Generalized estimating equations approach for spatial lattice data: A case study in adoption of improved maize varieties in Mozambique

Generalized estimating equations (GEE) are extension of generalized linear models (GLM) widely applied in longitudinal data analysis. GEE are also applied in spatial data analysis using geostatistics methods. In this paper, we advocate application of GEE for spatial lattice data by modeling the spatial working correlation matrix using the Moran's index and the spatial weight matrix. We present theoretical developments and results for simulated and actual data as well. For the former case, 1,000 samples of a random variable (response variable) defined in (0, 1) interval were generated using different values of the Moran's index. In addition, 1,000 samples of a binary and a continuous variable were also randomly generated as covariates. In each sample, three structures of spatial working correlation matrices were used while modeling: The independent, autoregressive, and the Toeplitz structure. Two measures were used to evaluate the performance of each of the spatial working correlation structures: the asymptotic relative efficiency and the working correlation selection criterions. The results showed that both measures indicated that the autoregressive spatial working correlation matrix proposed in this paper presents the best performance in general. For the actual data case, the proportion of small farmers who used improved maize varieties was considered as the response variable and a set of nine variables were used as covariates. Two structures of spatial working correlation matrices were used and the results showed consistence with those obtained in the simulation study.     

Point Processes for Fine‐Scale Spatial Genetics and Molecular Ecology

This paper introduces point processes into fine‐scale spatial genetics and molecular ecology. Datasets given in the form of a complete map of individuals and their genotypes can be analyzed by means of the theory of marked or multivariate point processes. Beginning with reformulation of conventional spatial autocorrelation statistics in genetics by the language of point processes, this paper first shows an example of point process models that describe spatial patterns of both tree locations and their genotypes, on the assumption of limited seed dispersal and long pollen movement. The results show that isolation‐by‐distance slightly occurs from the assumption above, and more importantly, an increment of the degree of clustering of trees reduces the degree of genetic clustering. Next, the point process model is applied to field data of secondary forest regenerated after seed tree harvesting, and tests the hypothesis that the current population was formed only from a small number of seed trees. The hypothesis was not acceptable, instead, the alternative assuming advance reproduction conducted prior to the harvesting is supported. The results of this first trial of point process models suggest that point processes can provide a useful mathematical methodology in fine‐scale spatial genetics and molecular ecology.     

典型亚热带森林生态系统碳密度及储量空间变异特征

以浙江省森林生态系统为研究对象,基于GIS网格布点,采集了838个森林样地样本(土壤、枯落物等),结合浙江省森林资源监测中心相关数据,利用地统计学和Moran's I相结合的方法系统研究了浙江省森林生态系统碳密度及碳储量空间变异特征。结果表明:浙江省森林生态系统平均碳密度为145.22 t/hm~2,其中森林植被、土壤、枯落物和枯死木层碳密度分别为27.34、108.89、1.79、1.38 t/hm~2。克里格空间插值和局部Moran's I指数结果表明碳密度空间分布规律呈现从西南向东北方向逐渐递减的趋势,与浙江省地形、地势较为一致,受海拔、树龄、森林类型、台风气候等自然因素和人类活动共同影响。浙江省森林生态系统碳储量为877.19 Tg C,森林植被、土壤、枯落物和枯死木层碳储量分别为203.88、656.20、10.84、6.27 Tg C,分别占总碳储量的23%、75%、1.3%、0.7%。在浙江省森林生态系统碳储量空间分布格局中,土壤层是森林生态系统中最大的碳库,约是森林植被层的3.22倍,是整个浙江省森林生态系统碳储量最主要的贡献者。浙江省森林资源丰富,大多数森林仍处于中幼龄林阶段,碳密度水平较低,但是中幼龄林生长速度较快,加强对全省中幼龄林的健康管理,是未来整体提升浙江省森林生态系统固碳潜力的关键。     

乡村生态系统文化服务供需关系研究——以浙江省湖州市为例

充分利用乡村文化资源,发挥生态系统的文化服务价值,是满足新需求发展新经济、推动乡村文化振兴的重要路径。以浙江省湖州市的乡村区域为研究对象,结合地理信息数据、社会调查数据和兴趣点数据(POI),优化Maxent模型的要素评价体系,对生态系统文化服务量化制图,同时对文化服务供需水平进行空间自相关分析,确定湖州市文化服务价值的分布特征。研究结果表明：(1)湖州市乡村地区3种文化服务类型中科教人文价值最高,自然风光价值和休闲娱乐价值次之;休闲娱乐价值所占面积最大,自然风光价值和科教人文价值次之。在空间分布上,德清县北部、安吉县南部和长兴县的西北部为文化价值突出区域。(2)POI、土地利用/覆被和距道路距离是贡献度最高的3个要素,POI的应用对提高结果可靠性、提升文化服务价值制图精度有较明显的积极作用;(3)结合常住人口和旅游人口,吴兴区的大部分区域具有最高的文化服务需求,其余依次为安吉县的北部和中部、长兴县、德清县的东部、南浔区;(4)根据文化服务供需匹配关系,将湖州市乡村地区划分为发达区、需求区、潜力区、发展区,四种类别面积相对平均但分布具有较强异质性。基于供需关系视角,探索了乡村地区生态系统文化服务发展路径的研究方法,为乡村文化服务综合开发奠定理论基础。     

A statistical theory for sampling species abundances

The pattern of species abundances is central to ecology. But direct measurements of species abundances at ecologically relevant scales are typically unfeasible. This limitation has motivated a long-standing interest in the relationship between the abundance distribution in a large, regional community and the distribution observed in a small sample from the community. Here, we develop a statistical sampling theory to describe how observed patterns of species abundances are influenced by the spatial distributions of populations. For a wide range of regional-scale abundance distributions we derive exact expressions for the sampled abundance distributions, as a function of sample size and the degree of conspecific spatial aggregation. We show that if populations are randomly distributed in space then the sampled and regional-scale species-abundance distribution typically have the same functional form: sampling can be expressed by a simple scaling relationship. In the case of aggregated spatial distributions, however, the shape of a sampled species-abundance distribution diverges from the regional-scale distribution. Conspecific aggregation results in sampled distributions that are skewed towards both rare and common species. We discuss our findings in light of recent results from neutral community theory, and in the context of estimating biodiversity.     

Spatial patterns in age- and colony-specific survival in a long-lived seabird across 14 contrasting colonies

Demographic rates such as recruitment and survival probability can vary considerably among populations of the same species due to variation in underlying environmental processes. If environmental processes are spatially correlated, nearby populations are expected to have more similar demographic rates than those further apart. Breeding populations and foraging ranges are spatially segregated in colonial seabirds, making them ideal for studying spatial patterns in demographic rates and their effects on local population dynamics. Here we explored variation in age-dependent survival probabilities across 14 colonies of Herring Gulls Larus argentatus breeding along the Dutch North Sea coast. We used long-term mark–recapture data of marked fledglings to estimate survival, and estimated spatial autocorrelation of survival probabilities. We assessed whether survival until recruitment age or until 10 years old (close to their expected lifespan) explained variation in population trajectories of each colony. Juvenile and adult survival showed a strong, but different, north-to-south gradient in survival probability, with lower juvenile but higher adult survival in northern colonies than southern colonies, whereas the spatial pattern of immature survival was less distinct. Neither recruitment nor the proportion of 10-year-old adults alive predicted whether a colony collapsed, declined, remained stable or increased. The distinct spatial pattern in survival suggests variation in regional food availability, which do not seem to drive local population dynamics. The absence of a link between survival and colony trajectories implies that connectivity between populations plays an important role affecting population dynamics.     

Livestock exclusion increases the spatial heterogeneity of vegetation in Colorado shortgrass steppe

Abstract. Spatial heterogeneity, an important characteristic in semi‐arid grassland vegetation, may be altered through grazing by large herbivores. We used Moran's I, a measure of autocorrelation, to test the effect of livestock grazing on the fine scale spatial heterogeneity of dominant plant species in the shortgrass steppe of northeastern Colorado. Autocorrelation in ungrazed plots was significantly higher than in grazed plots for the cover of the dominant species Bouteloua gracilis, litter cover and density of other bunchgrasses. No species had higher autocorrelation in grazed compared to ungrazed sites. B. gracilis cover was significantly auto‐correlated in seven of eight 60‐yr ungrazed exclosures, four of six 8‐yr exclosures, and only three of eight grazed sites. Autocorrelograms showed that B. gracilis cover in ungrazed sites was frequently and positively spatially correlated at lag distances less than 5 m. B. gracilis cover was rarely autocorrelated at any sampled lag distance in grazed sites. The greater spatial heterogeneity in ungrazed sites appeared linked to patches characterized by uniformly low cover of B. gracilis and high cover of C₃ grasses. This interpretation was supported by simple simulations that modified data from grazed sites by reducing the cover of B. gracilis in patches of ca. 8 m diameter and produced patterns quite similar to those observed in ungrazed sites. In the one exclosure where we intensively sampled soil texture, autocorrelation coefficients for sand content and B. gracilis cover were similar at lag distances up to 12 m. We suggest that the negative effect of sand content on B. gracilis generates spatial heterogeneity, but only in the absence of grazing. An additional source of heterogeneity in ungrazed sites may be the negative interaction between livestock exclusion and B. gracilis recovery following patchy disturbance.     

Wide variation in a tiny space: The microdistribution of meiobenthos in an artificial pond

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森林害虫发生的空间模式研究进展

森林昆虫种群表现出多样的时空模式,空间同步性是其中最常见的。回顾了森林昆虫空间同步性的特点、形成机制及研究方法方面的进展。森林害虫发生的同步性是广泛存在的,但不同昆虫种类的同步性大小不同。空间同步性常随距离的增大而下降,还与时间尺度有关。Moran效应和扩散是解释空间同步性的两种主要机制,通常Moran效应的影响要比扩散大。从虫害发生数据的获取、同步性的度量及成因3个方面介绍了空间同步性的研究方法方面的进展。利用树轮生态学原理重建森林虫害发生历史的方法可在事后获取可靠的数据,很值得国内研究者借鉴和应用。在空间自相关度量上,空间统计学方法和地统计学方法都是非常有力的手段,但由于不能处理多时间点数据而限制了其在同步性研究中的应用。在同步性成因研究中,利用变异分解将基于距离的Moran特征向量图(dbMEM)作为空间变量研究害虫发生的驱动力是比较新颖的研究方法。     

不同斑块类型的景观指数粒度效应响应——以无锡市为例

斑块类型与景观格局粒度效应响应关系密切。以无锡市为研究区域,针对地区社会经济活动频繁、人为干扰强烈和生态脆弱等特性,以土地利用类型、热力等级和生态贡献为斑块类型划分依据,构建出对应的3种不同景观格局。在相同粒度变化情况下,选用了19个景观水平指数和Moran's I指数,分析了不同景观格局粒度效应的响应情况。结果表明,随粒度变粗:1)土地利用类型、热力等级和生态贡献斑块的部分景观指数响应曲线变化剧烈程度依次减弱;2)3类斑块的Moran's I指数均存在尺度效应。其中,土地利用类型和生态贡献斑块的Moran's I指数存在负相关,热力等级斑块没有。生态贡献斑块响应曲线在正相关区域内变化相对平缓,土地利用类型与热力等级斑块响应曲线变化趋势相反;3)指数反映的第一临界粒度基本一致,但景观指数响应曲线的临界现象更为明显。总体上,不同类型斑块在同一研究区构成的景观格局、指数响应曲线变化趋势和第一临界粒度都较为相似;斑块类型对景观指数粒度效应响应存在影响,但还有待深入探讨。     

Determinants of fine‐scale plant species richness in a deciduous forest of northeastern North America

Question: What are the determinants of fine‐scale plant species richness (SR)? Location: Île‐aux‐Grues, Québec, Canada. Methods: Elevation, soil organic matter, soil pH, irradiance, tree basal area (BA) and plant SR (herbs, shrubs, and trees) were determined in 100 contiguous 25 m² quadrats in a deciduous forest. Each variable was analysed for spatial autocorrelation using Moran's I. Path analysis was used to determine the effects of different variables on tree, shrub and herb SR in a hierarchical modelling approach. Results: Most of the variables, except tree BA, PPFD (photo‐synthetic photon flux density) and shrub SR, were positively autocorrelated at a scale of ca. 20 m or less. The path analyses explained ca. ll%‐40% of the variance in plant SR; however, the model for shrub SR was not significant. Tree SR was positively associated, but herb SR was negatively associated with tree BA. Tree SR had a positive influence on shrub SR, but herb SR remained unaffected by tree or shrub SR. Conclusion: The positive association of tree BA and tree SR suggests that the data from the study site correspond to the left (ascending) portion of the SR‐biomass relationship (un‐dersaturated SR). The negative effect of tree BA on herb SR is direct and not mediated through reduced PPFD. High tree BA might cause high resource use, induce high litter production and affect soil properties, all of which might significantly affect herb SR. Several factors not considered here might influence fine‐scale SR, such as interspecific interactions, fine‐scale disturbances and heterogeneity (both spatial and temporal) in resources and abiotic conditions. Within‐site variations of SR might be difficult to model with precision because of the relative importance of stochastic vs deterministic processes at this spatial scale.     

A novel method for estimating the number of species within a region

Ecologists are often required to estimate the number of species in a region or designated area. A number of diversity indices are available for this purpose and are based on sampling the area using quadrats or other means, and estimating the total number of species from these samples. In this paper, a novel theory and method for estimating the number of species is developed. The theory involves the use of the Laplace method for approximating asymptotic integrals. The method is shown to be successful by testing random simulated datasets. In addition, several real survey datasets are tested, including forests that contain a large number (tens to hundreds) of tree species, and an aquatic system with a large number of fish species. The method is shown to give accurate results, and in almost all cases found to be superior to existing tools for estimating diversity.     

Carbon Emission Performance of China's Power Industry: Regional Disparity and Spatial Analysis

This study employs an undesirable‐output–oriented data envelopment analysis model to measure the carbon emission performance of the power industry throughout China's 30 administrative regions during the period of 2003–2012. Also, it further studies the regional disparity and spatial correlation of the carbon emission performance of China's power industry. The main findings are as follows: (1) The carbon emission performance of China's power industry is at a relatively low level, but shows a rising trend. (2) The regional carbon emission performance of China's power industry is extremely unbalanced: The eastern area ranks first, with the highest performance of 0.851, followed by the central area, whereas the western area falls behind, with the lowest performance of 0.760. Provinces in the eastern area generally perform better than those in other areas. (3) According to spatial analysis, the global Moran's I values of carbon emission performance are significantly positive during the sample period, which indicates that the carbon emission performance is a positive spatial correlation and has an obvious clustering effect. The estimate of the local spatial autocorrelation index confirms the imbalance of spatial distribution of the power sector's carbon emission performance. Based on the above findings, several policy suggestions are presented in this article.     

Spatial ordination of vegetation data using a generalization of Wartenberg's multivariate spatial correlation

Question: Are there spatial structures in the composition of plant communities? Methods: Identification and measurement of spatial structures is a topic of great interest in plant ecology. Univariate measurements of spatial autocorrelation such as Moran's I and Geary's c are widely used, but extensions to the multivariate case (i.e. multi‐species) are rare. Here, we propose a multivariate spatial analysis based on Moran's I (MULTISPATI) by introducing a row‐sum standardized spatial weight matrix in the statistical triplet notation. This analysis, which is a generalization of Wartenberg's approach to multivariate spatial correlation, would imply a compromise between the relations among many variables (multivariate analysis) and their spatial structure (autocorrelation). MULTISPATI approach is very flexible and can handle various kinds of data (quantitative and/or qualitative data, contingency tables). A study is presented to illustrate the method using a spatial version of Correspondence Analysis. Location: Territoire d'Etude et d'Expérimentation de Trois‐Fontaines (eastern France). Results: Ordination of vegetation plots by this spatial analysis is quite robust with reference to rare species and highlights spatial patterns related to soil properties.     

Spatial patterns,hotspot, and risk assessment of heavy metals in different land uses of urban soils (case study: Malayer city)

A study on identification of hotspots, spatial patterns, and risk evaluation of heavy metals in urban soils of Malayer city (Iran) was carried out. Fifty-nine composite surface soil samples were collected from six different land uses (urban parks, streets, and squares, boulevards, residential and agricultural areas) in Malayer city, and the total heavy metals were measured by atomic absorption spectroscopy. Average concentrations of Cd, Pb, Cu, and Zn, As, Cd, and Pb were 0.66, 15.51, 12.25, and 96.8 mg/kg, respectively. Among the six land uses, heavy metal contamination was heavier for street, while low contamination could be found for residential and urban parks. The spatial distribution of Pb in surface soil was similar to those of Cd, and Cu was similar to those of Zn with decreasing values from the central areas to the suburb. Also, there were several hotspots for studied heavy metals that Cd and Pb were mainly occurred in locations of heavy traffic in the city center and Cu and Zn in the west and northwestern in the city. The calculated result of risk evaluation showed that much of the city suffered from moderate to severe pollution by four of these heavy metals.     

Small-scale spatial distributions of long-finned pilot whales change over time,but foraging hot spots are consistent: Significance for marine wildlife tourism management

Data collected opportunistically aboard marine wildlife tourism vessels are an inexpensive source of spatial information on the target species. Although these data are often challenging to analyze, they can be used to monitor spatiotemporal changes in species distribution and behavior. Disruptions from whale-watching vessels to behaviors such as foraging can be particularly harmful to cetaceans, but impacts could be reduced if areas essential for these sensitive behaviors are identified. We used data collected onboard whale-watching vessels to explore space-use patterns in long-finned pilot whales (Globicephala melas) off northern Cape Breton Island, Canada, an area where tourism is essential. Encounters with pilot whales between 2011–2016 occurred twice as far offshore than during 2003–2006 and 2008, and foraging activity decreased. Despite the changes in distribution and activity budgets, we identified two hot spots of foraging activity that persisted through time. These identified foraging hot spots comprised only a small proportion (20 km² ) of the range used by whale-watching vessels. Adaptive local management (e.g., voluntary codes of conduct) focused on limiting interactions in these energetically important areas may help reduce any potential impacts from whale-watching and promote the continued viability of the whale population and the tourism industry that relies on it.     

密云水库流域多尺度景观生态风险时空演变趋势

密云水库作为北京重要的地表饮用水水源地、水资源战略储备基地受到广泛关注,相关研究多基于流域尺度,缺乏多尺度针对水源保护区的生态风险评价,开展多尺度生态风险评价有利于指导密云水库流域高质量和可持续发展。以1990、2000、2010和2018年4期土地利用数据为基础,基于景观指数,采用地统计学方法,分析流域土地利用类型及变化,从流域尺度、水源保护区尺度构建生态风险评价模型,揭示生态风险时空变化。结果表明：(1)流域内主要土地利用类型为林地和草地,随着城市扩张和“退耕还林”等政策实施,耕地和未利用地面积减少,建设用地面积增加,流域景观趋于复杂和分散,破碎化程度加剧;(2)生态风险区域在流域尺度呈“边缘高、中间低”的空间分布规律,高风险区域面积逐渐向低风险区域转移,高风险区域集中分布在流域边缘的南部密云区、兴隆县、赤城县和流域北部丰宁县,生态安全逐渐提高。(3)水源保护区尺度呈“中间高、边缘低”的空间分布规律,高风险面积逐渐减少且空间分布集中,生态风险趋于减弱。(4)流域景观生态风险呈正相关关系,Moran’s I指数均大于0,分别为0.322、0.305、0.298和0.317,1990年...