Residual Spatial Autocorrelation Research Articles

Non‐invasive mark–resight surveys for brown bears: Incorporating spatial information to improve landscape‐scale monitoring of density and distribution

Abstract Effective wildlife monitoring and management are reliant on unbiased estimators of population parameters. Most standard survey approaches ignore spatial pattern in the data although spatial relationships can be leveraged to produce more efficient designs for future surveys, thereby reducing project cost. Landscape‐scale surveys for brown bears are notoriously expensive and difficult to complete, leading to the development of a non‐invasive mark–resight aerial survey approach as a practical alternative to more commonly employed approaches for estimating brown bear density across large areas. Here we extend that model to accommodate spatial covariate information and explicitly model residual spatial autocorrelation. Using brown bear survey data from northwestern Alaska, USA from 2015 to 2021, we demonstrate how our extension can be useful in exploring ecological factors related to spatial variation in bear density and detection probability. We found that detection probability was higher in more rugged terrain, and occurrence probability was higher at mid‐elevations where denning habitat was more prevalent and in areas with more salmon streams. The descriptive model of residual autocorrelation confirmed that additional unmeasured factors were associated with bear distribution. While these findings were not unexpected, they are very useful when considering future survey effort. Using this information, we explored a hypothetical redesign of the 2021 brown bear survey that removed 50% of the survey subunits with elevation values below the mean, where bears were least likely to occur. We demonstrated that the resulting estimates were unbiased, suggesting that adopting the spatial approach to analysis could reduce overall project costs by ~20%–30% going forward. Overall, our work indicates that directly accounting for spatial pattern within the non‐invasive mark–resight framework has substantive advantages over the original non‐spatial approach and may be useful in increasing the amount of information available for brown bear populations.

Small Field Plots Can Cause Substantial Uncertainty in Gridded Aboveground Biomass Products from Airborne Lidar Data

Emerging satellite radar and lidar platforms are being developed to produce gridded aboveground biomass (AGB) predictions that are poised to expand our understanding of global carbon stocks and changes. However, the spatial resolution of AGB map products from these platforms is often larger than the available field plot data underpinning model calibration and validation efforts. Intermediate-resolution/extent remotely sensed data, like airborne lidar, can serve as a bridge between small plots and map resolution, but methods are needed to estimate and propagate uncertainties with multiple layers of data. Here, we introduce a workflow to estimate the pixel-level mean and variance in AGB maps by propagating uncertainty from a lidar-based model using small plots, taking into account prediction uncertainty, residual uncertainty, and residual spatial autocorrelation. We apply this workflow to estimate AGB uncertainty at a 100 m map resolution (1 ha pixels) using 0.04 ha field plots from 11 sites across four ecoregions. We compare uncertainty estimates using site-specific models, ecoregion-specific models, and a general model using all sites. The estimated AGB uncertainty for 1 ha pixels increased with mean AGB, reaching 7.8–33.3 Mg ha−1 for site-specific models (one standard deviation), 11.1–28.2 Mg ha−1 for ecoregion-specific models, and 21.1–22.1 Mg ha−1 for the general model for pixels in the AGB range of 80–100 Mg ha−1. Only 3 of 11 site-specific models had a total uncertainty of <15 Mg ha−1 in this biomass range, suitable for the calibration or validation of AGB map products. Using two additional sites with larger field plots, we show that lidar-based models calibrated with larger field plots can substantially reduce 1 ha pixel AGB uncertainty for the same range from 18.2 Mg ha−1 using 0.04 ha plots to 10.9 Mg ha−1 using 0.25 ha plots and 10.1 Mg ha−1 using 1 ha plots. We conclude that the estimated AGB uncertainty from models estimated from small field plots may be unacceptably large, and we recommend coordinated efforts to measure larger field plots as reference data for the calibration or validation of satellite-based map products at landscape scales (≥0.25 ha).

Improved prediction of tree species richness and interpretability of environmental drivers using a machine learning approach

Biodiversity is in decline globally and predicting species diversity is critically important if current trends are to be reversed. Tree species richness (TSR) has long been a key measure of biodiversity, but considerable uncertainties exist in current models, particularly given the classic statistical assumptions and poor ecological interpretability of machine learning outcomes. Here, we test several ecologically interpretable machine learning approaches to predict TSR and interpret the driving environmental factors in the continental United States. We develop two artificial neural networks (ANN) and one random forest (RF) model to predict TSR using Forest Inventory and Analysis data and 20 environmental covariates and compare them to a classic generalized linear model (GLM). Models were evaluated on an independent, unseen testing dataset using R2 and Mean Absolute Error (MAE) and residual spatial autocorrelation analysis. An Interpretable Machine Learning approach, SHapley Additive exPlanations (SHAP), was adopted to explain the major environmental factors driving TSR. Compared to a baseline GLM (R2 = 0.7; MAE = 4.7), the ANN and RF models achieved R2 greater than 0.9 and MAE<3.1. Additionally, the ANN and RF models produced less spatially clustered TSR residuals than the GLM. SHAP analysis suggested that TSR is best predicted by Aridity Index, Forest Area, Altitude, Mean Precipitation of the Driest Quarter and Mean Annual Temperature. SHAP further revealed a non-linear relationship of environmental covariates with TSR and complex interactions that were not revealed by the GLM. The study highlights the need for conservation efforts of forest areas and reducing precipitation-related physiological stress on tree species in low forested but arid regions. The machine learning approach used here is transferrable for studies of biodiversity for other organisms or prediction of TSR under future climatic scenarios.

Harnessing data assimilation and spatial autocorrelation for forest inventory

Spatially explicit uncertainties in forest above-ground biomass predictions for population units are underestimated if spatial structure in the form of residual spatial autocorrelation and heteroscedasticity is ignored. Methods that consider the spatial structure of biomass model residuals are needed to comprehensively estimate, as well as to effectively reduce, the uncertainty in biomass predictions, for pursuing higher levels of precision for measurement, reporting and verification of forest carbon stocks. The objectives of the study were threefold: (1) to demonstrate a spatial data assimilation (DA) procedure that harnesses small-footprint airborne LiDAR, the best linear unbiased predictor (BLUP) and the spatial structure of biomass model residuals to reduce prediction variances of individual tree biomass and plot-level biomass density; (2) to derive a variance estimator that decomposes the variance into components associated with corresponding error sources; and (3) to compare prediction variances for three methods used to calibrate a height-based allometric model for tree biomass: ordinary least squares (OLS), generalized least squares (GLS), and spatial DA using the BLUP. Five major conclusions are drawn. First, for individual tree biomass predictions, spatial DA decreased prediction variance by 40% and 20% relative to OLS and GLS. Because the decrease in residual variability accounted for 98% of the decrease in prediction variance in total, the assimilation effect was the largest for reducing residual variability. Second, for biomass density predictions, DA decreased prediction variance by 3% and 49% relative to OLS and GLS, with the largest decrease in residual covariance. Accumulated gain in precision for individual tree predictions in the DA procedure was offset by precision loss caused by residual covariance and the variance associated with omission and commission errors while predicting individual tree biomass from the LiDAR data. Third, OLS, which assumed no spatial structure, underestimated prediction variance for LiDAR-predicted biomass density by 48%. Fourth, from the perspective of prediction accuracy, DA reduced the RMSE for individual tree biomass predictions by 11% and 14% and reduced the RMSE for biomass density predictions by 28% and 33% relative to OLS and GLS. Fifth, the omission/commission difference model was effective for correcting the systematic prediction error in the LiDAR-predicted biomass density. Overall, the proposed spatial DA procedure demonstrated great potential for reducing the uncertainty in forest biomass predictions, thereby facilitating more efficient biomass inventories. The procedure can be generalized to other dependent variables of interest given their correlations with new information from LiDAR.

Exploring the use of Sentinel-2 datasets and environmental variables to model wheat crop yield in smallholder arid and semi-arid farming systems

Low levels of agricultural productivity are associated with the persistence of food insecurity, poverty, and other socio-economic stresses. Mapping and monitoring agricultural dynamics and production in real-time at high spatial resolution are essential for ensuring food security and shaping policy interventions. However, an accurate yield estimation might be challenging in some arid and semi-arid regions since input datasets are generally scarce, and access is restricted due to security challenges. This work examines how well Sentinel-2 satellite sensor-derived data, topographic and climatic variables, can be used as covariates to accurately model and predict wheat crop yield at the farm level using statistical models in low data settings of arid and semi-arid regions, using Sulaimani governorate in Iraq as an example. We developed a covariate selection procedure that assessed the correlations between the covariates and their relationships with wheat crop yield. Potential non-linear relationships were investigated in the latter case using regression splines. In the absence of substantial non-linear relationships between the covariates and crop yield, and residual spatial autocorrelation, we fitted a Bayesian multiple linear regression model to model and predict crop yield at 10 m resolution. Out of the covariates tested, our results showed significant relationships between crop yield and mean cumulative NDVI during the growing season, mean elevation, mean end of the season, mean maximum temperature and mean the start of the season at the farm level. For in-sample prediction, we estimated an R2 value of 51 % for the model, whereas for out-of-sample prediction, this was 41 %, both of which indicate reasonable predictive performance. The calculated root-mean-square error for out-of-sample prediction was 69.80, which is less than the standard deviation of 89.23 for crop yield, further showing that the model performed well by reducing prediction variability. Besides crop yield estimates, the model produced uncertainty metrics at 10 m resolution. Overall, this study showed that Sentinel-2 data can be valuable for upscaling field measurement of crop yield in arid and semi-arid regions. In addition, the environmental covariates can strengthen the model predictive power. The method may be applicable in other areas with similar environments, particularly in conflict zones, to increase the availability of agricultural statistics.

Health behaviors and the risk of COVID-19 incidence: A Bayesian hierarchical spatial analysis

ObjectivesEffective infection control measures, based on a sound understanding of geographical community-specific health behavioral characteristics, should be implemented from the early stage of disease transmission. However, few studies have explored health behaviors as a possible contributor to COVID-19 infection in the spatial context. We investigated health behaviors as potential factors of COVID-19 incidence in the early phase of transmission in the spatial context. MethodsWe extracted COVID-19 cumulative case data as of February 25, 2021—one day prior to nationwide COVID-19 vaccination commencement—regarding health behaviors and covariates, including health condition and socio-economic factors, at the municipal level from publicly available datasets. The spatial autocorrelation of incidence was analyzed using Global Moran’s I statistics. The associations between health behaviors and COVID-19 incidence were examined using Besag–York–Mollie models to deal with spatial autocorrelation of residuals. ResultsThe COVID-19 incidence had positive spatial autocorrelation across South Korea (I = 0.584, p = 0.001). The results suggest that individuals vaccinated against influenza in the preceding year had a negative association with COVID-19 incidence (relative risk=0.913, 95 % Credible Interval=0.838–0.997), even after adjusting for covariates. ConclusionsOur ecological study suggests an association between COVID-19 infection and health behaviors, especially influenza vaccination, in the early stage of COVID-19 transmission at the municipal level.

Neuroticism, urbanization, and the state prevalence of Parkinson’s disease in the USA

This study was conducted primarily to determine whether state prevalence rates of Parkinson’s disease (PD) among Medicare beneficiaries 65 and over are associated with U.S. state resident standing on the Big Five personality dimensions. Key variables for the 50 states were PD prevalence rates in 2014, Big Five scores based on 619,397 survey respondents, socioeconomic status (SES), White population percent, urban population percent, health environment, and overall health outcomes. A sequential multiple regression equation with the SES, White, and urbanization variables selected stepwise and followed by the Big Five selected stepwise showed state PD prevalence rate variance was significantly accounted for by urbanization (16.9 %, β = 0.53) and neuroticism (32.8 %, β = 0.59). This prediction pattern persisted in another equation when state health environment and health outcomes served as additional controls, with neuroticism accounting for an additional 17.4 % of the variance. The only independent predictors in that equation also were urbanization (β = 0.57) and neuroticism (β = 0.48). Essentially similar results were found using simultaneous entry equations. Spatial analysis using Moran’s I test for residual spatial autocorrelation also showed that spatial autocorrelation was not an issue. The present results based on the geographical psychology perspective underline the importance of corroborating correlative patterns found in personality studies with individuals as the analytic units with research using aggregates of individuals as the units of analysis. It also is speculated that health policy and promotion managers eventually might profit from tailoring PD initiatives according to resident neuroticism levels and degree of urbanization.

Three Common Machine Learning Algorithms Neither Enhance Prediction Accuracy Nor Reduce Spatial Autocorrelation in Residuals: An Analysis of Twenty‐five Socioeconomic Data Sets

Machine learning (ML) is being applied in an increasing volume of geographical research. However, the aspects of spatial autocorrelation (SAC) in the residuals produced by ML models have been understudied compared to the benefit of ML, namely, reduction of prediction errors. In this study, we examined the relationship between predictive accuracy and the reduction in the residual SAC for 597 variables from 25 geographical socio‐economic data sets using spatial and nonspatial cross‐validation of three ML algorithms such as random forests, support vector machine, and artificial neural network (ANN) to provide an extensive empirical diagnosis—but not a definitive theory—of the relationship between SAC and ML. Our results highlighted that the ML algorithms with tuned hyperparameters yielded marginal predictive accuracy gains and the minimal decreases in residual SAC. ANN revealed lower accuracy and higher reduction in the residual SAC than others. This implies ML algorithms in geographical research in socio‐economic domains would not always result in higher prediction accuracy. We suggest that ML in geographical research should be cautiously employed when the main objective is related to the residual SAC. We also showed that spatial cross‐validation neither improves predictive accuracy substantially nor reduce the residual SAC effectively.

Stream Distance-Based Geographically Weighted Regression for Exploring Watershed Characteristics and Water Quality Relationships

We developed a novel spatial stream network geographically weighted regression (SSN-GWR) by incorporating stream-distance metrics into GWR. The model was tested for predicting seasonal total nitrogen (TN) and total suspended solids (TSS) concentrations in relation to watershed characteristics for 108 sites in the Han River Basin, South Korea. The SSN-GWR model was run with the average seasonal water quality parameters from 2012 through 2016 and was validated with the data from 2017 through 2021. The model fit among ordinary least square regression, standard GWR (STD-GWR), and stream distance weighted SSN-GWR were compared based on their ability to explain the variation of seasonal water quality parameters. We also compared residual spatial autocorrelations as well as various error parameters from these models. Compared to the STD-GWR model, the SSN-GWR model generally provided better model fit, reduced residual spatial autocorrelation, and lessened overall modeling errors. Results show that the spatial patterns of model fit, as well as various coefficients from the upstream distance weighted regressions, capture local patterns as a product of upstream–downstream relations. We demonstrate that a successful model could be developed by integrating stream distance into the GWR, which not only improves model fit but also reveals realistic hydrological processes that relate watershed characteristics to water quality along with the stream network. The local variations in model fit derived from this work can be used to devise fine-scale interventions for water quality improvements in a spatially heterogeneous complex river basin.

Examining the Driving Factors of SOM Using a Multi-Scale GWR Model Augmented by Geo-Detector and GWPCA Analysis

A model incorporating geo-detector analysis and geographically weighted principal component analysis into Multi-scale Geographically Weighted regression (GWPCA-MGWR) was developed to reveal the factors driving spatial variation in soil organic matter (SOM). The regression accuracy and residuals from GWPCA-MGWR were compared to those of the classical Geographically Weighted regression (GWR), Multi-scale Geographically Weighted regression (MGWR), and GWPCA-GWR. Our results revealed that local multi-collinearity on model fitting negatively affects the results to different degrees. Additionally, compared to other models, GWPCA-MGWR provided the lowest MAE (0.001) and little-to-no residual spatial autocorrelation and is the best model for regression for SOM spatial distribution and identification of dominant driving factors. GWPCA-MGWR produced spatial non-stationary SOM that was variably affected by soil nutrient content, soil type, and human activity, and was geomorphic in the second place. In conclusion, the spatial information obtained from GWPCA-MGWR provides a valuable reference for understanding the factors that influence SOM variation.

Modeling the Determinants of PM2.5 in China Considering the Localized Spatiotemporal Effects: A Multiscale Geographically Weighted Regression Method

Many studies have identified the influences of PM2.5. However, very little research has addressed the spatiotemporal dependence and heterogeneity in the relationships between impact factors and PM2.5. This study firstly utilizes spatial statistics and time series analysis to investigate the spatial and temporal dependence of PM2.5 at the city level in China using a three-year (2015–2017) dataset. Then, a new local regression model, multiscale geographically weighted regression (MGWR), is introduced, based on which we measure the influence of PM2.5. A spatiotemporal lag is constructed and included in MGWR to account for spatiotemporal dependence and spatial heterogeneity simultaneously. Results of MGWR are comprehensively compared with those of ordinary least square (OLS) and geographically weighted regression (GWR). Experimental results show that PM2.5 is autocorrelated in both space and time. Compared with existing approaches, MGWR with a spatiotemporal lag (MGWRL) achieves a higher goodness-of-fit and a more significant effect on eliminating residual spatial autocorrelation. Parameter estimates from MGWR demonstrate significant spatial heterogeneity, which traditional global models fail to detect. Results also indicate the use of MGWR for generating local spatiotemporal dependence evaluations which are conditioned on various covariates rather than being simple descriptions of a pattern. This study offers a more accurate method to model geographic events.

Mapping Respiratory Disease Mortality in Turkey by Using Bayesian Conditional Autoregressive Model

Spatial analysis plays a prominent role in revealing and characterizing the spatial patterns over a geographical region by considering both the attributes of objects in a data set and their locations. The response variable can display spatial autocorrelation. The objects close together tend to produce more similar observations than objects further apart. Despite covariates in the model, we cannot capture spatial autocorrelation explicitly. It remains in the model residuals. Then, the independence assumption is violated by the residuals. We apply conditional autoregressive (CAR) model to prevent the residual spatial autocorrelation. In this study, we consider the problem of identifying the provinces at high risk to respiratory diseases mortality in Turkey. The number of deaths from respiratory diseases in 81 provinces of Turkey are modelled by using Leroux Model. We assume that the observed number of deaths have a Poisson distribution. Disease mapping is performed over calculated risk values. The results show that an increase in the household consumption of alcoholic beverages, cigarettes and tobacco and, also in the rate of people aged over 65 years in a province trigger a significant increase in respiratory disease mortality. Furthermore, Kastamonu has the highest mortality risk from respiratory diseases.

A geographically weighted deep neural network model for research on the spatial distribution of the down dead wood volume in Liangshui National Nature Reserve (China)

In natural forest ecosystems, there is often abundant down dead wood (DDW) due to wind disasters, which greatly changes the size and structure of forests. Accurately determining the DDW volume (DDWV) is crucial for sustaining forest management, predicting the dynamic changes in forest resources and assessing the risks of natural disasters or disturbances. However, existing models cannot accurately express the significant spatial nonstationarity or complexity in their spatial relationships. To this end, we established a geographically weighted deep neural network (GWDNN) model that constructs a spatially weighted neural network (SWNN) through geographic location data and builds a neural network through stand factors and remote sensing factors to improve the interpretability of the spatial model of DDWV. To verify the effectiveness of this method, using 2019 data from Liangshui National Nature Reserve, we compared model fit, predictive ability and residual spatial autocorrelation among the GWDNN model and four other spatial models: an ordinary least squares (OLS) model, a linear mixed model (LMM), a geographically weighted regression (GWR) model and a deep neural network (DNN) model. The experimental results show that the GWDNN model is far superior to the other four models according to various indicators; the coefficient of determination R2, root mean square error (RMSE), mean absolute error (MAE), Moran’s I and Z-statistic values of the GWDNN model were 0.95, 1.05, 0.77, -0.01 and -0.06, respectively. In addition, compared with the other models, the GWDNN model can more accurately depict local spatial variations and details of the DDWV in Liangshui National Nature Reserve.

Exploring spatial interaction effects in freight trip generation model for intermediate and pure receiver establishment

Freight trip generation (FTG) plays an essential role in urban planning and traffic assessments for developing long-term transportation demand modeling. This study explored the spatial interaction effects on the development of FTG models for intermediate and pure receiver establishment using spatial econometric techniques. FTG models are developed by considering three types of spatial interaction effects such as exogenous, endogenous, and residual spatial autocorrelation effects. Initially, the supply chain variables and demographic characteristics are collected in Tiruchirappalli city, Tamil Nadu, India. The spatial indicators for intermediate and pure receiver establishment are identified by estimating spatial autocorrection of the variables using Moran’s I method. Further, the locational information of the study area is incorporated for representing the spatial neighborhood structure in the spatial weight matrix. The spatial interaction effects are assessed using spatial econometric modeling techniques. FTG models are developed using the linear Ordinary Least Square (OLS) technique and Spatial Econometric techniques such as Spatially Lagged X model (SLX), Spatial Durbin Model (SDM), and Spatial Durbin Error model (SDEM). The developed models are compared using the Bayesian approach, and the suitable FTG model is identified to explain the spatial interaction effects in more precisely. The results show that the SDEM is the most suitable FTG model than other spatial econometric models for both intermediate and pure receiver establishment. Spatial indicators such as own effects and spillover effects associated with the SDEM are estimated and interpreted for explaining the freight trip activity. Moreover, local spatial spillover significantly recognizes the urban fright trip generation for both intermediate and pure receiver establishment.

Long-term exposure to air pollution and COVID-19 incidence: A multi-country study

The study of the impacts of air pollution on COVID-19 has gained increasing attention. However, most of the existing studies are based on a single country, with a high degree of variation in the results reported in different papers. We attempt to inform the debate about the long-term effects of air pollution on COVID-19 by conducting a multi-country analysis using a spatial ecological design, including Canada, Italy, England and the United States. The model allows the residual spatial autocorrelation after accounting for covariates. It is concluded that the effects of PM2.5 and NO2 are inconsistent across countries. Specifically, NO2 was not found to be an important factor affecting COVID-19 infection, while a large effect for PM2.5 in the US is not found in the other three countries. The Population Attributable Fraction for COVID-19 incidence ranges from 3.4% in Canada to 45.9% in Italy, although with considerable uncertainty in these estimates.

The effect of sociodemographic factors on COVID-19 incidence of 342 cities in China: a geographically weighted regression model analysis

BackgroundSince December 2019, the coronavirus disease 2019 (COVID-19) has spread quickly among the population and brought a severe global impact. However, considerable geographical disparities in the distribution of COVID-19 incidence existed among different cities. In this study, we aimed to explore the effect of sociodemographic factors on COVID-19 incidence of 342 cities in China from a geographic perspective.MethodsOfficial surveillance data about the COVID-19 and sociodemographic information in China’s 342 cities were collected. Local geographically weighted Poisson regression (GWPR) model and traditional generalized linear models (GLM) Poisson regression model were compared for optimal analysis.ResultsCompared to that of the GLM Poisson regression model, a significantly lower corrected Akaike Information Criteria (AICc) was reported in the GWPR model (61953.0 in GLM vs. 43218.9 in GWPR). Spatial auto-correlation of residuals was not found in the GWPR model (global Moran’s I = − 0.005, p = 0.468), inferring the capture of the spatial auto-correlation by the GWPR model. Cities with a higher gross domestic product (GDP), limited health resources, and shorter distance to Wuhan, were at a higher risk for COVID-19. Furthermore, with the exception of some southeastern cities, as population density increased, the incidence of COVID-19 decreased.ConclusionsThere are potential effects of the sociodemographic factors on the COVID-19 incidence. Moreover, our findings and methodology could guide other countries by helping them understand the local transmission of COVID-19 and developing a tailored country-specific intervention strategy.

Predicting the magnitude of residual spatial autocorrelation in geographical ecology

The level of spatial autocorrelation (SAC) present in model residuals can have a detrimental influence on statistical inferences in geographical ecology. There has been significant progress in understanding the nature and causes of residual SAC and developing new methods to reduce the SAC. However, ecologists have not yet found a suitable answer as to when the level of residual autocorrelation is likely to magnify and whether its shift through spatial regression (i.e. the difference in the residual SAC produced by non‐spatial and spatial approaches) can be predicted using a set of readily available variables. In this paper, I reanalyzed the outcomes reported by Bini et al. (2009), who originally compared the differences in the standardized regression coefficients resulting from non‐spatial ordinary least squares and various spatially explicit methods. Although these researchers were unable to identify reliable predictors of the coefficient shifts, in the present study, I observed that the level of residual autocorrelation significantly and linearly increased with an increase in the magnitude of the SAC inherently possessed by, especially, response and explanatory variables. Moreover, the amount of shift in the residual SAC varied as a linear function of the response and explanatory variables. These findings imply that, in general, specific conditions exist under which there is an increase in the magnitude of the residual SAC, that such a shift can be predicted by the nature and structure of the data sets involved, and that, after all, the residual SAC varies systematically regardless of the selection of the data type, statistical method and spatial scale. I suggest that the level of the SAC present in the input variables can directly indicate how much improvement (i.e. reduction in the residual SAC) a non‐spatial model will experience when a proper spatial approach is employed.

Spatial distribution of carbon storage in natural secondary forest based on geographically weighted regression expansion model.

To accurately assess carbon storage and its spatial distribution in natural secondary forest at the regional scale, we constructed seven expansion models by modifying the geographically weighted regression (GWR) in aspects of spatial dimension, parameter heterogeneity and residual spatial autocorrelation, based on data collected from 165 bureau level permanent plots in Langxi Forest Farm of Wangqing Forestry Bureau in Jilin Province. Stand factor, topography factor, and soil factor were selected as the influencing factors. The expansion models included geographically and altitudinal weighted regression (GAWR), semiparametric geographically weighted regression (SGWR), semiparametric geographically and altitudinal weighted regression (SGAWR), geographically weighted regression Kriging (GWRK), geographically and altitudinal weighted regression Kriging (GAWRK), semiparametric geographically weighted regression Kriging (SGWRK), and semiparametric geographically and altitudinal weighted regression Kriging (SGAWRK). Coefficient of determination (R2), mean square error (MSE) and Akaike's Information Criterion (AIC) were used to evaluate the fitness of these models. Finally, the spatial distribution diagram of forest carbon storage was drawn with the fitting results of the optimal regression model, and the distribution pattern of forest carbon storage in the research area was analyzed. The stand factor and topographic factor had strong influence on carbon storage of natural secondary forests, among which the average diameter at breast height (DBH) of stands was the dominant variable. There was positive correlation between stand factor and topographic factor. SGWR and SGAWR model could reduce the spatial autocorrelation of the GWR model residual. The geographically regression expansion model could improve the fitting effect of GWR model. Among them, the SGWRK model had the highest R2 and the lowest MSE and AIC. The method with altitude as the spatial weight did not effectively improve the fitting effect of the model. The total forest carbon storage of Langxi Forest Farm was 205×104 t, and the carbon density ranged from 8.56 to 145.74 t·hm-2, with a mean value of 57.98 t·hm-2. Overall, the distribution pattern of carbon storage was high in the northwest and low in the southeast, while high in the edge and low in the interior. By improving the parameter heterogeneity and residual spatial autocorrelation in the GWR model, we can accurately assess the spatial relationship between forest carbon storage and relevant variables in the study area, and improve the estimation accuracy of the forest carbon storage and its spatial distribution at the regional scale.

Are human natal sex ratio differences across the world adaptive? A test of Fisher's principle

Fisher's principle states that natural selection favours an equal number of male and female births at the population level, unless there are sex differences in rearing costs or sex differences in mortality before the end of the period of parental investment. Sex differences in rearing costs should be more pronounced in low- than in high-resource settings. We, therefore, examined whether human development index and sex differences in child mortality contribute to the natural variation in human sex ratio at birth across the globe. As predicted by Fisher's principle, the proportion of male births increased with both increasing male-biased childhood mortality and level of development of each country. However, these relationships were absent after accounting for spatial autocorrelation in the residuals, which our inference is conditioned on. This work shows how the failure to account for residual spatial autocorrelation can lead to incorrect conclusions regarding support for predictions from sex allocation theory.

Creating virtual species to test species distribution models: the importance of landscape structure, dispersal and population processes

The use of virtual species to test species distribution models is important for understanding how aspects of the model development process influence model performance. Typically, virtual species are simulated by defining their niche as a function of environmental variables and simulating occurrence probabilistically via Bernoulli trials. This approach ignores endogenous processes known to drive species distribution such as dispersal and population dynamics. To understand whether these processes are important for simulating virtual species we compared the probabilistic simulation approach to those incorporating endogenous processes. This comparison was done by evaluating changes in the relationship between species occurrence and habitat suitability over a number of landscapes with varying spatial structure. We found that the combined effects of population dynamics and dispersal meant the probability of occurrence of a single cell was not only dependent on habitat suitability, but also the number of occupied cells nearby. This resulted in a dependence on the size of clusters of high suitability cells (analogous to patch size) to maintain populations, increased residual spatial autocorrelation and non‐stationarity of the species response between landscapes. These data characteristics are attributes of real species distribution data and are not present in probabilistic simulations. Researchers using virtual species should consider the importance of these characteristics to their study objectives to decide whether the inclusion of endogenous processes is necessary.