Assessing the extinction risk of the spontaneous flora in urban tree bases.

As the spatial arrangement of trees planted along streets in cities makes their bases potential ecological corridors for the flora, urban tree bases may be a key contributor to the overall connectivity of the urban ecosystem. However, these tree bases are also a highly fragmented environment in which extinctions are frequent. The goal of this study was to assess the plant species' ability to survive and spread through urban tree bases. To do so, we developed a Bayesian framework to assess the extinction risk of a plant metapopulation using presence/absence data, assuming that the occupancy dynamics was described by a Hidden Markov Model. The novelty of our approach is to take into account the combined effect of low-distance dispersal and the potential presence of a seed bank on the extinction risk. We introduced a metric of the extinction risk and examined its performance over a wide range of metapopulation parameters. We applied our framework to yearly floristic inventories carried out in 1324 tree bases in Paris, France. While local extinction risks were generally high, extinction risks at the street scale varied greatly from one species to another. We identified 10 plant species that could survive and spread through urban tree bases, and three plant traits correlated with the extinction risk at the metapopulation scale: the maximal height, and the beginning and end of the flowering period. Our results suggest that some plant species can use urban tree bases as ecological corridors despite high local extinction risks by forming a seed bank. We also identified other plant traits correlated with the ability to survive in tree bases, related to the action of gardeners. Moreover, our findings demonstrate that our Bayesian estimation framework based on percolation theory has the potential to be extended to more general metapopulations.

Understanding the Variability in Graph Data Sets through Statistical Modeling on the Stiefel Manifold.

Network analysis provides a rich framework to model complex phenomena, such as human brain connectivity. It has proven efficient to understand their natural properties and design predictive models. In this paper, we study the variability within groups of networks, i.e., the structure of connection similarities and differences across a set of networks. We propose a statistical framework to model these variations based on manifold-valued latent factors. Each network adjacency matrix is decomposed as a weighted sum of matrix patterns with rank one. Each pattern is described as a random perturbation of a dictionary element. As a hierarchical statistical model, it enables the analysis of heterogeneous populations of adjacency matrices using mixtures. Our framework can also be used to infer the weight of missing edges. We estimate the parameters of the model using an Expectation-Maximization-based algorithm. Experimenting on synthetic data, we show that the algorithm is able to accurately estimate the latent structure in both low and high dimensions. We apply our model on a large data set of functional brain connectivity matrices from the UK Biobank. Our results suggest that the proposed model accurately describes the complex variability in the data set with a small number of degrees of freedom.