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Articles published on Distance-decay Model

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  • Research Article
  • 10.3390/computation14050100
Micro-Macro Modeling of Inherent Cognitive Biases in 5-Point Likert Scales: Uncovering the Non-Linearity of Critical Sample Sizes for Capturing Identical Statistical Populations
  • Apr 27, 2026
  • Computation
  • Yasuko Kawahata

As social infrastructure intensively developed during the high economic growth period of the 1970s faces simultaneous aging, there is an urgent need to transition from conventional reactive maintenance to preventive maintenance utilizing various data (data-driven asset management. However, the greatest barrier in practice is that inspection data is unevenly distributed in analog formats such as paper and unstructured files, and heavily relies on the subjective visual evaluation of expert engineers (e.g., discrete graded evaluations from A to D). The intervention of this “Assessor Bias” makes it difficult to ensure the robustness required for direct statistical analysis. This paper serves as a bridge between this analog expert knowledge and quantitative data science. It formulates human cognitive conflicts (true state, peer pressure, avoidance of cognitive load) using the distance-decay model of the Analytic Hierarchy Process (AHP) and the Softmax function, constructing a micro-macro link model accompanied by stochastic variations. Through large-scale multi-agent simulations (N=107) validating the model’s convergence, it was demonstrated that in long-tail distributions formed under peer pressure, macroscopic statistical distance metrics such as the Kullback-Leibler (KL) divergence ignore the fact that a small number of true signals are non-linearly suppressed, causing a statistical misinterpretation that “the error is within an acceptable range”. This implies that as long as macroscopic statistical indicators are over-trusted, signs of critical deterioration (minorities) will be structurally marginalized. Returning to the debate on “Homogeneity (Homogenität)” in German social statistics, this paper advocates that in order to realize objective “Micro-segmentation of Homogeneous Statistical Populations,” a paradigm shift from qualitative methods relying on human intuition to quantitative methods incorporating multi-criteria decision making is essential, rather than simply expanding the sample size.

  • Research Article
  • 10.1016/j.envres.2025.123027
Prenatal pesticide exposure and neuroblastoma - A statewide case-control study in California.
  • Dec 1, 2025
  • Environmental research
  • Darcy Van Deventer + 3 more

Prenatal pesticide exposure and neuroblastoma - A statewide case-control study in California.

  • Research Article
  • Cite Count Icon 1
  • 10.3390/buildings15101686
Which Distance-Decay Function Can Improve the Goodness of Fit of the Metro Station Ridership Regression Model? A Case Study of Beijing
  • May 16, 2025
  • Buildings
  • Zhenbao Wang + 2 more

Incorporating the distance-decay effects of facility points into the analysis of metro ridership helps generate more precise and actionable strategies for station area renewal. The majority of existing studies, however, calculated the built environment variables based on the same pedestrian catchment areas (PCAs) of metro stations and failed to consider the impact of distance decay from POIs (points of interest) on the accuracy of metro station ridership regression models. The objective of this study is to determine which distance-decay function best improves the fit of the metro ridership regression model and investigate the effect of the built environment on ridership under the optimal distance-decay model. Based on the distribution density of metro stations in Beijing, the research area is divided into three zones with different PCAs. Built environment variables for all metro stations are aggregated according to the PCA scope. Various distance-decay functions are examined to determine how the accuracy of the Multi-scale Geographically Weighted Regression (MGWR) model is affected by built environment variables calculated from POI facilities (Gaussian distance decay, power distance decay, piecewise distance decay). Finally, under optimal distance decay, the MGWR model is used to investigate how the built environment influences metro ridership. The results show the following: (1) The Gaussian distance-decay function improves the goodness of fit of the regression model, resulting in an 11.25% increase in the R2 value when compared to the model without a distance-decay function. (2) During morning peak hours, apartment and office density significantly impacts ridership. The proposed research framework is conducive to improving the accuracy of the metro station ridership regression model. Moreover, it facilitates the formulation of targeted strategies for the renewal of the built environment by government managers and planners.

  • Research Article
  • Cite Count Icon 2
  • 10.1016/j.reseneeco.2024.101472
Does quantity matter for distance decay? Evidence from two choice experiments on urban green
  • Feb 1, 2025
  • Resource and Energy Economics
  • Malte Welling + 3 more

The value of environmental goods to individuals often depends on spatial features such as distance. The most common approach of accounting for distance decay is to model utility as some function of distance. It has been suggested to instead model the value as a function of the quantity of an environmental good within a certain distance. We develop three novel quantity-within-distance models that may be more suited for evaluating quantity changes in an environmental good. We argue that these models could capture spatial patterns better than distance-based models when i) secondary benefits are a relevant source of welfare, ii) the environmental change is spatially scattered, iii) the distribution of the endowment, i.e. the present availability of the environmental good, matters. Using data from choice experiments on the extension of green space and trees in two urban areas, we compare required assumptions, model fit, and size and precision of aggregated welfare estimates. Our results indicate limited differences in model fit. However, the quantity-within-distance models consistently produce aggregate welfare estimates roughly half of common distance decay models and have narrower confidence intervals. While it is not possible to infer which is more accurate, the large differences can have considerable policy implications.

  • Research Article
  • Cite Count Icon 1
  • 10.1080/13683500.2024.2416024
Discovering implicit role of tourists’ perceived distance and emotions in decision-making: combining grounded theory and sentiment analysis
  • Oct 16, 2024
  • Current Issues in Tourism
  • Yewei Shang + 2 more

ABSTRACT Analysing the attitudes and emotions behind tourists’ perceptions of distance provides powerful assistance for destination marketers and scholars. However, there is yet to be a universally adopted scale of tourists’ perceived distance. It is hard to effectively extract tourists’ attitudes from the distance scale toward a destination. This paper identifies the critical dimensions of perceived distance voiced by 19 Chinese tourists with grounded analysis, an inductive, comparative, and interactive method that effectively captures nuanced information. Advanced techniques for linguistic analysis provide the opportunity to extract emotional meaning from tourists’ textual data through the Latent Dirichlet Allocation (LDA) algorithm. The results identify a set of appraisal dimensions as antecedents to perceived distance. With cognitive appraisal theory (CAT), different evaluations on these dimensions provide multiple paths to eliciting emotion change. The findings contrast with previous research in the distance decay model, which noted a single distance involving tourism demand. We also find differences based on demographic segments. Social network analysis helps further identify the relationship between dimensions. We conclude by discussing the study's implications for future studies and practice.

  • Research Article
  • Cite Count Icon 4
  • 10.3389/feart.2024.1432037
Study on the ecosystem service flow based on the relationship of between supply and demand in Yangtze River Economic Belt
  • Oct 2, 2024
  • Frontiers in Earth Science
  • Ming Lei + 6 more

Ecosystems supply goods and services to humans and are the basis for sustainable development of human society. The study of the supply of ecosystem services and the demand and consumption of ecosystem services by human society, and the analysis of the supply and demand characteristics and flow relationships of ecosystem service flows are of great significance for the management of regional ecosystems and the development of ecological compensation. Taking the Yangtze River Economic Belt as an example, this paper calculates the supply and demand indices of ecosystem services in 2015 and 2020, and determines the ecosystem spatial flow paths and flow volumes from the ecosystem supply area to the demand area based on various methods and models such as the minimum cumulative resistance (MCR) model and distance decay model. The results indicate that 1). In 2015 and 2020, the supply and demand of ecosystem services in the Yangtze River Economic Zone show an increasing trend numerically, and there is spatial heterogeneity in the spatial distribution. In terms of ecosystem service supply per unit area, the midstream region is higher than the upstream and downstream regions. In terms of the demand for ecosystem services per unit area, the downstream is higher than the midstream and upstream. 2). From the supply-demand balance of ecosystem services in the Yangtze River Economic Zone, the midstream region is mainly the area of surplus supply of ecosystem services, and the downstream region is mainly the area of deficit supply. From 2015 to 2020, the number of areas with balanced supply and demand of ecosystem services in the Yangtze River Economic Belt decreases and the number of areas with unbalanced supply and demand increases, which is related to the changes in the level of economic development and land use patterns. 3). The flow of ecosystem services in the Yangtze River Economic Belt shows an increasing trend, from 726.59 billion yuan in 2015 to 1,450.54 billion yuan in 2020, with Jiangxi Province being the main ecosystem service supply area and Zhejiang Province being the main ecosystem service demand area in the Yangtze River Economic Belt.

  • Research Article
  • Cite Count Icon 2
  • 10.3390/su16188021
Land Cover and Spatial Distribution of Surface Water Loss Hotspots in Italy
  • Sep 13, 2024
  • Sustainability
  • Irene Palazzoli + 2 more

Increasing water withdrawals and changes in land cover/use are critically altering surface water bodies, often causing a noticeable reduction in their area. Such anthropogenic modification of surface waters needs to be thoroughly examined to recognize the dynamics through which humans affect the loss of surface water. By leveraging remotely-sensed data and employing a distance–decay model, we investigate the loss of surface water resources that occurred in Italy between 1984 and 2021 and explore its association with land cover change and potential human pressure. In particular, we first estimate the land cover conversion across locations experiencing surface water loss. Next, we identify and analytically model the influence of irrigated and built-up areas, which heavily rely on surface waters, on the spatial distribution of surface water losses across river basin districts and river basins in Italy. Our results reveal that surface water losses are mainly located in northern Italy, where they have been primarily replaced by cropland and vegetation. As expected, we find that surface water losses tend to be more concentrated in the proximity of both irrigated and built-up areas yet showing differences in their spatial occurrence and extent. These observed spatial patterns are well captured by our analytical model, which outlines the predominant role of irrigated areas, mainly across northern Italy and Sicily, and more dominant effects of built-up areas across the Apennines and in Sardinia. By highlighting land cover patterns following the loss of surface water and evaluating the relative distribution of surface water losses with respect to areas of human pressure, our analysis provides key information that could support water management and prevent future conditions of water scarcity due to unsustainable water exploitation.

  • Research Article
  • 10.3390/f15081368
Interference Effect of Tree Spacing on Natural Volatile Organic Compound Concentrations Measured Using Passive Samplers
  • Aug 6, 2024
  • Forests
  • Doyun Song + 4 more

Research highlights: The increasing rates of mental health disorders during the COVID-19 pandemic have popularized the notion of access to natural environments as a solution, leading to a surge in demand for urban green spaces. The concentration of natural volatile organic compounds (NVOCs) in forests, resulting from plant metabolism, plays a crucial role in forest-based healing and ecosystem health. Background and objectives: This study aimed to investigate how tree spacing influences NVOC concentrations within forest ecosystems using passive samplers, thereby enhancing the understanding of optimal forest management practices to promote human health benefits. Methods: We employed passive samplers to investigate tree spacing effects on NVOC concentrations. We placed passive samplers among trees in the study area to measure NVOC concentrations in individual trees and analyzed the relationship between NVOC concentration and tree spacing and structure. Results: A multiple regression analysis using distance decay models showed that a tree spacing of 2.7–3 m had a significant impact on NVOC concentrations. These findings provide a better understanding of how tree structure, tree spacing, and microclimate within the forest influence NVOC concentration. Conclusion: These findings have important implications for forest management and the design of forest landscapes to promote human health and well-being by considering the spatial distribution of NVOC concentrations.

  • Research Article
  • Cite Count Icon 17
  • 10.1016/j.jhazmat.2024.135255
Heterogenization of microplastic communities in lakes of the Qinghai-Tibetan Plateau driven by tourism and transport activities
  • Jul 17, 2024
  • Journal of Hazardous Materials
  • Xu Han + 6 more

Heterogenization of microplastic communities in lakes of the Qinghai-Tibetan Plateau driven by tourism and transport activities

  • Research Article
  • Cite Count Icon 10
  • 10.1111/brv.13109
Models of bee responses to land use and land cover changes in agricultural landscapes - a review and research agenda.
  • Jun 28, 2024
  • Biological reviews of the Cambridge Philosophical Society
  • Abdelhak Rouabah + 3 more

Predictive modelling tools can be used to support the design of agricultural landscapes to promote pollinator biodiversity and pollination services. Despite the proliferation of such modelling tools in recent decades, there remains a gap in synthesising their main characteristics and representation capacities. Here, we reviewed 42 studies that developed non-correlative models to explore the impact of land use and land cover changes on bee populations, and synthesised information about the modelled systems, modelling approaches, and key model characteristics like spatiotemporal extent and resolution. Various modelling approaches are employed to predict the biodiversity of bees and the pollination services they provide, with a prevalence of models focusing on wild populations compared to managed ones. Of these models, landscape indicators and distance decay models are relatively simple, with few parameters. They allow mapping bee visitation probabilities using basic land cover data and considering bee foraging ranges. Conversely, mechanistic or agent-based models delineate, with varying degrees of complexity, a multitude of processes that characterise, among others, the foraging behaviour and population dynamics of bees. The reviewed models collectively encompass 38 ecological, agronomic, and economic processes, producing various outputs including bee abundance, habitat visitation rate, and crop yield. To advance the development of predictive modelling tools aimed at fostering pollinator biodiversity and pollination services in agricultural landscapes, we highlight future avenues for increasing biophysical realism in models predicting the impact of land use and land cover changes on bees. Additionally, we address the challenges associated with balancing model complexity and practical usability.

  • Open Access Icon
  • Research Article
  • Cite Count Icon 4
  • 10.1111/geb.13837
Ectomycorrhizal fungi are influenced by ecoregion boundaries across Europe
  • Apr 5, 2024
  • Global Ecology and Biogeography
  • Guillaume Delhaye + 5 more

Abstract AimEcoregions and the distance decay in community similarity are fundamental concepts in biogeography and conservation biology that are well supported across plants and animals, but not fungi. Here we test the relevance of these concepts for ectomycorrhizal (ECM) fungi in temperate and boreal regions.LocationEurope.Time Period2008–2015.Major Taxa StudiedEctomycorrhizal fungi.MethodsWe used a large dataset of ~24,000 ectomycorrhizas, assigned to 1350 operational taxonomic units, collected from 129 forest plots via a standardized protocol. We investigated the relevance of ecoregion delimitations for ECM fungi through complementary methodological approaches based on distance decay models, multivariate analyses and indicator species analyses. We then evaluated the effects of host tree and climate on the observed biogeographical distributions.ResultsEcoregions predict large‐scale ECM fungal biodiversity patterns. This is partly explained by climate differences between ecoregions but independent from host tree distribution. Basidiomycetes in the orders Russulales and Atheliales and producing epigeous fruiting bodies, with potentially short‐distance dispersal, show the best agreement with ecoregion boundaries. Host tree distribution and fungal abundance (as opposed to presence/absence only) are important to uncover biogeographical patterns in mycorrhizas.Main ConclusionsEcoregions are useful units to investigate eco‐evolutionary processes in mycorrhizal fungal communities and for conservation decision‐making that includes fungi.

  • Research Article
  • Cite Count Icon 3
  • 10.1093/ismeco/ycae119
Imbalanced intracellular nutrient stoichiometries drive the regional structural variation of microeukaryotic communities in paddy fields.
  • Jan 8, 2024
  • ISME communications
  • Pengfei Sun + 3 more

Periphytons serve as critical microbial nutrient sinks at the soil-water interface, influencing biogeochemical cycles and nutrient migration in paddy fields. Despite their importance, the impact of accumulated intracellular nutrients on the spatial dynamics and community assembly of periphytons, particularly their microeukaryote communities, remains unclear. To address this gap, we examined the nutrient accumulation potential and its effects on microeukaryotes in periphytons from 220 paddy fields spanning up to 3469km across three temperature zones. Our study reveals that the periphytons exhibit varying capacities to accumulate carbon, nitrogen, and phosphorus, leading to imbalanced intracellular nutrient stoichiometries (carbon-to-nitrogen ratio = 10.3 ± 2.1, carbon-to-phosphorus ratio = 30.9 ± 13.1, nitrogen-to-phosphorus ratio = 3.1 ± 1.3). This stoichiometric imbalance induces intracellular environmental heterogeneity, which partially influences the local species richness of microeukaryotic communities and their regional structural variations on a large scale. Contrary to the typical latitudinal diversity gradient theory, local microeukaryotic species richness follows a distance-decay model, with both deterministic and stochastic processes contributing to community assembly. These results underscore the complex interplay of environmental filtering, species interactions, and dispersal dynamics in shaping the structure and adaptability of microeukaryotic communities within periphytons. This study contributes to a broader understanding of the factors driving regional structural variations of microeukaryotes at the soil-water interface in agricultural landscapes.

  • Research Article
  • Cite Count Icon 19
  • 10.1016/j.avrs.2024.100170
Deterministic processes drive turnover-dominated beta diversity of breeding birds along the central Himalayan elevation gradient
  • Jan 1, 2024
  • Avian Research
  • Zhifeng Ding + 5 more

Deterministic processes drive turnover-dominated beta diversity of breeding birds along the central Himalayan elevation gradient

  • Research Article
  • Cite Count Icon 16
  • 10.1016/j.tre.2023.103390
Exploring the distance decay in port hinterlands under port regionalization using truck GPS data
  • Dec 8, 2023
  • Transportation Research Part E: Logistics and Transportation Review
  • Zhangyuan He + 5 more

Exploring the distance decay in port hinterlands under port regionalization using truck GPS data

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  • Research Article
  • Cite Count Icon 9
  • 10.1038/s41598-023-48440-7
Regional climate contributes more than geographic distance to beta diversity of copepods (Crustacea Copepoda) between caves of Italy
  • Dec 1, 2023
  • Scientific Reports
  • Emma Galmarini + 8 more

Despite the study of subterranean biodiversity facing harsh sampling and mapping challenges, the huge diversity of taxa, ecological adaptations and evolutionary trajectories in subterranean environments is gaining increasing attention. Yet, the spatial and environmental factors driving the composition of groundwater communities are still poorly understood. To partially fill this knowledge gap, we collected copepod crustaceans from 12 caves along the Italian peninsula between 2019 and 2022, sampling each cave twice. The resulting presence-absence data were analysed to assess: (i) between-cave taxonomic beta diversity, also partitioning between turnover and nestedness-resultant dissimilarity; (ii) the relative weight of geographic distance and climatic differences in shaping observed beta diversity. Seventy-one species of copepods were collected overall. Pairwise beta diversity was high for most pairs of caves, with turnover being the major component. Geographic distance-decay models partially explained total beta diversity and turnover patterns. However, in Generalized Dissimilarity Models (GDM), including surface climatic conditions as predictors, the contribution of seasonal temperature averages was generally higher than that of geographic distance. Further, the explanatory and predictive performance of the GDMs notably increased, along with temperature contribution, when widening the spatial extent from which climate data were gathered. Our results confirmed a high spatial turnover in groundwater copepods’ assemblages and strengthened the link between regional climate and subterranean biodiversity.

  • PDF Download Icon
  • Research Article
  • 10.1002/ldr.4778
Moderation and mediation of land use change! Interplay between β‐diversity and landscape structures in agri‐ and silvicultural modified grasslands of South America
  • Jun 7, 2023
  • Land Degradation & Development
  • Leonardo R Ramírez + 1 more

Abstract Although land use change is the main driver of biodiversity decline in the South American temperate grasslands, its impacts on β‐diversity have not yet been evaluated. We investigated relationships between β‐diversity, landscape features, and geographical variables by surveying vegetation from 163 plots distributed in eight different land use types in Uruguay. We created land use maps using Landsat images and calculated landscape metrics, determining β‐diversity across all plots and exploring variation of β‐diversity among different land use types. We ran distance decay models to explore relationships between β‐diversity and geographical location, climate, and landscape metrics. Plant species communities were characterized by a high turnover and low nestedness of species, indicating high dissimilarity across Uruguay. Native forest showed higher β‐diversity than grassland, timber plantation, and crops. β‐diversity increased with geographical distance and environmental dissimilarity. At landscape scale, turnover decreased negatively and nestedness increased to contagion, number of patches, and area‐weighted mean. Nestedness increased with timber plantation and species turnover with crop area. Higher Landscape Shape Index of grassland and crops decreased species turnover. An increase of grassland and crop patches in the surrounding landscape was directly related to a higher species turnover. The high β‐diversity across Uruguay resulting from land use change, moderated by landscape configurations, suggests that numerous protected areas for different habitats are urgently required. A more inclusive vision on biodiversity conservation is necessary, extending the predominant focus from native forests to grasslands, and convincing a broad range of stakeholders, especially landowners and managers, about biodiversity‐friendly land‐use approaches.

  • Research Article
  • Cite Count Icon 14
  • 10.1109/mits.2022.3207411
High-Speed Rail Station Location Optimization Using Customized Utility Functions
  • May 1, 2023
  • IEEE Intelligent Transportation Systems Magazine
  • Sandeepan Roy + 1 more

High-speed rail station location (HSR-SL) is a complex problem with multiple conflicting factors, such as local transportation network connectivity, regional accessibility, downtown proximity, and feasibility. The proposed novel methodology quantified these factors using customized nonlinear, linear, or integer utility functions. Suitable distance decay models to quantify the local transport access to and from existing bus stops, train stations, and downtown proximity; a gravity model for potential regional accessibility to the residential population or workforce; linear models for connectivity with the existing public transit routes and normalized land cost; and a binary model with a threshold value for geographical feasibility in terms of environmental sensitivity were developed. These models were evaluated using a geospatial and network analysis-based approach, and the overall nonlinear HSR-SL problem was optimized using the particle swarm optimization algorithm. The results of a real-world study area in downtown Tokyo, Japan, revealed that customized utility functions for various factors reduced the possibility of over- or underestimation and the selection of suboptimal SLs. The proposed method improved estimation of the land cost feasibility, access to transfer points, and connectivity by 100%, 185%, and 222%, respectively, for the given case study. It was most sensitive to connectivity and proximity to the downtown area, followed by location cost, transportation access, and population or workforce potential accessibility.

  • Research Article
  • Cite Count Icon 48
  • 10.1016/j.jenvman.2023.118011
Homogenization of microplastics in alpine rivers: Analysis of microplastic abundance and characteristics in rivers of Qilian Mountain, China
  • Apr 26, 2023
  • Journal of Environmental Management
  • Qian Liu + 7 more

Homogenization of microplastics in alpine rivers: Analysis of microplastic abundance and characteristics in rivers of Qilian Mountain, China

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  • Research Article
  • Cite Count Icon 16
  • 10.1016/j.geoderma.2023.116447
Soil salinity determines the assembly of endophytic bacterial communities in the roots but not leaves of halophytes in a river delta ecosystem
  • Mar 31, 2023
  • Geoderma
  • Yi Zhou + 9 more

Although soil and rhizosphere microbiomes in highly saline environments have been well-studied, the role of soil salinity in the ecological processes affecting endophyte colonization and persistence remain largely unclear in halophytic plants. The present study sampled young and mature plants of the halophyte Suaeda salsa from 42 sites in the Yellow River Delta, China that varied in soil salinity. Soil physicochemical properties, root and leaf microbiomes, phylogenetic variation among plant ecotypes, and leaf metabolites were analysed. In the roots of both young and mature plants, soil salinity significantly influenced the composition of the endophytic microbiota (r = 0.29 ∼ 0.45, P < 0.001), and negatively correlated with endophyte alpha-diversity (r = -0.75 ∼ -0.78, P < 0.001). Leaf microbiome dissimilarity increased with geographic distance (r = 0.17 ∼ 0.26, P < 0.001), based on a distance-decay model, and was associated with plant phylogenetic variation (r = 0.15, P = 0.015 for young plants only). Additionally, leaf microbiome diversity and composition were correlated with soil age, pH, P content, and certain leaf metabolite compounds, but not with soil salinity. The dominant genera observed in young roots were Mesorhizobium spp. and Rhodomicrobium spp., while Pelagibius spp. was dominant in mature roots, and Pseudomonas spp. and Kushneria spp. were dominant in leaves. Soil salinity exerted a strong deterministic effect on the diversity and composition of the root endophyte community, while the acquisition and assembly of the leaf microbiome was affected by the dispersal effects, and the leaf metabolism of the host halophyte.

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  • Research Article
  • Cite Count Icon 9
  • 10.1016/j.ecoinf.2022.101894
Comparing distance-decay parameters: A novel test under pairwise dependence
  • Nov 11, 2022
  • Ecological Informatics
  • Ramiro Martín-Devasa + 4 more

Distance-decay models fit parametric functions to assess the relationship between similarity and spatial or environmental distance. Despite the widespread use of distance-decay models in ecology and biogeography, no method has been previously developed and validated to assess the significance of differences between the parameters (i.e. intercept and slope) of two distance-decay models. The pairwise autocorrelation of similarity and spatial distance affects the variance of parameter estimates, precluding the use of ordinary t-tests. Here, we provide a test statistic (zdep) for the equality of parameters between two distance-decay models. The test can be applied, independently, to any of the model parameters (i.e. intercept and/or slopes). The zdep statistic accounts for pairwise dependence, thus avoiding biases associated to the inflation of degrees of freedom, and it is based on the estimation of parameters' variance using site-block resampling. To validate the zdep statistic, type I and type II errors were empirically evaluated through a simulation study. We simulated six scenarios (three under the null and three under the alternative hypothesis) of distance-decay relationships using different functions: negative exponential, power-law or Gompertz function. We applied the zdep statistic and computed the proportion of rejections of the null hypothesis for α = 0.01, 0.05 and 0.1 in each scenario. As a case-study, we also compared distance-decay parameters across several groups of Iberian vertebrates (cyprinids, frogs, lizards and snakes, bats, rodents and carnivores). In the simulation study, the zdep statistic showed a good approximation of the nominal level (α, type I error) and a good statistical power (1 − type II error), the later increasing with sample size, as expected. In Iberian vertebrates, we found significant differences between ectotherms and endotherms, but not within these groups except between cyprinids and other ectotherms. The good performance of the zdep statistic makes it the best option to test for differences in parameters obtained from models fitted from data with pairwise dependence, as distance-decay models. It can also be used beyond distance-decay approaches to compare parameters of any other regression models of pairwise dependent data (as genetic distances, for example).

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