Populations and Evolution (q-bio.PE)

Abstract: In this paper, we consider an individual-based model with power law mutation probability. In this setting, we use the large population limit with a subsequent ``small mutations'' limit to derive the canonical equation of adaptive dynamics. For a one-dimensional trait space this corresponds to well established results and we can formulate a criterion for evolutionary branching in the spirit of Champagnat and M\'el\'eard (2011). In higher dimensional trait spaces, we find that the speed at which the solution of the canonical equation moves through space is reduced due to mutations being restricted to the underlying grid on the trait space. However, as opposed to the canonical equation with rare mutations, we can explicitly calculate the path which the dominant trait will take without having to solve the equation itself.

Abstract: In the last years algebraic tools have been proven to be useful in phylogenetic reconstruction and model selection by means of the study of phylogenetic invariants. However, up to now, the models studied from an algebraic viewpoint are either too general or too restrictive (as group-based models with a uniform stationary distribution) to be used in practice. In this paper we provide a new framework to work with time-reversible models, which are the most widely used by biologists. In our approach we consider algebraic time-reversible models on phylogenetic trees (as defined by Allman and Rhodes) and introduce a new inner product to make all transition matrices of the process diagonalizable through the same orthogonal eigenbasis. This framework generalizes the Fourier transform widely used to work with group-based models and recovers some of the well known results. As illustration, we exploit the combination of our technique with algebraic geometry tools to provide relevant phylogenetic invariants for trees evolving under the Tamura-Nei model of nucleotide substitution.

Abstract: Climate change substantially impacts ecological systems. Marine species are shifting their distribution because of climate change towards colder waters, potentially compromising the benefits of currently established Marine Protected Areas (MPAs). Therefore, we demonstrate how three case study regions will be impacted by warming ocean waters to prepare stakeholders to understand how the fisheries around the MPAs is predicted to change. We chose the case studies to focus on large scale MPAs in i) a cold, polar region, ii) a tropical region near the equator, and iii) a tropical region farther from the equator. We quantify the biological impacts of shifts in species distribution due to climate change for fishing communities that depend on the Palau National Marine Sanctuary, the Great Barrier Reef Marine National Park Zone, and the North Bering Sea Research Area MPAs. We find that fisheries sectors will be impacted differently in different regions and show that all three regions can be supported by this methodology for decision making that joins sector income and species diversity.