Residual Autocorrelation Research Articles

A guide to Bayesian model checking for ecologists

AbstractChecking that models adequately represent data is an essential component of applied statistical inference. Ecologists increasingly use hierarchical Bayesian statistical models in their research. The appeal of this modeling paradigm is undeniable, as researchers can build and fit models that embody complex ecological processes while simultaneously accounting for observation error. However, ecologists tend to be less focused on checking model assumptions and assessing potential lack of fit when applying Bayesian methods than when applying more traditional modes of inference such as maximum likelihood. There are also multiple ways of assessing the fit of Bayesian models, each of which has strengths and weaknesses. For instance, BayesianPvalues are relatively easy to compute, but are well known to be conservative, producingPvalues biased toward 0.5. Alternatively, lesser known approaches to model checking, such as prior predictive checks, cross‐validation probability integral transforms, and pivot discrepancy measures may produce more accurate characterizations of goodness‐of‐fit but are not as well known to ecologists. In addition, a suite of visual and targeted diagnostics can be used to examine violations of different model assumptions and lack of fit at different levels of the modeling hierarchy, and to check for residual temporal or spatial autocorrelation. In this review, we synthesize existing literature to guide ecologists through the many available options for Bayesian model checking. We illustrate methods and procedures with several ecological case studies including (1) analysis of simulated spatiotemporal count data, (2) N‐mixture models for estimating abundance of sea otters from an aircraft, and (3) hidden Markov modeling to describe attendance patterns of California sea lion mothers on a rookery. We find that commonly used procedures based on posterior predictivePvalues detect extreme model inadequacy, but often do not detect more subtle cases of lack of fit. Tests based on cross‐validation and pivot discrepancy measures (including the “sampled predictivePvalue”) appear to be better suited to model checking and to have better overall statistical performance. We conclude that model checking is necessary to ensure that scientific inference is well founded. As an essential component of scientific discovery, it should accompany most Bayesian analyses presented in the literature.

Eigenvector Spatial Filtering Regression Modeling of Ground PM2.5 Concentrations Using Remotely Sensed Data

This paper proposes a regression model using the Eigenvector Spatial Filtering (ESF) method to estimate ground PM2.5 concentrations. Covariates are derived from remotely sensed data including aerosol optical depth, normal differential vegetation index, surface temperature, air pressure, relative humidity, height of planetary boundary layer and digital elevation model. In addition, cultural variables such as factory densities and road densities are also used in the model. With the Yangtze River Delta region as the study area, we constructed ESF-based Regression (ESFR) models at different time scales, using data for the period between December 2015 and November 2016. We found that the ESFR models effectively filtered spatial autocorrelation in the OLS residuals and resulted in increases in the goodness-of-fit metrics as well as reductions in residual standard errors and cross-validation errors, compared to the classic OLS models. The annual ESFR model explained 70% of the variability in PM2.5 concentrations, 16.7% more than the non-spatial OLS model. With the ESFR models, we performed detail analyses on the spatial and temporal distributions of PM2.5 concentrations in the study area. The model predictions are lower than ground observations but match the general trend. The experiment shows that ESFR provides a promising approach to PM2.5 analysis and prediction.

Effects of spatial autocorrelation and imperfect detection on species distribution models

Abstract Species distribution models (SDMs) are widely used in ecology and related fields. They are frequently adopted to predict the expected occurrence (presence/absence) or abundance over large spatial scales, that is, to produce a species distribution map. Two issues that almost universally affect these models are measurement errors (especially imperfect detection) and residual spatial autocorrelation. We explored the effects of imperfect detection and autocorrelation in abundance models by simulating datasets which did or did not contain these two effects and analysing them with four different models that did or did not accommodate them. Specifically, we used a Poisson GLM as a baseline, an N‐mixture model accounting only for imperfect detection and two N‐mixture models that accounted for imperfect detection, but differed in their specification of spatial autocorrelation (CAR random effects vs. two‐dimensional splines). In a case study, we then applied these models to Common Redstart Phoenicurus phoenicurus data from the second Swiss Breeding Bird Atlas (1993–1996) and validated them using an independent monitoring dataset. We found that both imperfect detection and autocorrelation strongly affected the quality and the uncertainty of abundance maps, especially when they occurred together. Spatial N‐mixture models were well able to estimate the true abundance maps. Explicit modelling of measurement error and spatial autocorrelation can thus greatly improve the quality of SDMs and should not be ignored when producing large‐scale abundance or occurrence maps.

Modeling spatial and temporal dynamics of plant species richness across tidal creeks in a temperate salt marsh

In salt marsh ecology, various indicators, including environmental, biological, and anthropogenic factors, have been used to predict the patterns of plant species richness. The potential impact of spatial autocorrelation on this prediction, however, has yet to receive much attention. In this paper, two sets of regression models were developed to predict spatial patterns (in 2006) and temporal changes (from 2006 to 2012) of richness across selected tidal creeks at a Danish salt marsh: (1) traditional ordinary least squares (OLS) using soil and topographic parameters as independent variables and (2) spatial regressions in which spatial filters produced by spatial eigenvector mapping were included into the non-spatial OLS as additional independent variables. Such incorporation led to a general improvement of model outcomes, that is, increases in R2 and decreases in both Akaike’s information criterion and residual autocorrelation. Notably, only spatial filters were always significant independent variables for both the spatial and temporal dynamics of species richness. In contrast, no environmental variables were consistently significant because of the substantial reduction in their regression coefficients after spatial regression. These results imply that identifying the relevant indicators of richness patterns in salt marshes may be a much more complicated job than previously thought. By revealing the new and statistically more rigorous predictive power of these environmental (i.e., non-spatial) variables, the spatially explicit modeling employed in this paper will provide benefits to the literature on ecological indicators.

Examining the rainfall–topography relationship using non-stationary modelling technique in semi-arid Aseer region, Saudi Arabia

The mountainous region of Aseer, corresponding to the Afromontane phytogeographic region, is an eco-sensitive zone and has complex relationship between topography and rainfall. The region is located inland of the red sea escarpment edge in the west. Therefore, rainfall can occur during any month of the year in the mountain of the high Aseer region when moist air forces up the escarpment from the red sea. Monitoring the rainfall data and its topographical elevation variable in Aseer region is an essential requirement for feasible and accurate rainfall-based data for different applications, such as hydrological and ecological resource management in rugged terrain and remote areas. The relationship of elevation and rainfall are spatially non-stationary, non-linear, scale dependent, and often modelled by conventional regression models. Therefore, a local modelling technique, geographically weighted regression (GWR), was applied to deal with non-stationary, non-linear, scale-dependent problems. The GWR using topoclimatic data (elevation and rainfall) to analyse the cumulative rainfall data for rainy months (March to June) of the 4 years estimated from CHIRPS (Climate Hazards Group InfraRed Precipitation with Stations) product for Aseer region. The bandwidth (scale-size) of the Aseer region rainfall–elevation relationship has stabilised at round off 12 km. By selecting the suitable bandwidth, the spatial pattern of the rainfall–elevation relationship was significantly enhanced by using the GWR than the traditional ordinary least squares (OLS) regression model. GWR local modelling techniques estimated well in terms of accuracy, predictive power and decreased residual autocorrelation. Additionally, GWR assesses the significance of local statistic at each location and identified the location of spatial clusters with local regression coefficients significantly improved as compared with global OLS model, thereby highlighting local variations. Therefore, the GWR, local modelling approach managed to produce more accurate estimates by taking into account local characteristics.

Variable-top stem biomass equations at tree-level generated by a simultaneous density-integral system for second growth forests of roble, raulí, and coigüe in Chile

Variable-top stem biomass models at the tree level for second growth forests of roble (Nothofagus obliqua), rauli (Nothofagus alpina), and coigue (Nothofagus dombeyi) were fitted by a simultaneous density-integral system, which combines a stem taper model and a wood basic density model. For each model, an autoregressive structure of order 2 and a power equation of residual variance were incorporated to reduce residual autocorrelation and heteroscedasticity, respectively. By using dummy variables in the regression analysis, zonal effects on the parameters in the variable-top stem biomass equations were detected in roble. Consequently, equations for clusters of zones were obtained. These equations presented significant parameters and a high precision in both fitting and validation processes (i.e., CV < 11.5% and CVp < 11.9%, respectively), demonstrating that they are unbiased. The advantage of these types of functions is that they provide estimates of volume and biomass of sections of the stem, defined between any two points of the stem in the three species. Thus, depending on the final use of the wood and the dimensions of the tree, a stem fraction can be quantified in units of volume and the remaining fraction in units of weight.

Development of an Integrated DBH Estimation Model Based on Stand and Climatic Conditions

Using Korean National Forest Inventory (NFI) data, our study developed a model to estimate stand mean diameter at breast height (DBH) reflecting the influence of site and climate factors on forest growth for the major tree species in South Korea. A DBH estimation model was developed using stand-level variables (stand age, site index and number of trees per hectare) as independent factors. The spatial autocorrelation of residuals of the model was identified using semi-variogram analysis for each tree species. Further, a residual model, in which residuals were estimated by climatic factors (mean temperature, sum temperature in the growing season and precipitation), was developed assuming that the spatial autocorrelation of residuals reflects the differences in regional climatic conditions. Linear regression analysis showed that residuals of all tree species were significantly correlated with temperature and precipitation. The DBH and residual models were integrated to estimate the current DBH under different climatic factors (temperature and precipitation) and stand-level variables. This model had high reliability (R2 = 0.74–0.79), and no obvious dependencies or patterns in residuals were noted. Our results indicated that temperature increases caused by climate change would negatively affect the DBH estimate of coniferous trees, but not of oak species.

Prediction of humpback whale group densities along the Brazilian coast using spatial autoregressive models

AbstractAt the breeding grounds of most baleen whales the patchiness and gaps in spatial distribution results from interactions between behavior patterns and environmental conditions. We evaluated the influence of environmental factors (bathymetry and distance from shore with quadratic terms, and wind speed), effort, and spatial autocorrelation effects to predict humpback whale group density in the Southwest Atlantic Ocean. Count data of groups by grid cells were fitted with conditional autoregressive models (CAR). Bayesian inference was performedviaintegrated nested Laplace approximation. The best‐fit model contained distance from shore and its quadratic term, bathymetry, and the autoregressive component. Occupancy probability was high for the Abrolhos Bank, some cells from the northeast continental shelf and southeast margin, but gaps in occurrence were identified. High densities were estimated in the east continental margin, with the highest density in the Abrolhos Bank, in some cells of the northeast continental margin and in the southernmost area. We report that intermediate distances from the coast, and shallow waters were preferred for breeding and calving activities. We suggest that CAR models may incorporate aggregation mechanisms into habitat modeling and may provide advances in marine mammal analyses by accounting for residual autocorrelation.

Disentangling good from bad practices in the selection of spatial or phylogenetic eigenvectors

Eigenvector mapping techniques are widely used by ecologists and evolutionary biologists to describe and control for spatial and/or phylogenetic patterns in their data. The selection of an appropriate subset of eigenvectors is a critical step (misspecification can lead to highly biased results and interpretations), and there is no consensus yet on how to proceed. We conducted a ten‐year review of the practices of eigenvector selection and highlighted three main procedures: selecting the subset of descriptors minimising the Akaike information criterion (AIC), using a forward selection with double stopping criterion after testing the global model significance (FWD), and selecting the subset minimising the autocorrelation in the model residuals (MIR). We compared the type I error rates, statistical power, and R² estimation accuracy of these methods using simulated data. Finally, a real dataset was analysed using variation partitioning analysis to illustrate to what extent the different selection approaches affected the ecological interpretation of the results. We show that, while the FWD and MIR approaches presented a correct type I error rate and were accurate, the AIC approach displayed extreme type I error rates (100%), and strongly overestimated the R². Moreover, the AIC approach resulted in wrong ecological interpretations, as it overestimated the pure spatial fraction (and the joint spatial‐environmental fraction to a lesser extent) of the variation partitioning. Both the FWD and MIR methods performed well at broad and medium scales but had a very low power to detect fine‐scale patterns. The FWD approach selected more eigenvectors than the MIR approach but also returned more accurate R² estimates. Hence, we discourage any future use of the AIC approach, and advocate choosing between the MIR and FWD approaches depending on the objective of the study: controlling for spatial or phylogenetic autocorrelation (MIR) or describing the patterns as accurately as possible (FWD).

The resilience of pollination interactions: importance of temporal phases

The loss of species that engage in close ecological interactions, such as pollination, has been shown to lead to secondary extinctions, ultimately threatening the overall ecosystem stability and functioning. Pollination studies are currently flourishing at all possible levels of interaction organization (i.e., species, guild, group and network), and different methodological protocols aimed to define the resilience of pollination interactions have been proposed. However, the temporal dimension of the resilience of pollination interactions has been often overlooked. In the light of these considerations, we addressed the following questions: does a temporal approach help to reveal critical moments during the flowering season, when pollination interactions are less resilient to perturbations? Do pollination interactions evaluated at species, guild, group and network level show different patterns when assessed through time? We monitored contacts between plant and pollinator species in dry grassland communities every 15 days during the overall community flowering season (12 surveys). For each survey, we built a quantitative plant–pollinator interaction matrix and we calculated two sets of metrics characterizing, respectively, the diversity and the distribution of interactions across hierarchical levels. To describe the diversity of interactions, we calculated partner diversity (PD) at the species level, vulnerability/generality (V/G) at the guild level, and interaction diversity and evenness at the network level. The distribution of interactions was characterized by calculating selectiveness at the species and the network level, and modularity at the group level. We assessed the temporal variation of PD, V/G at the level of plants and pollinators, and species selectiveness, by means of Linear Mixed Models (LMMs). To investigate the temporal variation of indexes calculated at group and network level, we applied simple linear and quadratic regressions after checking for temporal autocorrelation in residuals. When taking into account the temporal dimension of interactions, the diversity of interactions showed different patterns at different levels of organization. At the species level, no relationship was disclosed between PD and time, when assessing the temporal trend of V/G separately for the guild of plants and pollinators we observed an asymmetric structure of interactions. Pollination interactions showed to be asymmetric throughout the flowering season; however, evenness of interactions and network selectiveness showed significant positive relationships with time, revealing a poorer network of interactions during the end of the flowering season. The temporal analysis of pollination interactions revealed a stronger risk of secondary extinctions at the end of the flowering season, due to a lower degree of redundancy and thus of resilience of the overall network of interactions.

Environmental uniformity, site quality and tree competition interact to determine stand productivity of clonal Eucalyptus

Abstract The major determinants of productivity in Eucalyptus plantations include the site productive capacity, local environmental uniformity, and the tree genetics, which impact their growth potential and competitiveness. While these factors have received a lot of attention individually, less attention has been given to the relative importance of these factors and the interactions between them. We examined these factors and their interactions using eight experiments located along a gradient in site productivity, consisting of 54 clonal genotypes (Eucalyptus urophylla × E. grandis hybrids) at two plant spacings (3 × 3.33 and 3 × 2 m). Stand productivity was quantified as the mean annual increment at age 6 years (m3 ha−1 year−1). Site productive capacity was represented using a site index based on mean dominant height at age 6 years. Environmental uniformity was calculated from within-plot variability in growth of very young stands using residual spatial autocorrelation. The competitive ability of a given phenotype was calculated as the percent loss in potential growth due to neighbor competition. Productivity increased with all variables but site quality had the greatest effect, followed by environmental uniformity and then competitive ability, with corresponding changes in productivity of about 30, 20 and 10 m3 ha−1 year−1, respectively, across the range of the given variable. With higher environmental heterogeneity, competition among genotypes increased, especially at dense spacing, showing that in such situations, highly competitive genotypes may display productivities similar to the less competitive genotypes in uniform environments. Experimental plots distributed across site quality and uniformity gradients provide opportunity for greater genetic differentiation than plots covering more homogeneous environments, reinforcing the recommendation of establishing genetic tests in locations with extreme site qualities. Our work suggests that the G × E interaction is linked to site quality and, to a lesser degree, to the local environmental uniformity. This work shows the value of adopting environmental gradient-based approaches in tree genetic testing and clone recommendation as a way to more accurately match genotypes to specific sites.

Accurate determination of parameters relationship for photovoltaic power output by augmented dickey fuller test and engle granger method

Power output from photovoltaic (PV) systems in outdoor conditions is substantially influenced by climatic parameters such as solar irradiance and temperature. PV manufacturers always provide technical specifications in laboratory conditions but reliable relationship for the power output must be determined for accurate prediction under real operating conditions. For the present study, solar irradiance G, temperature T and electrical power output P data under real conditions are methodically and regularly inscribed in dataloggers. Hence, in this paper, we investigate rigorous and robust statistical methods for small sample such as Augmented Dickey-Fuller and Engle Granger for stationary series to determine the estimate regression between variables P, G & T. A first regression of power output P time series variable on solar irradiance G time series has shown spurious results and thus spurious regression. The first differences of such time series are stationary and a regression is proposed whereas temperature variable is identified as not significant and where autocorrelation of residuals is suspected. Finally, the novelty of this paper is the Engle & Granger method that is used to provide a relationship between variables P and G in a difference level. A final relationship without suspicious heteroscedasticity has been determined. Our model is formulated on the basis of PV real conditions statistical approach and is more realistic than steady approach models.

Prediction and spatial distribution of recruitment trees of natural secondary forest based on geographically weighted Poisson model

Based on the data collected from 108 permanent plots of the forest resources survey in Maoershan Experimental Forest Farm during 2004-2016, this study investigated the spatial distribution of recruitment trees in natural secondary forest by global Poisson regression and geographically weighted Poisson regression (GWPR) with four bandwidths of 2.5, 5, 10 and 15 km. The simulation effects of the 5 regressions and the factors influencing the recruitment trees in stands were analyzed, a description was given to the spatial autocorrelation of the regression residuals on global and local levels using Moran's I. The results showed that the spatial distribution of the number of natural secondary forest recruitment was significantly influenced by stands and topographic factors, especially average DBH. The GWPR model with small scale (2.5 km) had high accuracy of model fitting, a large range of model parameter estimates was generated, and the localized spatial distribution effect of the model parameters was obtained. The GWPR model at small scale (2.5 and 5 km) had produced a small range of model residuals, and the stability of the model was improved. The global spatial auto-correlation of the GWPR model residual at the small scale (2.5 km) was the lowe-st, and the local spatial auto-correlation was significantly reduced, in which an ideal spatial distribution pattern of small clusters with different observations was formed. The local model at small scale (2.5 km) was much better than the global model in the simulation effect on the spatial distribution of recruitment tree number.

Mapping of soil properties at high resolution in Switzerland using boosted geoadditive models

Abstract. High-resolution maps of soil properties are a prerequisite for assessing soil threats and soil functions and for fostering the sustainable use of soil resources. For many regions in the world, accurate maps of soil properties are missing, but often sparsely sampled (legacy) soil data are available. Soil property data (response) can then be related by digital soil mapping (DSM) to spatially exhaustive environmental data that describe soil-forming factors (covariates) to create spatially continuous maps. With airborne and space-borne remote sensing and multi-scale terrain analysis, large sets of covariates have become common. Building parsimonious models amenable to pedological interpretation is then a challenging task. We propose a new boosted geoadditive modelling framework (geoGAM) for DSM. The geoGAM models smooth non-linear relations between responses and single covariates and combines these model terms additively. Residual spatial autocorrelation is captured by a smooth function of spatial coordinates, and non-stationary effects are included through interactions between covariates and smooth spatial functions. The core of fully automated model building for geoGAM is component-wise gradient boosting. We illustrate the application of the geoGAM framework by using soil data from the Canton of Zurich, Switzerland. We modelled effective cation exchange capacity (ECEC) in forest topsoils as a continuous response. For agricultural land we predicted the presence of waterlogged horizons in given soil depths as binary and drainage classes as ordinal responses. For the latter we used proportional odds geoGAM, taking the ordering of the response properly into account. Fitted geoGAM contained only a few covariates (7 to 17) selected from large sets (333 covariates for forests, 498 for agricultural land). Model sparsity allowed for covariate interpretation through partial effects plots. Prediction intervals were computed by model-based bootstrapping for ECEC. The predictive performance of the fitted geoGAM, tested with independent validation data and specific skill scores for continuous, binary and ordinal responses, compared well with other studies that modelled similar soil properties. Skill score (SS) values of 0.23 to 0.53 (with SS = 1 for perfect predictions and SS = 0 for zero explained variance) were achieved depending on the response and type of score. GeoGAM combines efficient model building from large sets of covariates with effects that are easy to interpret and therefore likely raises the acceptance of DSM products by end-users.

The challenge of estimating a residual spatial autocorrelation from forest inventory data

Estimates of stand averages are needed by forest management for planning purposes. In forest enterprise inventories supported by remotely sensed auxiliary data, these estimates are typically derived exclusively from a model that does not consider stand effects in the study variable. Variance estimators for these means may seriously underestimate uncertainty, and confidence intervals may be too narrow when a model used for computing a stand mean omits a nontrivial stand effect in one or more of the model parameters, a nontrivial spatial distance dependent autocorrelation in the model residuals, or both. In simulated sampling from 36 populations with stands of different sizes and differing with respect to (i) the correlation between a study variable (Y) and two auxiliary variables (X), (ii) the magnitude of stand effects in the intercept of a linear population model linking X to Y, and (iii) a first-order autoregression in Y and X, we learned that none of the tested designs provided reliable estimates of the within-stand autocorrelation among model residuals. More-reliable estimates were possible from stand-wide predictions of Y. The anticipated bias in an estimated autoregression parameter had a modest influence on estimates of variance and coverage of nominal 95% confidence intervals for a synthetic stand mean.

Forecasting the Probability of Future Groundwater Levels Declining Below Specified Low Thresholds in the Conterminous U.S.

AbstractWe present a logistic regression approach for forecasting the probability of future groundwater levels declining or maintaining below specific groundwater‐level thresholds. We tested our approach on 102 groundwater wells in different climatic regions and aquifers of the United States that are part of the U.S. Geological Survey Groundwater Climate Response Network. We evaluated the importance of current groundwater levels, precipitation, streamflow, seasonal variability, Palmer Drought Severity Index, and atmosphere/ocean indices for developing the logistic regression equations. Several diagnostics of model fit were used to evaluate the regression equations, including testing of autocorrelation of residuals, goodness‐of‐fit metrics, and bootstrap validation testing. The probabilistic predictions were most successful at wells with high persistence (low month‐to‐month variability) in their groundwater records and at wells where the groundwater level remained below the defined low threshold for sustained periods (generally three months or longer). The model fit was weakest at wells with strong seasonal variability in levels and with shorter duration low‐threshold events. We identified challenges in deriving probabilistic‐forecasting models and possible approaches for addressing those challenges.

PHENOTYPIC MODELS OF COMPETITION FOR Pinus taeda L GENETIC PARAMETERS ESTIMATION

ABSTRACT The objective of this study was to evaluate the efficiency of the phenotypic models of competition, through spatial analysis in the genetic evaluation of Pinus taeda L progenies. For this, four competition covariates were used to adjust the phenotypic values in a P. taeda progeny test installed in four different locations in the state of Santa Catarina. The test was implemented in randomized block design, with seven repetitions, linear plots containing six plants per plot in 2.5 m x 2.0 m spacing. The test installed in sites A, B, and D present 63 families and site C 53 families. At nine years old, the diameter at the breast height was measured for all individuals. The presence or absence of competition was based on the residual autocorrelation coefficients, which had its significance tested by the Durbin-Watson test. In general, the use of covariates corrected the competition effect. The variances among and within plots, as well as the residual variation coefficient, were reduced. The classification by the genetic effect of the individuals in the progeny test was extremely altered for this data set with and without the use of covariates for sites A and D, as well as the genotype x environment interaction. The use of these two tools is of great importance in the analysis of data in P. taeda progeny tests, since the effects of competition can lead to mistakes in the selection of individuals and in the definition of improvement zones.

The Chow-Lin method extended to dynamic models with autocorrelated residuals

Abstract I provide a closed-form solution to temporal disaggregation or interpolation models which is both general in terms of dynamic structure of the model (lags of the high-frequency variable) and flexible in terms of autocorrelation of its residual. As for static models, I show that assuming autocorrelated residuals in dynamic models is practically convenient. To illustrate the potential of the solution proposed, I provide an example for quarterly non-financial corporations’ capital stock in computers and communication equipment.

Developing spatial models to guide conservation of grassland birds in the U.S. Northern Great Plains

ABSTRACT Conservation of bird populations is increasingly focused on landscapes. We combined data collected in 2005–2011 from 16,250 North American Breeding Bird Survey (BBS) survey points with local and remotely sensed environmental data to model the distribution of 7 grassland bird species in the Northern Great Plains of the United States. We analyzed data at the survey point level, which is consistent with the scale of conservation treatments that we apply, and avoided information loss caused by pooling data at the BBS route level. By accounting for observer effects, nesting of survey points within routes, and sequence of survey points, we accommodated BBS survey design, refined estimates of important habitat predictors, improved model fit, and reduced or eliminated positive spatial autocorrelation in model residuals. The predictive power of models was greatly increased by including variables that characterized annual and long-term precipitation, as well as local land cover attributes not available fro...

Accounting for the temporal variation of spatial effect improves inference and projection of population dynamics models

Population dynamics models incorporating density dependence and habitat heterogeneity are useful tools to explain and project the spatiotemporal variation of wildlife abundance. Despite their wide application in ecology and conservation biology, the inference and projection of these models may be problematic when residual spatial autocorrelation (SAC) is found. We aimed to improve the inference and projection of population dynamics models by accounting for residual SAC. We considered three Gompertz models that incorporated density dependence and the effect of wetland habitat to explain and project the abundance of Mallard (Anas platyrhynchos). We compared a conventional model that did not account for residual SAC (ENV) with two novel models accounting for residual SAC, one incorporating a spatial effect (a spatially autocorrelated process error) that did not vary over time (STA) and the other incorporating a spatial effect that varied over time (DYN). We evaluated model inference using data from 1974 to 1998 and projection using data from 1999 to 2010. We then forecasted Mallard abundance from 2011 to 2100 under different levels of wetland habitat loss. The DYN model eliminated residual SAC and had better model fit than the ENV and STA models (ΔD¯=2498.3 and 1988.8, respectively). The projection coverage rate of the DYN model was the closest to the nominal value among the three models. The DYN model forecasted smaller areas with decrease in Mallard abundance under future wetland habitat loss than the ENV and STA models. The novel and conventional population dynamics models we considered in this study, combined with the practical model evaluation approach, can provide reliable inference and projection of wildlife abundance, and thus have wide application in ecological studies and conservation practices that aim to understand and project the spatiotemporal variation of wildlife abundance under environmental changes. In particular, when conservation decision-making is based on model projections, the DYN may be used to minimize the risk of reducing conservation effort in areas that still have high conservation value, due to its favorable projection performance.