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      Enforced symmetry: the necessity of symmetric waxing and waning

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      PeerJ

      PeerJ Inc.

      Symmetry, Range size, Extinction risk, Ecology, Limit theorems, Diversity, Conditioning, Occupancy, Paleontology, Averaging

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          Abstract

          A fundamental question in ecology is how the success of a taxon changes through time and what drives this change. This question is commonly approached using trajectories averaged over a group of taxa. Using results from probability theory, we show analytically and using examples that averaged trajectories will be more symmetric as the number of averaged trajectories increases, even if none of the original trajectories they were derived from is symmetric. This effect is not only based on averaging, but also on the introduction of noise and the incorporation of a priori known origination and extinction times. This implies that averaged trajectories are not suitable for deriving information about the processes driving the success of taxa. In particular, symmetric waxing and waning, which is commonly observed and interpreted to be linked to a number of different paleobiological processes, does not allow drawing any conclusions about the nature of the underlying process.

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          Most cited references 40

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          Stochastic Models of Phylogeny and the Evolution of Diversity

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            Diversity dynamics: molecular phylogenies need the fossil record.

            Over the last two decades, new tools in the analysis of molecular phylogenies have enabled study of the diversification dynamics of living clades in the absence of information about extinct lineages. However, computer simulations and the fossil record show that the inability to access extinct lineages severely limits the inferences that can be drawn from molecular phylogenies. It appears that molecular phylogenies can tell us only when there have been changes in diversification rates, but are blind to the true diversity trajectories and rates of origination and extinction that have led to the species that are alive today. We need to embrace the fossil record if we want to fully understand the diversity dynamics of the living biota.
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              Extinctions in ancient and modern seas.

              In the coming century, life in the ocean will be confronted with a suite of environmental conditions that have no analog in human history. Thus, there is an urgent need to determine which marine species will adapt and which will go extinct. Here, we review the growing literature on marine extinctions and extinction risk in the fossil, historical, and modern records to compare the patterns, drivers, and biological correlates of marine extinctions at different times in the past. Characterized by markedly different environmental states, some past periods share common features with predicted future scenarios. We highlight how the different records can be integrated to better understand and predict the impact of current and projected future environmental changes on extinction risk in the ocean. Copyright © 2012 Elsevier Ltd. All rights reserved.
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                Author and article information

                Contributors
                Journal
                PeerJ
                PeerJ
                peerj
                peerj
                PeerJ
                PeerJ Inc. (San Diego, USA )
                2167-8359
                6 November 2019
                2019
                : 7
                Affiliations
                Friedrich-Alexander Universität Erlangen-Nürnberg , Erlangen, Germany
                Article
                8011
                10.7717/peerj.8011
                6842294
                ©2019 Hohmann and Jarochowska

                This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ) and either DOI or URL of the article must be cited.

                Funding
                The authors received no funding for this work.
                Categories
                Biodiversity
                Ecology
                Mathematical Biology
                Paleontology
                Statistics

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