A review of techniques for spatial modeling in geographical, conservation and landscape genetics

Most evolutionary processes occur in a spatial context and several spatial analysis techniques have been employed in an exploratory context. However, the existence of autocorrelation can also perturb significance tests when data is analyzed using standard correlation and regression techniques on modeling genetic data as a function of explanatory variables. In this case, more complex models incorporating the effects of autocorrelation must be used. Here we review those models and compared their relative performances in a simple simulation, in which spatial patterns in allele frequencies were generated by a balance between random variation within populations and spatially-structured gene flow. Notwithstanding the somewhat idiosyncratic behavior of the techniques evaluated, it is clear that spatial autocorrelation affects Type I errors and that standard linear regression does not provide minimum variance estimators. Due to its flexibility, we stress that principal coordinate of neighbor matrices (PCNM) and related eigenvector mapping techniques seem to be the best approaches to spatial regression. In general, we hope that our review of commonly used spatial regression techniques in biology and ecology may aid population geneticists towards providing better explanations for population structures dealing with more complex regression problems throughout geographic space.     

Inferring population history from fine-scale spatial genetic analysis in Oryza rufipogon (Poaceae)

Determining the genetic structure of an in situ conserved population can provide insight into the dynamics of population genetic processes associated with successful plant conservation. We used 21 microsatellite loci to analyse the genetic relationships among individuals (n = 813) collected from a small Oryza rufipogon population conserved since 1993 in Hunan Province of China. The analysis revealed four distinct genetic subpopulations (F(ST) = 0.145) without geographic isolation. One subpopulation was composed of possible introgressed individuals, two subpopulations were composed of seed recruits and their descendants, and the fourth subpopulation consisted of reintroduced individuals, seed recruits and their descendants. Positive spatial genetic structures were detected by spatial autocorrelation statistics at the population (c. 63 m) and subpopulation levels (11-30 m), but the degree of autocorrelation was stronger at the population level. These results showed that prejudging the cryptic structure is important before autocorrelation analysis for the entire population. Our study suggests that population history can be a significant determinant on population structure for plant restoration projects.     

Comparison of the Mantel test and alternative approaches for detecting complex multivariate relationships in the spatial analysis of genetic data

The Mantel test is widely used to test the linear or monotonic independence of the elements in two distance matrices. It is one of the few appropriate tests when the hypothesis under study can only be formulated in terms of distances; this is often the case with genetic data. In particular, the Mantel test has been widely used to test for spatial relationship between genetic data and spatial layout of the sampling locations. We describe the domain of application of the Mantel test and derived forms. Formula development demonstrates that the sum-of-squares (SS) partitioned in Mantel tests and regression on distance matrices differs from the SS partitioned in linear correlation, regression and canonical analysis. Numerical simulations show that in tests of significance of the relationship between simple variables and multivariate data tables, the power of linear correlation, regression and canonical analysis is far greater than that of the Mantel test and derived forms, meaning that the former methods are much more likely than the latter to detect a relationship when one is present in the data. Examples of difference in power are given for the detection of spatial gradients. Furthermore, the Mantel test does not correctly estimate the proportion of the original data variation explained by spatial structures. The Mantel test should not be used as a general method for the investigation of linear relationships or spatial structures in univariate or multivariate data. Its use should be restricted to tests of hypotheses that can only be formulated in terms of distances.     

Population genetic structure of Japanese wild soybean (Glycine soja) based on microsatellite variation

The research objectives were to determine aspects of the population dynamics relevant to effective monitoring of gene flow in the soybean crop complex in Japan. Using 20 microsatellite primers, 616 individuals from 77 wild soybean (Glycine soja) populations were analysed. All samples were of small seed size (< 0.03 g), were directly collected in the field and came from all parts of Japan where wild soybeans grow, except Hokkaido. Japanese wild soybean showed significant reduction in observed heterozygosity, low outcrossing rate (mean 3.4%) and strong genetic differentiation among populations. However, the individual assignment test revealed evidence of rare long-distance seed dispersal (> 10 km) events among populations, and spatial autocorrelation analysis revealed that populations within a radius of 100 km showed a close genetic relationship to one another. When analysis of graphical ordination was applied to compare the microsatellite variation of wild soybean with that of 53 widely grown Japanese varieties of cultivated soybean (Glycine max), the primary factor of genetic differentiation was based on differences between wild and cultivated soybeans and the secondary factor was geographical differentiation of wild soybean populations. Admixture analysis revealed that 6.8% of individuals appear to show introgression from cultivated soybeans. These results indicated that population genetic structure of Japanese wild soybean is (i) strongly affected by the founder effect due to seed dispersal and inbreeding strategy, (ii) generally well differentiated from cultivated soybean, but (iii) introgression from cultivated soybean occurs. The implications of the results for the release of transgenic soybeans where wild soybeans grow are discussed.     

黄土丘陵区小流域土壤碳氮磷生态化学计量特征的空间变异性

土壤碳、氮、磷是植物重要的营养来源和保障生态系统健康的重要生态因子,其含量及化学计量比的动态平衡对生态系统的生产力具有重要影响,分析土壤碳、氮、磷养分含量及化学计量比的空间变异性和影响机制,对区域土壤养分管理以及土地可持续利用具有重要意义。本研究选取位于黄土高原东缘的三眼井小流域,利用经典统计与地统计相结合的方法,分析了研究区表层土壤(0～20 cm)有机碳(SOC)、全氮(TN)和全磷(TP)以及土壤碳氮磷的化学计量比的空间变异性和影响机制。结果表明:(1)研究区表层土壤SOC、TN和TP的平均值分别为3.97、0.83和0.6 g·kg-1,C∶N、C∶P、N∶P的平均值分别为4.73、6.02、1.26,均属于中等变异水平。(2)土地利用类型和地貌类型对研究区土壤SOC、TN具有显著影响,林地和荒草地高于梯田和退耕地,梁上高于沟谷; TP主要受土地利用类型的显著影响,梯田显著高于其他三种土地利用类型;土地利用类型对土壤C∶N、C∶P和N∶P的影响较为一致,表现为梯田显著低于其他土地利用类型; C∶N还受到坡度和地貌类型的显著影响,C∶P和N∶P还分别受到坡度和海拔的显著影响。(3...     

Soil CO2 efflux and its spatial variation in a Florida slash pine plantation

The efflux of CO2 from the soil surface can vary markedly in magnitude both in time and space and its correct determination is crucial in many ecological studies. In this paper, we report results of field measurements, using an open-top dynamic chamber, of soil CO2 efflux in a mature Florida slash pine (Pinus elliottii Engelm. var.elliottii) plantation. The daily average efflux was 0.217 mg CO2 m-2s-1 in the autumn and 0.087 mg CO2 m-2s-1 in the winter. Soil temperature, which accounts for most of the temporal variability in CO2 efflux, is by far the most influential factor controlling soil respiration rate and its temporal variation. The CO2 efflux in the slash pine plantation is highly spatially variable and effluxes from the soil under palmetto is significantly higher than that from the open floor. The CO2 efflux generally increases with increase in soil fine root biomass, litter and humus amount on the forest floor but is inversely related to the amount of organic matter in the mineral soil. The spatial variation in CO2 efflux can be well characterised by a simple multiple regression model incorporating live and dead biomass and soil total porosity as predictor variables. Understorey plants, mostly Serenoa repens, are an important component of the C cycle and the major contributor to the spatial heterogeneity of soil CO2 efflux. The influence of understorey plants on soil respiration is probably via two approaches: increasing litterfall and root metabolism, both consequently stimulating microbial activity in the mineral soil.     

The latitudinal gradient of species diversity among North American grasshoppers (Acrididae) within a single habitat: a test of the spatial heterogeneity hypothesis

Abstract. The spatial heterogeneity hypothesis predicts a positive relationship between habitat complexity and species diversity: the greater the heterogeneity of a habitat, the greater the number of species in that habitat. On a regional scale, this hypothesis has been proposed to explain the increases in species diversity from the poles to the tropics: the tropics are more diverse because they contain more habitats. On the local scale, the spatial heterogeneity hypothesis suggests that the tropics are more diverse because they contain more microhabitats. The positive relationship between habitat heterogeneity and species diversity, on the local scale, is well documented. In this paper, we test whether habitat heterogeneity on the local scale can explain the latitudinal gradient of species diversity on the regional scale. We determined the latitudinal gradient of species diversity of 305 species of North American grasshoppers using published distribution maps. We compared the slope of this multihabitat (regional-scale) gradient with the slope of a within-habitat (local-scale) gradient in the prairie grasslands. Our results show no significant difference between the slopes at the two scales. We tested the generality of our results by comparing multi- and within-habitat latitudinal gradients of species diversity for ants, scorpions and mammals using data from the literature. These results are in accordance with those from grasshoppers. We can therefore reject the local-scale spatial heterogeneity hypothesis as a mechanism explaining the regional-scale latitudinal gradient of species diversity. We discuss alternative mechanisms that produce this gradient.     

Application of a geographically-weighted regression analysis to estimate net primary production of Chinese forest ecosystems

Aim The objective of this paper is to obtain a net primary production (NPP) regression model based on the geographically weighted regression (GWR) method, which includes spatial non‐stationarity in the parameters estimated for forest ecosystems in China. Location We used data across China. Methods We examine the relationships between NPP of Chinese forest ecosystems and environmental variables, specifically altitude, temperature, precipitation and time‐integrated normalized difference vegetation index (TINDVI) based on the ordinary least squares (OLS) regression, the spatial lag model and GWR methods. Results The GWR method made significantly better predictions of NPP in simulations than did OLS, as indicated both by corrected Akaike Information Criterion (AIC_c) and R². GWR provided a value of 4891 for AIC_c and 0.66 for R², compared with 5036 and 0.58, respectively, by OLS. GWR has the potential to reveal local patterns in the spatial distribution of a parameter, which would be ignored by the OLS approach. Furthermore, OLS may provide a false general relationship between spatially non‐stationary variables. Spatial autocorrelation violates a basic assumption of the OLS method. The spatial lag model with the consideration of spatial autocorrelation had improved performance in the NPP simulation as compared with OLS (5001 for AIC_c and 0.60 for R²), but it was still not as good as that via the GWR method. Moreover, statistically significant positive spatial autocorrelation remained in the NPP residuals with the spatial lag model at small spatial scales, while no positive spatial autocorrelation across spatial scales can be found in the GWR residuals. Conclusions We conclude that the regression analysis for Chinese forest NPP with respect to environmental factors and based alternatively on OLS, the spatial lag model, and GWR methods indicated that there was a significant improvement in model performance of GWR over OLS and the spatial lag model.     

Understanding the main factors in the extent and distribution of wild boar rooting on alpine grasslands

Wild boar Sus scrofa L. rooting is a large and frequent disturbance, very extended all over the world. However, its impact in some sensitive habitats, such as alpine and subalpine grasslands remains unknown. These grasslands are considered important sites for biological conservation and traditional grazing activities, and are frequently affected by wild boar rootings. In this study, we selected three study sites representing a range of scenarios in Pyrenean alpine and subalpine grasslands, with differing protection status and grazing management. We assessed the extent of wild boar rooting, and determined the main variables that influence their distribution, taking into account the interactions among them. Our results showed that wild boar rooting significantly affected alpine and subalpine grasslands in the Pyrenees especially in protected non-hunting areas (up to 12% of the surface). The distribution of disturbed areas was influenced by a hierarchical suite of variables, among which vegetation, that is certain plant communities, was the most important. The apparent preference for dense grasslands might be associated with its soil depth, soil hardness and diversity of feeding resources. The importance of other variables, such as topography, distance to primary resources or grazing management, was site dependent. A broad understanding of the effects of variables and their relationships provide insights into the actual factors affecting the rooting selection. We hypothesize that the selection of feeding habitat, followed by the conditions of the soil to be uprooted and human management, are the main underlying factors that shape the distribution of wild boar rooting in alpine and subalpine grasslands.     

The comparative biology of diving in two genera of European Dytiscidae (Coleoptera)

Surfacing behaviour is fundamental in the ecology of aquatic air-breathing organisms; however, it is only in vertebrates that the evolutionary ecology of diving has been well characterized. Here, we explore the diving behaviour of dytiscid beetles, a key group of surface-exchanging freshwater invertebrates, by comparing the dive responses of 25 taxa (Deronectes and Ilybius spp.) acclimated at two temperatures. The allometric slopes of dive responses in these dytiscids appear similar to those of vertebrate ectotherms, supporting the notion that metabolic mode shapes the evolution of diving performance. In both genera, beetles spend more time submerged than on the surface, and surface time does not vary with the temperature of acclimation. However, presumably in order to meet increased oxygen demand at higher temperatures, Deronectes species increase surfacing frequency, whereas Ilybius species decrease dive time, an example of 'multiple solutions.' Finally, widespread northern species appear to possess higher diving performances than their geographically restricted southern relatives, something which may have contributed to their range expansion ability.     

Population structure, genetic diversity, and clone formation in Quercus chrysolepis (Fagaceae)

Stands of canyon live oak (Quercus chrysolepis, Fagaceae) are maintained for fuelwood, fire management, recreation, and as habitat for wildlife. Information about the link between the oak's reproductive ecology and its extent of genetic diversity is important in developing land management policies that will maintain the long-term viability of populations. Basal sprouting is the primary means of reproduction following fire or cutting, and stands frequently include groups of visibly connected trees in a clustered distribution that suggests cloning. We determined the extent to which clusters of trees were clonal and defined the spatial pattern and diversity of genotypes for six populations across nearly the entire east-west extent of the San Bernardino Mountains in southern California. We mapped over 100 trees at each of five sites and genotyped each tree for allozymes at seven polymorphic loci. We identified clones using these multilocus genotypes and detected an average of 34.4 ± 7.3 (SD) clones per site, most of which had unique genotypes. In general, clustered trees belong to single clones and most clones consist of few trees (mean = 3.4 ± 0.6 trees per clone). However, clone size increased significantly with increased individual heterozygosity, suggesting that selection may favor highly heterozygous clones. Clonal diversity and evenness were high relative to reports for most other clonal species; an average of 97% of clones had distinct genotypes, and Simpson's index of diversity averaged 0.95 ± 0.02. Population genetic analyses of 319 clones from six sites revealed high genetic diversity within sites (mean HS = 0.443). Only a small proportion of the total genetic diversity was explained by variation among sites (mean GST = 0.018), which is consistent with high gene flow among sites (Nm = 9.5). We found no significant substructure among plots within sites, and fixation indices within sites were generally small, suggesting that either little inbreeding occurs, and/or few inbred progeny survive. However, spatial autocorrelation analysis of clones indicated fine-scale genetic structure at distances under 4 m, possibly due to limited seed dispersal. Our data suggest that guidelines for seed collection of canyon live oak for use in restoration can be specified in a manner similar to that recommended for conifer species within the region studied.     

长鞘卷叶甲种群空间分布格局的生物地理统计学分析

应用生物地理统计学方法分析了长鞘卷叶甲成虫种群的空间分布格局,在3 m×3 m样方下建立东南→西北方向的半方差函数理论模型,并应用克立格插值方法对其种群密度和空间结构进行估计和模拟。结果表明:球状模型对长鞘卷叶甲成虫种群在该方向上的理论半方差函数有较好拟合效果,其空间分布格局为弱聚集型;成虫在山坡竹林与河岸竹林的变程分别为21.2157和38.8266 m,空间聚集分布的连续性强度分别只有0.3633和0.1758,说明种群在研究区内由空间自相关而产生的结构性变异在总变异中所占比例较小,即变异主要由种群结构的随机性成分引起。     

Pollen dispersal and genetic structure of the tropical tree Dipteryx panamensis in a fragmented Costa Rican landscape

In the face of widespread deforestation, the conservation of rainforest trees relies increasingly on their ability to maintain reproductive processes in fragmented landscapes. Here, we analysed nine microsatellite loci for 218 adults and 325 progeny of the tree Dipteryx panamensis in Costa Rica. Pollen dispersal distances, genetic diversity, genetic structure and spatial autocorrelation were determined for populations in four habitats: continuous forest, forest fragments, pastures adjacent to fragments and isolated pastures. We predicted longer but less frequent pollen movements among increasingly isolated trees. This pattern would lead to lower outcrossing rates for pasture trees, as well as lower genetic diversity and increased structure and spatial autocorrelation among their progeny. Results generally followed these expectations, with the shortest pollen dispersal among continuous forest trees (240 m), moderate distances for fragment (343 m) and adjacent pasture (317 m) populations, and distances of up to 2.3 km in isolated pastures (mean: 557 m). Variance around pollen dispersal estimates also increased with fragmentation, suggesting altered pollination conditions. Outcrossing rates were lower for pasture trees and we found greater spatial autocorrelation and genetic structure among their progeny, as well as a trend towards lower heterozygosity. Paternal reproductive dominance, the pollen contributions from individual fathers, did not vary among habitats, but we did document asymmetric pollen flow between pasture and adjacent fragment populations. We conclude that long-distance pollen dispersal helps maintain gene flow for D. panamensis in this fragmented landscape, but pasture and isolated pasture populations are still at risk of long-term genetic erosion.