Bias-corrected variance estimation and hypothesis testing for spatial point and marked point processes using subsampling

Summary We introduce novel regression extrapolation based methods to correct the often large bias in subsampling variance estimation as well as hypothesis testing for spatial point and marked point processes. For variance estimation, our proposed estimators are linear combinations of the usual subsampling variance estimator based on subblock sizes in a continuous interval. We show that they can achieve better rates in mean squared error than the usual subsampling variance estimator. In particular, for n×n observation windows, the optimal rate of n^?2 can be achieved if the data have a finite dependence range. For hypothesis testing, we apply the proposed regression extrapolation directly to the test statistics based on different subblock sizes, and therefore avoid the need to conduct bias correction for each element in the covariance matrix used to set up the test statistics. We assess the numerical performance of the proposed methods through simulation, and apply them to analyze a tropical forest data set.     

Tree roots as self-similar branching structures: axis differentiation and segment tapering in coarse roots of three boreal forest tree species

We applied a fractal root model to the 3D architecture of the coarse root systems of Betula pendula Roth, Picea abies (L.) H. Karst., and Pinus sylvestris L. in mixed boreal forests. Our dataset consisted of 60 root systems excavated in five different mixed forest stands. We analyzed the variability of the model parameters with respect to species, site type, and different root axes. According to our results, the cross-sectional area of root segments (i.e. second power of diameter) was a suitable variable for analyzing the values of parameters of the fractal model. The parameter values varied with generation and order of root segments; the roots thus did not follow the simple fractal branching. The variation of parameters along the root axes showed the existence of a zone of rapid tapering in all tree species. The model was, with parameter values analyzed from the data, moderately capable of accounting for the main coarse root characteristics. It was important for model predictions to take into account the tapering of root segments. We conclude that, in boreal forests, tree root systems are the output of the axis-specific morphogenetic branching rules and functional adaptation to spatial heterogeneity in the soil.     

Clustered root distribution in mature stands of <Emphasis Type="Italic">Fagus sylvatica</Emphasis> and <Emphasis Type="Italic">Picea abies</Emphasis>

Distribution of small roots (diameter between 2 mm and 5 mm) was studied in 19 pits with a total of 72 m² trench profile walls in pure stands of Fagus sylvatica and Picea abies. Root positions within the walls were marked and transformed into x-coordinates and y-coordinates. In a GIS-based evaluation, zones of potential influence around each root were calculated. The total potential influence produced isoline maps of relative root influence zones, thus indicating small root clustering. The questions studied were (1) whether there were marked clusters of small roots in the soil and (2) whether trees surrounding the pit (defined as tree density) correlate with the root abundance and distribution on the trench profile walls. Small roots of both species showed maximum abundance in the top 20 cm of the soil, where pronounced root clusters occurred next to areas with only low root accumulation. The area of root clusters did not differ significantly between the two stands. Weighted clumping, WC, calculated as a product of root class, and its area was used as an index of root clustering, which again did not differ between beech and spruce stands. However, evaluations on a single root level showed that beech achieved the same degree of clustering with lower number of roots. Regardless of soil properties related to root clusters, a significantly higher clustering acquired per root for beech than for spruce suggests beech to be more efficient in belowground acquisition of space. Because none of the parameters describing root clustering were correlated with tree density around the investigated soil profiles, clusters of small roots are inherently present within the tree stands.     

Bayesian Wombling for Spatial Point Processes

Summary In many applications involving geographically indexed data, interest focuses on identifying regions of rapid change in the spatial surface, or the related problem of the construction or testing of boundaries separating regions with markedly different observed values of the spatial variable. This process is often referred to in the literature as boundary analysis or wombling. Recent developments in hierarchical models for point‐referenced (geostatistical) and areal (lattice) data have led to corresponding statistical wombling methods, but there does not appear to be any literature on the subject in the point‐process case, where the locations themselves are assumed to be random and likelihood evaluation is notoriously difficult. We extend existing point‐level and areal wombling tools to this case, obtaining full posterior inference for multivariate spatial random effects that, when mapped, can help suggest spatial covariates still missing from the model. In the areal case we can also construct wombled maps showing significant boundaries in the fitted intensity surface, while the point‐referenced formulation permits testing the significance of a postulated boundary. In the computationally demanding point‐referenced case, our algorithm combines Monte Carlo approximants to the likelihood with a predictive process step to reduce the dimension of the problem to a manageable size. We apply these techniques to an analysis of colorectal and prostate cancer data from the northern half of Minnesota, where a key substantive concern is possible similarities in their spatial patterns, and whether they are affected by each patient's distance to facilities likely to offer helpful cancer screening options.     

Belowground drought response of European beech: fine root biomass and carbon partitioning in 14 mature stands across a precipitation gradient

How tree root systems will respond to increased drought stress, as predicted for parts of Central Europe, is not well understood. According to the optimal partitioning theory, plants should enhance root growth relative to aboveground growth in order to reduce water limitations. We tested this prediction in a transect study with 14 mature forest stands of European beech (Fagus sylvatica L.) by analysing the response of the fine root system to a large decrease in annual precipitation (970–520 mm yr⁻¹). In 3 years with contrasting precipitation regimes, we investigated leaf area and leaf biomass, fine root biomass and necromass (organic layer and mineral soil to 40 cm) and fine root productivity (ingrowth core approach), and analysed the dependence on precipitation, temperature, soil nutrient availability and stand structure. In contrast to the optimal partitioning theory, fine root biomass decreased by about a third from stands with >950 mm yr⁻¹ to those with <550 mm yr⁻¹, while leaf biomass remained constant, resulting in a significant decrease, and not an increase, in the fine root/leaf biomass ratio towards drier sites. Average fine root diameter decreased towards the drier stands, thereby partly compensating for the loss in root biomass and surface area. Both δ¹³C‐signature of fine root mass and the ingrowth core data indicated a higher fine root turnover in the drier stands. Principal components analyses (PCA) and regression analyses revealed a positive influence of precipitation on the profile total of fine root biomass in the 14 stands and a negative one of temperature and plant‐available soil phosphorus. We hypothesize that summer droughts lead to increased fine root mortality, thereby reducing root biomass, but they also stimulate compensatory fine root production in the drier stands. We conclude that the optimal partitioning theory fails to explain the observed decrease in the fine root/leaf biomass ratio, but is supported by the data if carbon allocation to roots is considered, which would account for enhanced root turnover in drier environments.     

Regeneration and coexistence of two Abies species dominating subalpine forests in central Japan

Summary The mechanism of coexistence of the dominant firs Abies veitchii and A. mariesii is described in relation to regeneration patterns for climax subalpine forests of the northern Yatsugatake Mountains, central Honshu, Japan. Two mature stand types, pure conifer stands of Abies spp., and mixed stands of Abies spp. and hardwoods (mainly the birch Betula ermanii), are distinguished. Pure stands are likely to show simultaneous decay, followed by evenaged regeneration of stand-floor seedlings (<20 cm tall), Rapidly growing A. veitchii dominates over A. mariesii in this type of regeneration, which is occasionally invaded by light-demanding Betula. In constrast, mixed stands degenerate rather slowly, followed by the regeneration of Abies from the bank of suppressed saplings (>20 cm tall), which persist only in mixed stands. The more shade-tolerant A. mariesii is supeior in this type of regeneration, while Betula does not succeed, and mixed stands change to pure stands with time. The fact that two patterns of Abies regeneration occur in a certain ratio in the forest is what enables the two Abies species to coexist. A simple dynamical system model supports this conclusion.     

Nondetection sampling bias in marked presence‐only data

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Temporal variation of competition and facilitation in mixed species forests in Central Europe

Facilitation, reduced competition or increased competition can arise in mixed stands and become essential to the performance of these stands when compared to pure stands. Facilitation and over‐yielding are widely held to prevail on poor sites, whereas neutral interactions or competition, leading to under‐yielding of mixed versus pure stands, can occur on fertile sites. While previous studies have focused on the spatial variation of mixing effects, we examine the temporal variation of facilitation and competition and its effect on growth. The study is based on tree ring measurement on cores from increment borings from 559 trees of Norway spruce (Picea abies [L.] Karst.), European beech (Fagus sylvatica [L.]) and sessile oak (Quercus petraea (Matt.) Liebl.) in southern Germany, half of which were in pure stands and half in adjacent mixed stands. Mean basal area growth indices were calculated from tree ring measurements for pure and mixed stands for every species and site. The temporal variation, with positive correlations between species‐specific growth indices during periods of low growth and neutral or negative correlations during periods of high growth, is more distinct in mixed than in neighbouring pure stands. We provide evidence that years with low growth trigger over‐yielding of trees in mixed as opposed to pure stands, while years with high growth lead to under‐yielding. We discuss the relevance of the results in terms of advancing our understanding and modelling of mixed stands, extension of the stress gradient hypothesis, and the performance of mixed versus pure stands in the face of climate change.     

重庆酸雨区马尾松纯林改造对土壤酸化特征及团聚体稳定性的影响

马尾松对酸沉降危害极其敏感,生产实践中往往通过林分改造来应对酸沉降危害。为掌握酸雨区马尾松纯林改造对土壤酸化环境的影响及科学指导经营管理,采用空间代替时间的方法,对重庆铁山坪林场的马尾松纯林及其阔叶化改造后的香樟林、木荷林、马尾松×香樟混交林和马尾松×木荷混交林土壤养分、酸化特征及团聚体稳定性进行研究。结果表明：（1）除木荷混交林的腐殖质层土壤有机碳和全氮含量显著增加外,其他森林类型总体均减少（P<0.05）;香樟林及其混交林的各层土壤全磷和全钾含量均增加,但木荷林及其混交林均减少（P<0.05）。（2）改造为香樟林及其混交林能显著提高土壤pH值、交换性盐基离子含量和盐基饱和度,降低交换性Al³⁺含量,但改造为木荷林及其混交林则总体对土壤酸化特征影响不明显（P>0.05）。（3）木荷林及其混交林淀积层的水稳性大团聚体含量增加,香樟林及其混交林则是微团聚体含量增加（P<0.05）。（4）改造对各森林类型腐殖质层和木荷林淋溶层及淀积层的土壤团聚体稳定性均无显著影响,但能增强马尾松混交林和香樟林淋溶层或淀积层的土壤团聚体稳定性（P<0.05）。综合来看,改造能改变土壤酸化环境,但各森林类型的影响不同,改造为香樟林或其混交林的改善效果总体好于木荷林或其混交林。因而对酸雨区马尾松纯林改造,还应根据改造树种特性及林分特征,科学确定相应的改造方法,尤其应注重改造林分的全过程抚育经营,以营造良好的林下环境。     

Spatial patterns on the sagebrush steppe/Western juniper ecotone

Analysis of the spatial patterns of woody plants is important to better understand the ecological processes that govern the worldwide expansion of woody plants across semi-arid ecosystems. Second-order characteristics of a marked spatial point pattern of western juniper (Juniperus occidentalis subsp. occidentalis) were analyzed using Ripley’s K-functions and the pair-correlation function g. The marked point process of crown diameters was produced via two-dimensional wavelet analysis of a fine scale aerial photograph at the woodland-steppe ecotone in the Reynolds Creek watershed in the Owyhee Mountains, southwestern Idaho. Colonization of J. occidentalis stems from mature juniper trees growing in rocky, fire resistant areas. Although these areas introduce components of natural heterogeneity within the landscape, the selected study area is situated within a single soil type, and we modeled the expansion of juniper plants into previously juniper-free sagebrush steppe as a homogeneous point process with constant intensity. Through this research we have identified two statistically significant spatial scales characteristic of J. occidentalis on the woodland/steppe ecotone: (1) We observed inhibition between J. occidentalis plants at distances <15 m, resulting in a regular pattern, rather than clumped or random. This short-distance inhibition can be attributed to competition for water and other resources. Recruitment of young J. occidentalis occurs significantly more often in a direction away from older plants, maximizing the utilization of water and light resources, and perpetuating the spread of the species into previously juniper-free shrub-steppe. (2) J. occidentalis on the ecotone exhibits significant clustering within a 30–60 m radius. Bivariate point pattern analyses provide evidence that, within a distance of 50–70 m, there is a spatial dependence in tree size such that medium trees are more likely than small trees to be close to large trees. We attribute these phenomena to the fact that juniper seeds are commonly dispersed by berry-eating birds with small territories (0.3–1 ha). Beyond a distance of 50–70 m, juniper plants are randomly distributed, suggesting that additional long-range seed dispersal processes are at work. We further acknowledge the importance of including a reference to spatial scale when formulating hypotheses in statistical analysis of spatio-temporal point patterns.     

Relationships between tree dimension and coarse root biomass in mixed stands of European beech (Fagus sylvatica L.) and Norway spruce (Picea abies[L.] Karst.)

Relationships between tree parameters above ground and the biomass of the coarse root system were examined in six mixed spruce-beech stands in the Solling Mountain region in northwest Germany. The selected stands were located on comparable sites and covered an age range of 44 to 114 years. Coarse roots (d?\ge?2 mm) of 42 spruce and 27 beech trees were sampled by excavating the entire root system. A linear model with logarithmic transformation of the variables was developed to describe the relationship between the coarse root biomass (CRB, dry weight) and the corresponding tree diameter at breast height (DBH). The coefficients of determination (R ²) attained values between 0.92 for spruce and 0.94 for beech; the logarithmic standard deviation values were between 0.29 and 0.43. A significantly different effect of tree species on the model estimates could not be detected by an analysis of co-variance (ANCOVA). For spruce, the derived relationships were similar to those reported in previous studies, but not for beech. Biomass partitioning in the tree compartments above and below ground differs significantly between spruce (coarse root/shoot ratio 0.16±0.06) and beech (coarse root/shoot ratio 0.10±0.03) in the mixed stands. These results are similar to those given in other studies involving pure spruce and beech stands on comparable sites in the region, although the ratios of pure stands in other regions growing under different site conditions are somewhat higher. Comparing trees of the same DBH classes, root/shoot ratios of spruce are 1.2 to 3 times higher than those of beech. Dominant spruce trees (DBH>60 cm) attained the highest ratios, suppressed beech trees (DBH<10 cm) the lowest. Site conditions of varying climate and soils and interspecific tree competition are likely to affect root/shoot ratio and DBH-coarse root biomass relationships. The greater variability in beech compared with spruce indicates a high 'plasticity' and adaptability of beech carbon allocation. Thus, the derived equations are useful for biomass estimates of coarse roots involving trees of different ages in mixed stands of spruce and beech in the Solling Mountains. However, application of these relationships to stands in other regions would need further testing.     

Detecting population decline of birds using long-term monitoring data

Abrupt population change in birds may be caused by various factors. When such events occur, it is important to understand the population-level impact on the species. We applied a change point analysis with Markov chain Monte Carlo using long-term population count data to address this question. We first investigated the method with a simple Poisson model using synthetic data sets for different population decline scenarios and number of observations. Estimated change points were particularly accurate when a large decline in counts occurred. Accuracy and precision of posterior change magnitude tended to increase when actual change magnitude became larger. We applied the method to two cases using data from the North American Breeding Bird Survey: epidemic mortality of Florida scrub-jays (Aphelocoma coerulescens) in central Florida and population decline of American crows (Corvus brachyrhynchos) in Maryland and Virginia after West Nile virus emergence. The Florida scrub-jay case study indicated that the estimated change point was accurate compared with that reported by local monitoring. A Poisson-log model that included observer and year variability resulted in better fit to the data than a simple Poisson model. The American crow case study showed that the method detected change points towards the end of observational data, but not all change point parameters converged, which may suggest that a population decline did not occur or was small for some survey routes we analyzed. Our study demonstrates the utility of change point analysis to examine abrupt population change. Data from systematic long-term monitoring can be a basis of such an analysis.     

植物空间分布格局中邻体距离的概率分布模型及参数估计

最近邻体法是一类有效的植物空间分布格局分析方法,邻体距离的概率分布模型用于描述邻体距离的统计特征,属于常用的最近邻体法之一。然而,聚集分布格局中邻体距离(个体到个体)的概率分布模型表达式复杂,参数估计的计算量大。根据该模型期望和方差的特性,提出了一种简化的参数估计方法,并利用遗传算法来实现参数优化,结果表明遗传算法可以有效地估计的该模型的两个参数。同时,利用该模型拟合了加拿大南温哥华岛3个寒温带树种的空间分布数据,结果显示:该概率分布模型可以很好地拟合美国花旗松(P.menziesii)和西部铁杉(T.heterophylla)的邻体距离分布,但由于西北红柏(T.plicata)存在高度聚集的团簇分布,拟合结果不理想;美国花旗松在样地中近似随机分布,空间聚集参数对空间尺度的依赖性不强,但西北红柏和西部铁杉空间聚集参数具有尺度依赖性,随邻体距离阶数增加而变大。最后,讨论了该模型以及参数估计方法的优势和限制。     

Tree species identity and forest composition affect the number of oak processionary moth captured in pheromone traps and the intensity of larval defoliation

1. Pure forests are often seen as being more prone to damage by specialist pest insects than mixed forests, and particularly mixed forests associating host and nonhost species. We addressed the effect of tree diversity on oak colonization and defoliation by a major specialist pest, the oak processionary moth (OPM)
2. We quantified the number of male OPM moths captured and larval defoliation in pure stands of two oak host species (Quercus robur and Quercus petraea) and in mixed stands associating the two oak species or each oak species with another nonhost broadleaved species. We conducted two complementary studies to test the effect of host species and stand composition: (i) we used pheromone trapping to compare the number of males OPM captured throughout the distribution of oak hosts in France and (ii) we noted the presence of OPM nests and estimated defoliation in mature forests of north‐eastern France.
3. Oak species and stand composition significantly influenced the number of male OPM captured and defoliation by OPM larvae. Quercus petraea was consistently more attractive to and more defoliated by OPM than Q. robur. Both oak trees were attacked more in pure stands than in mixed stands, in particular mixed stands associating oaks with another (nonhost) broadleaved species.
4. The results of the present study support the view that mixed forests are more resistant to specialist pest insects than pure stands, and also indicate that this trend depends on forest composition. Our study provides new insights into OPM ecology and has potential implications for forest management, including the management of urban forests where OPM causes serious human health issues.

     

Resprouting of <Emphasis Type="Italic">Echinacea angustifolia</Emphasis> Augments Sustainability of Wild Medicinal Plant Populations

Resprouting of Echinacea angustifolia Augments Sustainability of Wild Medicinal Plant Populations. Overharvest of wild Echinacea species root has been a significant concern to the herbal industry. Harvesters of wild Echinacea angustifolia showed us that even after harvesting the top 15 to 20 cm of root, some plants resprout. We marked locations of harvested plants at sites in Kansas and Montana and reexamined them two years later to see if they resprouted from remaining root reserves. Approximately 50% of the roots resprouted at both Kansas and Montana sampling sites, despite droughty weather conditions in Montana. The length of root harvested significantly affected the ability of the plant to resprout. Those plants that were more shallowly harvested and had less root length removed were more likely to resprout. These data indicate that echinacea stands can recover over time from intensive harvest if periods of nonharvest occur. Our echinacea harvest study emphasizes that the entire biology of medicinal plants must be considered when evaluating their conservation status.     

Tests for independence between marks and points of a marked point process

A convenient assumption while modeling a marked point process is that the observations (i.e., marks) and the locations (i.e., points) are independent. We propose new graphical and formal testing approaches to test for this assumption. The proposed graphical procedures are easy to obtain and can be used to diagnose the nature and range of dependence between marks and points. The formal testing procedures require only minimal conditions on marks and thus can be applied to a variety of settings. We illustrate these procedures through a simulation study and an application to some real data.     

Variation in fine root biomass of three European tree species: Beech (Fagus sylvatica L.), Norway spruce (Picea abies L. Karst.), and Scots pine (Pinus sylvestris L.)

Abstract

Fine roots (<2 mm) are very dynamic and play a key role in forest ecosystem carbon and nutrient cycling and accumulation. We reviewed root biomass data of three main European tree species European beech, (Fagus sylvatica L.), Norway spruce (Picea abies L. Karst.) and Scots pine (Pinus sylvestris L.), in order to identify the differences between species, and within and between vegetation zones, and to show the relationships between root biomass and the climatic, site and stand factors. The collected literature consisted of data from 36 beech, 71 spruce and 43 pine stands. The mean fine root biomass of beech was 389 g m^?2, and that of spruce and pine 297 g m^?2 and 277 g m^?2, respectively. Data from pine stands supported the hypothesis that root biomass is higher in the temperate than in the boreal zone. The results indicated that the root biomass of deciduous trees is higher than that of conifers. The correlations between root biomass and site fertility characteristics seemed to be species specific. There was no correlation between soil acidity and root biomass. Beech fine root biomass decreased with stand age whereas pine root biomass increased with stand age. Fine root biomass at tree level correlated better than stand level root biomass with stand characteristics. The results showed that there exists a strong relationship between the fine root biomass and the above-ground biomass.     

A point process driven multiple change point model: A robust resistant approach

Helicases are a class of enzymes involved in Ribonucleic Acid (RNA) metabolism. In this work a statistical method is proposed to analyze the individual mechanistic cycle of these motor proteins which are crucial to the understanding of their cellular functions. The RNA unwinding by NS3 helicase is hypothesized to occur in a series of discrete steps and the steps themselves occurring in accordance to an underlying point process. A point process driven multiple change point model is proposed to model the RNA unwinding mechanism. The methods are portable to other areas of applications as well. Algorithms based on robust-resistant statistical procedures are proposed to detect the change points. Both sequential and a posteriori change point models are considered. The relevant parameters of interest are estimated using a maximum likelihood approach. Simulations are performed to assess the performance of the methodology.     

Dynamics of Thuja occidentalis in an agricultural landscape of southern Quebec

Abstract. Human impact influences patterns of plant distribution and dominates disturbance dynamics in the agricultural landscape of Haut-Saint-Laurent, Québec. We investigated the influence of such impact on the dynamics of Thuja occidentalis in the hardwood forest of southern Québec. A bimodal species of either dry or wet habitats, T. occidentalis has successfully invaded mesic sites of the study area where, although generally considered a poor competitor, it persists as dense populations that seem to resist invasion by more tolerant species. As Acer saccharum is expected to be a dominant latesuccessional species under mesic conditions, we first evaluated the relative importance of abiotic and historical factors in the distribution of 34 T. occidentalis stands and 21 A. saccharum stands. We then classified 55 stands that include T. occidentalis and investigated the dynamic relationships between the species and its associates in 13 mixed mesic sites. Canonical correspondence analysis (CCA) of T. occidentalis and A. saccharum stands suggested that land use and drainage are the most important variables correlated with plant community composition. A partial CCA with drainage as the constraining variable showed that T. occidentalis stands were significantly associated to present or past use as pasture. Correspondence analysis of 55 stands where T. occidentalis is present produced a clear segregation between nearly monospecific stands and mixed communities, but the chosen environmental variables were not significant in explaining the vegetation gradient at this scale. In all mixed stands, Thuja occidentalis was most often associated with Ulmus americana, Acer rubrum, Betula populifolia, Fraxinus americana, A. saccharum, and Tsuga canadensis. Finally, size-class ordination of 13 mixed mesic stands did not show convergence toward A. saccharum. Our results suggest that grazing has played a significant part in the appearance of T. occidentalis stands on mesic sites, whereas competition processes and landscape patterns possibly contribute to the maintenance of relatively persistent T. occidentalis stands in the landscape.     

Variations in the configuration of algae in subtidal forests: Implications for invertebrate assemblages

Abstract The ecology of Australia's most extensive canopy‐forming alga, Ecklonia radiata, is often studied with little regard as to whether it occurs in monospecific stands or as part of a mixed assemblage of canopy‐forming algae. We tested the hypothesis that E. radiata does not primarily occur as monospecific stands, rather it occurs more often in stands of mixed algae. At a 1‐m² scale we recognized three main configurations within forests of algae (hereafter called stands): E. radiata that occurs as (i) monospecific stands; (ii) clumps (four or more individuals together) surrounded by species of Fucales; or (iii) individual plants (or clusters of fewer than three plants) interspersed among species of Fucales. All three types of stand occurred in similar proportions (percentage cover) across two regions of Australia's southern coastline (Western and South Australia). We also tested the hypothesis that these three types of stands (identified at 1 m²) contain different assemblages of invertebrates associated with the holdfast of E. radiata. Assemblages of invertebrates varied between monospecific and interspersed stands, but not between monospecific and clumped stands. These results suggest that variation in the configuration of subtidal algae (stands measured at a 1‐m² scale) has the potential to influence the composition and abundance of associated biota. We suggest that although studies in stands of monospecific E. radiata may provide useful information for the majority of forests containing E. radiata (monospecific and clumped stands made up 65% of forests sampled), caution must be used when extrapolating to stands of mixed, interspersed algae (>31% of forests sampled).