On the Consequences of Using Moving Window Segmentation to Analyze the Structural Stand Heterogeneity and Debatable Patchiness of Old-Growth Temperate Forests

(1) Background: Early research in natural forests on decennia implanted conviction concerning the patchy patterns of their structural heterogeneity. Due to the variety of methodological approaches applied, verification of this fundamental assumption remains open. The aim of this study was to discuss the methodological limitations associated with the use of moving windows with overlap for the delineation of homogeneous patch mosaics in forest ecosystems. (2) Methods: The “patchiness” hypothesis was tested in six old-growth forests formed by Abies alba Mill., Fagus sylvatica L., and Picea abies (L.) H. Karst. localized in Bosnia and Herzegovina and southern Poland. In each stand, the tree diameter at breast height (dbh) was recorded on circular sample plots of 154 m2 regularly distributed in a 20 × 20 m lattice over an area of 10 ha. (3) Results: Computer simulations showed that patch classification based on overlapping windows results in apparent patchiness, even for completely randomized tree distributions. Analyses carried out on the empirical data indicated prevalent random patterns of structural heterogeneity. (4) Conclusions: Patchiness is not a universal feature of the investigated forest communities. The size of the moving window and the noise-smoothing procedure exert strong effects on the biasedness of patch classification, the frequency of structural types, and the mean patch size.

Efficient Computation of Expectations under Spanning Tree Distributions

We give a general framework for inference in spanning tree models. We propose unified algorithms for the important cases of first-order expectations and second-order expectations in edge-factored, non-projective spanning-tree models. Our algorithms exploit a fundamental connection between gradients and expectations, which allows us to derive efficient algorithms. These algorithms are easy to implement with or without automatic differentiation software. We motivate the development of our framework with several cautionary tales of previous research, which has developed numerous inefficient algorithms for computing expectations and their gradients. We demonstrate how our framework efficiently computes several quantities with known algorithms, including the expected attachment score, entropy, and generalized expectation criteria. As a bonus, we give algorithms for quantities that are missing in the literature, including the KL divergence. In all cases, our approach matches the efficiency of existing algorithms and, in several cases, reduces the runtime complexity by a factor of the sentence length. We validate the implementation of our framework through runtime experiments. We find our algorithms are up to 15 and 9 times faster than previous algorithms for computing the Shannon entropy and the gradient of the generalized expectation objective, respectively.

Distance metrics for ranked evolutionary trees

Genealogical tree modeling is essential for estimating evolutionary parameters in population genetics and phylogenetics. Recent mathematical results concerning ranked genealogies without leaf labels unlock opportunities in the analysis of evolutionary trees. In particular, comparisons between ranked genealogies facilitate the study of evolutionary processes of different organisms sampled at multiple time periods. We propose metrics on ranked tree shapes and ranked genealogies for lineages isochronously and heterochronously sampled. Our proposed tree metrics make it possible to conduct statistical analyses of ranked tree shapes and timed ranked tree shapes or ranked genealogies. Such analyses allow us to assess differences in tree distributions, quantify estimation uncertainty, and summarize tree distributions. We show the utility of our metrics via simulations and an application in infectious diseases.

A Metric Space of Ranked Tree Shapes and Ranked Genealogies

Genealogical tree modeling is essential for estimating evolutionary parameters in population genetics and phylogenetics. Recent mathematical results concerning ranked genealogies without leaf labels enable new opportunities in the analysis of evolutionary trees. In particular, comparisons between ranked genealogies facilitate the study of evolutionary processes for organisms sampled in multiple time periods. We propose a metric space on ranked genealogies for lineages sampled from both isochronous and time-stamped heterochronous sampling. Our new tree metrics make it possible to conduct statistical analyses of ranked tree shapes and timed ranked tree shapes, or ranked genealogies. Such analyses allow us to assess differences in tree distributions, quantify estimation uncertainty, and summarize tree distributions. We show the utility of our metrics via simulations and an application in infectious diseases.

Spatial patterning among savanna trees in high-resolution, spatially extensive data

In savannas, predicting how vegetation varies is a longstanding challenge. Spatial patterning in vegetation may structure that variability, mediated by spatial interactions, including competition and facilitation. Here, we use unique high-resolution, spatially extensive data of tree distributions in an African savanna, derived from airborne Light Detection and Ranging (LiDAR), to examine tree-clustering patterns. We show that tree cluster sizes were governed by power laws over two to three orders of magnitude in spatial scale and that the parameters on their distributions were invariant with respect to underlying environment. Concluding that some universal process governs spatial patterns in tree distributions may be premature. However, we can say that, although the tree layer may look unpredictable locally, at scales relevant to prediction in, e.g., global vegetation models, vegetation is instead strongly structured by regular statistical distributions.