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Inverse problems are ubiquitous in science and engineering. Two categories of inverse problems concerning a physical system are (1) estimate parameters in a model of the system from observed input–output pairs and (2) given a model of the system, reconstruct the input to it that caused some observed output. Applied inverse problems are challenging because a solution may (i) not exist, (ii) not be unique, or (iii) be sensitive to measurement noise contaminating the data. Bayesian statistical inversion (BSI) is an approach to tackle ill-posed and/or ill-conditioned inverse problems. Advantageously, BSI provides a “solution” that (i) quantifies uncertainty by assigning a probability to each possible value of the unknown parameter/input and (ii) incorporates prior information and beliefs about the parameter/input. Herein, we provide a tutorial of BSI for inverse problems by way of illustrative examples dealing with heat transfer from ambient air to a cold lime fruit. First, we use BSI to infer a parameter in a dynamic model of the lime temperature from measurements of the lime temperature over time. Second, we use BSI to reconstruct the initial condition of the lime from a measurement of its temperature later in time. We demonstrate the incorporation of prior information, visualize the posterior distributions of the parameter/initial condition, and show posterior samples of lime temperature trajectories from the model. Our Tutorial aims to reach a wide range of scientists and engineers.

 

We develop a method to identify how ecological, evolutionary, and eco-evolutionary feedbacks influence system stability. We apply our method to nine empirically parametrized eco-evolutionary models of exploiter–victim systems from the literature and identify which particular feedbacks cause some systems to converge to a steady state or to exhibit sustained oscillations. We find that ecological feedbacks involving the interactions between all species and evolutionary and eco-evolutionary feedbacks involving only the interactions between exploiter species (predators or pathogens) are typically stabilizing. In contrast, evolutionary and eco-evolutionary feedbacks involving the interactions between victim species (prey or hosts) are destabilizing more often than not. We also find that while eco-evolutionary feedbacks rarely altered system stability from what would be predicted from just ecological and evolutionary feedbacks, eco-evolutionary feedbacks have the potential to alter system stability at faster or slower speeds of evolution. As the number of empirical studies demonstrating eco-evolutionary feedbacks increases, we can continue to apply these methods to determine whether the patterns we observe are common in other empirical communities. 

Hylexetasteswoodcreepers are endemic to theterra firmeforests of the Amazon basin. Currently, most taxonomic sources recognize two species ofHylexetastes(H. perrotiiandH. stresemanni), each divided into three subspecies. Some authors maintain that theH. perrotiisubspecies should be elevated to full species status. In particular,Hylexetastes perrotii brigidaiis endemic to the eastern Amazon, the second Amazonian area of endemism (Xingu) most affected by deforestation and habitat degradation. Consequently, the taxonomic status ofH. p. brigidaiis of particular concern for conservation. Thus far, only morphological characters have been evaluated for the taxonomic delimitation of species and subspecies ofHylexetastes. We present a molecular phylogenetic analysis of all subspecies to help delimitHylexetastesinterspecific limits. Fragments of two mitochondrial (CytbandND2) and three nuclear genes (FGB5, G3PDHandMUSK) from 57Hylexetastesspecimens were sequenced. An ecological niche model was estimated to describe more accurately the potential distributions of taxa and to evaluate their vulnerability to ongoing deforestation. Phylogenetic analyses support the paraphyly of the polytypicH. perrotiias currently delimited and the elevation ofHylexetastes perrotii uniformisto full species rank, as well as the presence of three evolutionary significant units (ESUs) within this newly delimited species, including one grouping allH. p. brigidaispecimens. Alternatively, under lineage‐based species concepts, our results support at least five evolutionary species inHylexetastes:H. stresemanni,H. undulatus,H. perrotii,H. uniformisandH. brigidai. Each of these taxa andESUs are distributed in different interfluvial areas of the Amazon basin, which have different degrees of disturbance. Because they occupy the most heavily impacted region among allHylexetastesESUs, regular assessments of the conservation statuses ofH. p. brigidaiand bothH. uniformisESUs are paramount.