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1. Declines of large vertebrates in tropical forests may reduce dispersal of tree species that rely on them, and the resulting undispersed seedlings might suffer increased distance- and density-dependent mortality. Consequently, extirpation of large vertebrates may alter the composition and spatial structure of plant communities and impair ecosystem functions like carbon storage. 2. We analysed spatial patterns of tree recruitment within six forest plots along a defaunation gradient in western Amazonia. We divided recruits into two size cohorts (\"saplings\": ≤1 m tall and <1 cm diameter at breast height [dbh], and juveniles, 1-2 cm dbh) and examined the spatial organisation of conspecific recruits within each cohort (within-cohort) and around conspecific reproductive-sized trees (between-cohort). We used replicated spatial point pattern analysis to quantify relationships between recruit clustering and cohort, defaunation intensity, each tree species reliance on hunted dispersers and the interactions among these three covariates. 3. Within-cohort clustering of conspecific saplings increased with reliance of tree species on hunted dispersers, and this trend strengthened significantly as defaunation increased, probably because of reduced dispersal. 4. Within-cohort clustering of conspecifics declined from saplings to juveniles, suggesting density-dependent mortality of saplings. However, the positive relationship between sapling clustering and defaunation did not lead to greater reductions in within-cohort clustering during the sapling-juvenile transition, suggesting that higher conspecific densities did not translate into increased mortality. Instead, the increased spatial clustering associated with defaunation was retained for juvenile recruits. 5. Between-cohort clustering was unrelated to defaunation and did not change during the sapling–juvenile transition. 6. Synthesis. Defaunation increased spatial aggregation of saplings of tree species reliant on hunted dispersers. The increase in sapling clustering did not increase density-dependent thinning, and persisted into older recruit cohorts, suggesting that hunting may initiate long-term spatial reorganisation of Amazonian tree communities. The lack of increased density-dependent thinning indicates that reduced dispersal did not increase mortality of large-vertebrate dispersed tree species that contribute disproportionately to forest biomass. We, therefore, caution against the fait accompli acceptance of the prediction by recent modelling studies that overhunting will precipitate a collapse in carbon sequestration by tropical forests.

The biggest problem when analyzing the brain is that its synaptic connections are extremely complex. Generally, the billions of neurons making up the brain exchange information through two types of highly specialized structures: chemical synapses (the vast majority) and so-called gap junctions (a substrate of one class of electrical synapse). Here we are interested in exploring the three-dimensional spatial distribution of chemical synapses in the cerebral cortex. Recent research has showed that the three-dimensional spatial distribution of synapses in layer III of the neocortex can be modeled by a random sequential adsorption (RSA) point process, i.e., synapses are distributed in space almost randomly, with the only constraint that they cannot overlap. In this study we hypothesize that RSA processes can also explain the distribution of synapses in all cortical layers. We also investigate whether there are differences in both the synaptic density and spatial distribution of synapses between layers. Using combined focused ion beam milling and scanning electron microscopy (FIB/SEM), we obtained three-dimensional samples from the six layers of the rat somatosensory cortex and identified and reconstructed the synaptic junctions. A total volume of tissue of approximately 4500μm(3) and around 4000 synapses from three different animals were analyzed. Different samples, layers and/or animals were aggregated and compared using RSA replicated spatial point processes. The results showed no significant differences in the synaptic distribution across the different rats used in the study. We found that RSA processes described the spatial distribution of synapses in all samples of each layer. We also found that the synaptic distribution in layers II to VI conforms to a common underlying RSA process with different densities per layer. Interestingly, the results showed that synapses in layer I had a slightly different spatial distribution from the other layers.

The paper compares non-parametric (design-based) and parametric (model-based) approaches to the analysis of data in the form of replicated spatial point patterns in two or more experimental groups. Basic questions for data of this kind concern estimating the properties of the underlying spatial point process within each experimental group, and comparing the properties between groups. A non-parametric approach, building on work by Diggle et. al. (1991), summarizes each pattern by an estimate of the reduced second moment measure or K-function (Ripley (1977)) and compares mean K-functions between experimental groups using a bootstrap testing procedure. A parametric approach fits particular classes of parametric model to the data, uses the model parameter estimates as summaries and tests for differences between groups by comparing fits with and without the assumption of common parameter values across groups. The paper discusses how either approach can be implemented in the specific context of a single-factor replicated experiment and uses simulations to show how the parametric approach can be more efficient when the underlying model assumptions hold, but potentially misleading otherwise.

Neuropathological studies frequently determine the positions of cells on multiple brain tissue sections taken from multiple individuals. Interest arises in group comparisons of the spatial dependencies between cells, in particular the spatial dependencies of a single cell type (clustering or regularity as measured by the univariate K-function), or the spatial interaction of two different cell types (attraction or repulsion as measured by the bivariate K-function). While the nonparametric statistical analysis of spatial dependencies in the one-way design is fairly well-established, investigations often employ more complex designs. In this paper we develop a residual bootstrapping approach for K-functions arising from a general repeated measures design by assuming an underlying linear mixed-effects model. We illustrate our methodology by re-analysing the spatial interaction between neurons and astrocytes (brain cells that are functionally related to neurons) in a study of HIV associated dementia.

Factorial experiments are well-understood when the given observations are outcomes of random variables. However, when we observe spatial point patterns in each combination of factors cells, the methodology is much less developed. Motivated by a real problem of locations of bubbles in a mineral flotation experiment where the interest is analysing if the spatial distribution might be affected by frother concentrations and volumetric airflow rates, we develop an approach for statistical testing of two-way factorial experiments for spatial point patterns. We describe the point patterns through the K -function, a second-order summary statistic, and develop a set of new Fisher-based statistics using weighted means. For inference by Monte Carlo, we use random permutations of weighted residuals depending on the null hypothesis. We conduct simulation experiments to demonstrate the performance of the new test statistics and present the results of the real problem.

Techniques for analysing three-dimensional spatial point patterns are demonstrated on data from a confocal microscope recording the locations of cells in three dimensions. New computational techniques are proposed for edge corrections and empty space measurement. A novel feature of the data is replication and nesting in a sampling design: multiple spatial patterns were observed from each of several animals. For this we develop a ratio regression approach.