multiple data sources as well as movement behaviour at different temporal scales. The Bayesian framework allows us to calculate derived quantities that describe temporally varying movement behaviour, such as residence time, speed and persistence in direction. The model is flexible, easy to implement and computationally efficient. We apply this model to data from Colorado Canada lynx ( Lynx canadensis ) and use derived quantities to identify changes in movement behaviour.

Methods in Ecology and Evolution↗

USGS2015

Occupancy estimation for rare species using a spatially-adaptive sampling design

Summary 1. Spatially clustered populations create unique challenges for conservation monitoring programmes. Advances in methodology typically are focused on either the design or the modelling stage of the study but do not involve integration of both. 2. We integrate adaptive cluster sampling and spatial occupancy modelling by developing two models to handle the dependence induced by cluster sampling. We compare these models to scenarios using simple random sampling and traditional occupancy models via simulation and data collected on a rare plant species, Tamarix ramosissima , found in China. 3. Our simulations show a marked improvement in confidence interval coverage for the new models combined with cluster sampling compared to simple random sampling and traditional occupancy models, with greatest improvement in the presence of low detection probability and spatial correlation in occupancy. 4. Accounting for the design using the simple cluster random-effects model reduces bias considerably, and full spatial modelling reduces bias further, especially for large n when the spatial covariance parameters can be estimated reliably. Both new models build on the strength of occupancy modelling and adaptive sampling and perform at least as well, and often better, than occupancy modelling alone. 5. We believe our approach is unique and potentially useful for a variety of studies directed at patchily distributed, clustered or rare species exhibiting spatial variation.

Methods in Ecology and Evolution↗

USGS2016

Uncertainty in biological monitoring: a framework for data collection and analysis to account for multiple sources of sampling bias

Biological monitoring programmes are increasingly relying upon large volumes of citizen-science data to improve the scope and spatial coverage of information, challenging the scientific community to develop design and model-based approaches to improve inference. Recent statistical models in ecology have been developed to accommodate false-negative errors, although current work points to false-positive errors as equally important sources of bias. This is of particular concern for the success of any monitoring programme given that rates as small as 3% could lead to the overestimation of the occurrence of rare events by as much as 50%, and even small false-positive rates can severely bias estimates of occurrence dynamics. We present an integrated, computationally efficient Bayesian hierarchical model to correct for false-positive and false-negative errors in detection/non-detection data. Our model combines independent, auxiliary data sources with field observations to improve the estimation of false-positive rates, when a subset of field observations cannot be validated a posteriori or assumed as perfect. We evaluated the performance of the model across a range of occurrence rates, false-positive and false-negative errors, and quantity of auxiliary data. The model performed well under all simulated scenarios, and we were able to identify critical auxiliary data characteristics which resulted in improved inference. We applied our false-positive model to a large-scale, citizen-science monitoring programme for anurans in the north-eastern United States, using auxiliary data from an experiment designed to estimate false-positive error rates. Not correcting for false-positive rates resulted in biased estimates of occupancy in 4 of the 10 anuran species we analysed, leading to an overestimation of the average number of occupied survey routes by as much as 70%. The framework we present for data collection and analysis is able to efficiently provide reliable inference for occurrence patterns using data from a citizen-science monitoring programme. However, our approach is applicable to data generated by any type of research and monitoring programme, independent of skill level or scale, when effort is placed on obtaining auxiliary information on false-positive rates.

Methods in Ecology and Evolution↗

USGS2016

Estimating abundance in the presence of species uncertainty

1.N-mixture models have become a popular method for estimating abundance of free-ranging animals that are not marked or identified individually. These models have been used on count data for single species that can be identified with certainty. However, co-occurring species often look similar during one or more life stages, making it difficult to assign species for all recorded captures. This uncertainty creates problems for estimating species-specific abundance and it can often limit life stages to which we can make inference. 2.We present a new extension of N-mixture models that accounts for species uncertainty. In addition to estimating site-specific abundances and detection probabilities, this model allows estimating probability of correct assignment of species identity. We implement this hierarchical model in a Bayesian framework and provide all code for running the model in BUGS-language programs. 3.We present an application of the model on count data from two sympatric freshwater fishes, the brook stickleback ( Culaea inconstans ) and the ninespine stickleback ( Pungitius pungitius ), ad illustrate implementation of covariate effects (habitat characteristics). In addition, we used a simulation study to validate the model and illustrate potential sample size issues. We also compared, for both real and simulated data, estimates provided by our model to those obtained by a simple N-mixture model when captures of unknown species identification were discarded. In the latter case, abundance estimates appeared highly biased and very imprecise, while our new model provided unbiased estimates with higher precision. 4.This extension of the N-mixture model should be useful for a wide variety of studies and taxa, as species uncertainty is a common issue. It should notably help improve investigation of abundance and vital rate characteristics of organisms’ early life stages, which are sometimes more difficult to identify than adults.

Methods in Ecology and Evolution↗

USGS2016

Immunoglobulin detection in wild birds: Effectiveness of three secondary anti-avian IgY antibodies in direct ELISAs in 41 avian species

1.Immunological reagents for wild, non-model species are limited or often non-existent for many species. 2. In this study, we compare the reactivity of a new anti-passerine IgY secondary antibody with existing secondary antibodies developed for use with birds. Samples from 41 species from the following six avian orders were analysed: Anseriformes (1 family, 1 species), Columbiformes (1 family, 2 species), Galliformes (1 family, 1 species), Passeriformes (16 families, 34 species), Piciformes (1 family, 2 species) and Suliformes (1 family, 1 species). Direct ELISAs were performed to detect total IgY using goat anti-passerine IgY, goat anti-chicken IgY or goat anti-bird IgY secondary antibodies. 3.The anti-passerine antibody exhibited significantly higher IgY reactivity compared to the anti-chicken and/or anti-bird antibodies in 80% of the passerine families tested. Birds in the order Piciformes (woodpeckers) and order Suliformes (cormorants) were poorly detected by all three secondary antibodies. A comparison of serum and plasma IgY levels was made within the same individuals for two passerine species (house finch and white-crowned sparrow), and serum exhibited significantly more IgY than the plasma for all three secondary antibodies. This result indicates that serum may be preferred to plasma when measuring total antibody levels in blood. 4.This study indicates that the anti-passerine IgY secondary antibody can effectively be used in immunological assays to detect passerine IgY for species in most passerine families and is preferred over anti-chicken and anti-bird secondary antibodies for the majority of passerine species. This anti-passerine antibody will allow for more accurate detection and quantification of IgY in more wild bird species than was possible with previously available secondary antibodies.

Methods in Ecology and Evolution↗

USGS2016

Critical considerations for the application of environmental DNA methods to detect aquatic species

Species detection using environmental DNA (eDNA) has tremendous potential for contributing to the understanding of the ecology and conservation of aquatic species. Detecting species using eDNA methods, rather than directly sampling the organisms, can reduce impacts on sensitive species and increase the power of field surveys for rare and elusive species. The sensitivity of eDNA methods, however, requires a heightened awareness and attention to quality assurance and quality control protocols. Additionally, the interpretation of eDNA data demands careful consideration of multiple factors. As eDNA methods have grown in application, diverse approaches have been implemented to address these issues. With interest in eDNA continuing to expand, supportive guidelines for undertaking eDNA studies are greatly needed. Environmental DNA researchers from around the world have collaborated to produce this set of guidelines and considerations for implementing eDNA methods to detect aquatic macroorganisms. Critical considerations for study design include preventing contamination in the field and the laboratory, choosing appropriate sample analysis methods, validating assays, testing for sample inhibition and following minimum reporting guidelines. Critical considerations for inference include temporal and spatial processes, limits of correlation of eDNA with abundance, uncertainty of positive and negative results, and potential sources of allochthonous DNA. We present a synthesis of knowledge at this stage for application of this new and powerful detection method.

Methods in Ecology and Evolution↗

USGS2016

State-and-transition simulation models: a framework for forecasting landscape change

Summary A wide range of spatially explicit simulation models have been developed to forecast landscape dynamics, including models for projecting changes in both vegetation and land use. While these models have generally been developed as separate applications, each with a separate purpose and audience, they share many common features. We present a general framework, called a state-and-transition simulation model (STSM), which captures a number of these common features, accompanied by a software product, called ST-Sim, to build and run such models. The STSM method divides a landscape into a set of discrete spatial units and simulates the discrete state of each cell forward as a discrete-time-inhomogeneous stochastic process. The method differs from a spatially interacting Markov chain in several important ways, including the ability to add discrete counters such as age and time-since-transition as state variables, to specify one-step transition rates as either probabilities or target areas, and to represent multiple types of transitions between pairs of states. We demonstrate the STSM method using a model of land-use/land-cover (LULC) change for the state of Hawai'i, USA. Processes represented in this example include expansion/contraction of agricultural lands, urbanization, wildfire, shrub encroachment into grassland and harvest of tree plantations; the model also projects shifts in moisture zones due to climate change. Key model output includes projections of the future spatial and temporal distribution of LULC classes and moisture zones across the landscape over the next 50 years. State-and-transition simulation models can be applied to a wide range of landscapes, including questions of both land-use change and vegetation dynamics. Because the method is inherently stochastic, it is well suited for characterizing uncertainty in model projections. When combined with the ST-Sim software, STSMs offer a simple yet powerful means for developing a wide range of models of landscape dynamics.

Methods in Ecology and Evolution↗

USGS2016

CDMetaPOP: An individual-based, eco-evolutionary model for spatially explicit simulation of landscape demogenetics

1. Combining landscape demographic and genetics models offers powerful methods for addressing questions for eco-evolutionary applications. 2. Using two illustrative examples, we present Cost–Distance Meta-POPulation, a program to simulate changes in neutral and/or selection-driven genotypes through time as a function of individual-based movement, complex spatial population dynamics, and multiple and changing landscape drivers. 3. Cost–Distance Meta-POPulation provides a novel tool for questions in landscape genetics by incorporating population viability analysis, while linking directly to conservation applications.

Methods in Ecology and Evolution↗

USGS2016

Designing occupancy studies when false-positive detections occur

1.Recently, estimators have been developed to estimate occupancy probabilities when false-positive detections occur during presence-absence surveys. Some of these estimators combine different types of survey data to improve estimates of occupancy. With these estimators, there is a tradeoff between the number of sample units surveyed, and the number and type of surveys at each sample unit. Guidance on efficient design of studies when false positives occur is unavailable. 2.For a range of scenarios, I identified survey designs that minimized the mean square error of the estimate of occupancy. I considered an approach that uses one survey method and two observation states and an approach that uses two survey methods. For each approach, I used numerical methods to identify optimal survey designs when model assumptions were met and parameter values were correctly anticipated, when parameter values were not correctly anticipated, and when the assumption of no unmodelled detection heterogeneity was violated. 3.Under the approach with two observation states, false positive detections increased the number of recommended surveys, relative to standard occupancy models. If parameter values could not be anticipated, pessimism about detection probabilities avoided poor designs. Detection heterogeneity could require more or fewer repeat surveys, depending on parameter values. If model assumptions were met, the approach with two survey methods was inefficient. However, with poor anticipation of parameter values, with detection heterogeneity, or with removal sampling schemes, combining two survey methods could improve estimates of occupancy. 4.Ignoring false positives can yield biased parameter estimates, yet false positives greatly complicate the design of occupancy studies. Specific guidance for major types of false-positive occupancy models, and for two assumption violations common in field data, can conserve survey resources. This guidance can be used to design efficient monitoring programs and studies of species occurrence, species distribution, or habitat selection, when false positives occur during surveys.

Methods in Ecology and Evolution↗

USGS2016

Do we need demographic data to forecast plant population dynamics?

Rapid environmental change has generated growing interest in forecasts of future population trajectories. Traditional population models built with detailed demographic observations from one study site can address the impacts of environmental change at particular locations, but are difficult to scale up to the landscape and regional scales relevant to management decisions. An alternative is to build models using population-level data that are much easier to collect over broad spatial scales than individual-level data. However, it is unknown whether models built using population-level data adequately capture the effects of density-dependence and environmental forcing that are necessary to generate skillful forecasts. Here, we test the consequences of aggregating individual responses when forecasting the population states (percent cover) and trajectories of four perennial grass species in a semi-arid grassland in Montana, USA. We parameterized two population models for each species, one based on individual-level data (survival, growth and recruitment) and one on population-level data (percent cover), and compared their forecasting accuracy and forecast horizons with and without the inclusion of climate covariates. For both models, we used Bayesian ridge regression to weight the influence of climate covariates for optimal prediction. In the absence of climate effects, we found no significant difference between the forecast accuracy of models based on individual-level data and models based on population-level data. Climate effects were weak, but increased forecast accuracy for two species. Increases in accuracy with climate covariates were similar between model types. In our case study, percent cover models generated forecasts as accurate as those from a demographic model. For the goal of forecasting, models based on aggregated individual-level data may offer a practical alternative to data-intensive demographic models. Long time series of percent cover data already exist for many plant species. Modelers should exploit these data to predict the impacts of environmental change.

Methods in Ecology and Evolution↗