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We consider a dependent thinning of a regular point process with the aim of obtaining aggregation on the large scale and regularity on the small scale in the resulting target point process of retained points. Various parametric models for the underlying processes are suggested and the properties of the target point process are studied. Simulation and inference procedures are discussed when a realization of the target point process is observed, depending on whether the thinned points are observed or not. The paper extends previous work by Dietrich Stoyan on interrupted point processes.

1. The spatial pattern of tree species retains signatures of factors and processes such as dispersal, available resource patches for establishment, competition and demographics. Comparison of the spatial pattern of different size classes can thus help to reveal the importance and characteristics of the underlying processes. However, tree dynamics may be masked by large-scale heterogeneous site conditions, e.g. when the restricting size of regeneration sites superimposes emergent patterns. 2. Here we ask how environmental heterogeneity may influence the spatial dynamics of plant communities. We compared the spatial patterns and demographics of western hemlock in a homogeneous and a heterogeneous site of old-growth Douglas-fir forests on Vancouver Island using recent techniques of point pattern analysis. We used homogeneous and inhomogeneous K- and pair-correlation functions, and case-control studies to quantify the change in spatial distribution for different size classes of western hemlock. 3. Our comparative analyses show that biological processes interacted with spatial heterogeneity, leading to qualitatively different population dynamics at the two sites. Population structure, survival and size structure of western hemlock were different in the heterogeneous stand in such a way that, compared to the homogeneous stand, seedlings were more clustered, seedling densities higher, seedling mortality lower, adult growth faster and adult mortality higher. Under homogeneous site conditions, seedling survival was mainly abiotically determined by random arrival in small gaps with limiting light. At the heterogeneous site, seedling densities and initial survival were much higher, leading to strong density-dependent mortality and selection for faster growing individuals in larger size classes. We hypothesise that the dynamics of the heterogeneous stand were faster due to asymmetric competition with disproportionate benefit to taller plants. 4. Synthesis. Our study supports the hypothesis that successional dynamics are intensified in heterogeneous forest stands with strong spatial structures and outlines the importance of spatial heterogeneity as a determinant of plant population dynamics and pattern formation.

Questions: What are the prevailing types of intraspecific spatial distributions and interspecific association patterns at species and life stage levels of trees in a tropical rain forest? Which ecological processes could structure these patterns? Possible processes include dispersal limitation, self-thinning, facilitation and competition between species and life stages. Location: A tropical broad-leaved forest in north-central Vietnam. Methods: We used univariate and bivariate pair-correlation functions to investigate the spatial distribution and association patterns of 18 abundant tree species.To disentangle first-and second-order effects, we used a scale separation approach with the heterogeneous Poisson process as null model. Results: (1) Sixteen of 18 species had aggregated patterns at various scales and regardless of their abundance. (2) Significant and aggregated patterns were found in 64% of all specific life stages. (3) At scales up to 15 m, 12.4% species pairs showed significant associations, among that 71% were spatial attractions, 5% were spatial repulsions and 24% were non-essential interactions. (4) In different life stage associations, attractions (81%) predominated over repulsions (19%) at small scales of up to 15 m. Conclusions: Our findings provide evidence that dispersal limitation may regulate the spatial patterns of tree species. Moreover, positive spatial associations between tree species and life stages suggest the presence of species herd protection and/or facilitation in this forest stand, while the persistence of intraspecific aggregation through life stages suggests a very late onset or even absence of selfthinning.Habitat heterogeneity plays an important role for species distribution patterns, and the spatial segregation occurs at a scale around 15 m in this forest.

QUESTIONS: What are the spatial patterns of adult trees and recruits in natural Picea abies forests? How are these patterns related to each other? Does the relationship differ before and after stand‐replacing disturbance? What are the ecological processes behind these spatial patterns? LOCATION: Mountain Picea abies forests in the Šumava Mts. (Bohemian Forest), Czech Republic, affected by a high‐severity outbreak of bark beetle (Ips typographus) that caused large‐scale dieback of the forest canopy. METHODS: We measured the spatial coordinates and heights of all recruits and the coordinates and DBH of all adult trees in nine plots across a wide range of recruit densities. We distinguished pre‐ and post‐disturbance recruits, trees killed by the disturbance and trees already dead before it. To analyse spatial relationship among these groups, we used univariate and bivariate pair‐correlation functions. To provide further insight into the mechanisms behind the observed patterns, we fitted Thomas and Matérn point processes to the observed data. RESULTS: Recruits formed tight clusters (2–9 m), whereas trees were distributed randomly or weakly clustered at short distances (1–2 m). Both pre‐disturbance and post‐disturbance recruits were highly clustered (cluster radii < 2 m) around trees before and after the stand–replacing disturbance. This fine‐scale pattern was likely driven by a combination of: (1) seed accumulation in tree wells during winter; (2) nurse effects of tree trunks extending the vegetation period, suppressing competitive vegetation and enhancing nutrient supply from decomposed litter; and (3) suitable seedbeds on some decaying wood. The Thomas point process fitted the observed pattern of decreasing recruit density with increasing distance from mature trees better than the Matérn process. CONCLUSIONS: Tree spatial pattern in mountain P. abies forests showed high resilience to stand‐replacing disturbance. After a self‐thinning of recruits tightly clustered around parental trees, their spatial pattern will mirror the pattern of trees that formed the stand before the disturbance. This ‘memory’ of tree spatial patterns is an important biological legacy and should be viewed as a fundamental property of natural P. abies forests.

We introduce a new multivariate product-shot-noise Cox process which is useful for modeling multi-species spatial point patterns with clustering intra-specific interactions and neutral, negative, or positive inter-specific interactions. The auto-and cross-pair correlation functions of the process can be obtained in closed analytical forms and approximate simulation of the process is straightforward. We use the proposed process to model interactions within and among five tree species in the Barro Colorado Island plot.

Tree and shrub abundance has increased in many grasslands causing changes in ecosystem carbon and nitrogen pools that are related to patterns of woody plant distribution. However, with regard to spatial patterns of shrub proliferation, little is known about how they are influenced by grazing or the extent to which they are influenced by intraspecific interactions. We addressed these questions by quantifying changes in the spatial distribution of Prosopis velutina (mesquite) shrubs over 74 years on grazed and protected grasslands. Livestock are effective agents of mesquite dispersal and mesquite plants have lateral roots extending well beyond the canopy. We therefore hypothesized that mesquite distributions would be random on grazed areas mainly due to cattle dispersion and clustered on protected areas due to decreased dispersal and interspecific interference with grasses; and that clustered or random distributions at early stages of encroachment would give way to regular distributions as stands matured and density-dependent interactions intensified. Assessments in 1932, 1948, and 2006 supported the first hypothesis, but we found no support for the second. In fact, clustering intensified with time on the protected area and the pattern remained random on the grazed site. Although shrub density increased on both areas between 1932 and 2006, we saw no progression toward a regular distribution indicative of density-dependent interactions. We propose that processes related to seed dispersal, grass-shrub seedling interactions, and hydrological constraints on shrub size interact to determine vegetation structure in grassland-to-shrubland state changes with implications for ecosystem function and management.

Fairy circles (FCs) are extremely ordered round patches of bare soil within arid grasslands of southwestern Africa and northwestern Australia. Their origin is disputed because biotic factors such as insects or abiotic factors such as edaphic and eco‐hydrological feedback mechanisms have been suggested to be causal. In this research, we used a multi‐scale approach to shed light on the origin of Australian FCs. At a local scale, we investigated the potential cause of FCs using analyses of soil compaction and texture within FCs, the surrounding matrix vegetation, and in nearby large bare‐soil areas. We found that soil hardness and clay content were similarly higher inside the FCs and in the large bare‐soil areas. When compared to the matrix soils with protective grass cover, the 2.6–2.8 times higher clay content in FCs and large bare‐soil areas is likely sourced via multiple abiotic weathering processes. Intense rainfall events, particle dispersion, surface heat, evaporation, and mechanical crust building inhibit plant growth in both areas. At the landscape scale, a systematic survey of 154 soil excavations within FCs was undertaken to evaluate the presence of pavement termitaria that could inhibit plant growth. We show that in up to 100% and most of the excavations per plot, no hard pavement termitaria were present in the FCs. This fact is substantiated by the observation that small, newly forming FCs are initiated on soft sand without evidence of termite activity. At the regional scale, we investigated the spatial properties of FCs and common termite‐created gaps in Western Australia, using spatially explicit statistics. We mapped three 25‐ha FC plots with a drone and compared them with three aerial images of typical vegetation gaps created by harvester and spinifex termites. We demonstrate that the small diameters, the lower ordering, and the heterogeneous patterns of these common termite gaps strongly differ from the unique spatial signature of FCs. Our multi‐scale approach emphasizes that FCs are not trivial termite gaps and that partial correlation with termites at some sites does not imply causation. Instead, we highlight the need to study the edaphic and eco‐hydrological drivers of vegetation‐pattern formation in water‐limited environments.

Impacts of global change, such as land-use and climate changes, could produce significant alterations in the elevational patterns of alpine tree line ecotones and their adjacent vegetation zones. Because the responses of the tree line to environmental variations are directly related to successful tree regeneration, understanding recruitment dynamics is an indispensable step in tree line research. We aimed to compare potential ecological limitations on recent tree line regeneration in undisturbed and disturbed sites by analysing the demographic structure and spatiotemporal patterns of recruits and large trees. Alpine tree line ecotones comprising Pinus uncinata in the Catalan Pyrenees (north-east Spain) and Andorra. We assessed the demographic structure and spatial pattern of recent recruitment using techniques of point-pattern and autocorrelation analyses. A total of 3639 P. uncinata individuals were mapped, measured and aged at 12 sites. To evaluate the effects of past disturbances on recent tree line response we compared tree lines that had either been recently affected by human-induced disturbances or had remained undisturbed for many years. The age structure of the tree lines, together with the lack of an age gap between seedlings and saplings, did not indicate recent episodes of high seedling mortality and suggest that recruitment has been frequent under current climate conditions. Seedlings appeared highly aggregated at short distances (up to 3 m), irrespective of disturbance history, and were spatially segregated with respect to large trees. However, we found no evidence of patches of even-aged seedlings, and our results suggest that dispersal events at intermediate distances (10-17 m) may be frequent. Autocorrelation analyses revealed different patterns of density and age of recruits between disturbed and undisturbed tree lines, but the strength and small-scale clustering of seedlings and saplings were very similar between sites. We found no recruitment limitation on recent tree line dynamics in the Pyrenees. Furthermore, processes affecting tree recruitment seem to be similar among populations regardless of their past disturbance regime. Our results suggest that constraints on tree line dynamics causing differential responses between sites may operate on older life stages and not upon recruits, and that such constraints may be more contingent on local site conditions than on disturbance history.

1 We use a grid- and simulation-based approach to extend point pattern analysis to deal with plants of finite size and irregular shape, and compare the results of our approach with that of the conventional point approximation. The plants are approximated by using an underlying grid and may occupy several adjacent grid cells depending on their size and shape. Null models correspond to that of point pattern analysis but need to be modified to account for the finite size and irregular shape of plants. 2 We use a mapped area of a grass-shrub steppe in semi-arid Patagonia, Argentina, to show that the shrub community is essentially randomly structured, but that shrubs facilitate grasses in their immediate neighbourhood. 3 The occurrence of this random spatial structure provides important new information on the biology of shrub populations. In general, previous data from semi-arid and arid ecosystems have shown that adult shrubs tend to show over-dispersed patterns, whereas juveniles are clumped. 4 We find that the point approximation may produce misleading results (i) if plant size varies greatly, (ii) if the scale of interest is of the same order of magnitude as the size of the plants, and (iii) if the plants of a given pattern are constrained through competition for space by the presence of other plants. The point approximation worked well in all other cases, but usually depicted weaker significant effects than when the size and shape of plants were taken into account. 5 Our approach to quantifying small-scale spatial patterns in plant communities has broad applications, including the study of facilitation and competition. Ecologists will be able to use the software available to take advantage of these methods.

In the analysis of spatial point patterns, an important role is played by statistical tests based on simulation envelopes, such as the envelope of simulations of Ripley's K function. Recent ecological literature has correctly pointed out a common error in the interpretation of simulation envelopes. However, this has led to a widespread belief that the tests themselves are invalid. On the contrary, envelope-based statistical tests are correct statistical procedures, under appropriate conditions. In this paper, we explain the principles of Monte Carlo tests and their correct interpretation, canvas the benefits of graphical procedures, measure the statistical performance of several popular tests, and make practical recommendations. There are several caveats including the under-recognized problem that Monte Carlo tests of goodness of fit are probably conservative if the model parameters have to be estimated from data. Finally, we discuss whether graphs of simulation envelopes can be used to infer the scale of spatial interaction.