Drivers of redistribution of fishing and non-fishing effort after the implementation of a marine protected area network

Marine spatial planning (MSP) is increasingly utilized to sustainably manage ocean uses. Marine protected areas (MPAs), a form of spatial management in which parts of the ocean are regulated to fishing, are now a common tool in MSP for conserving marine biodiversity and managing fisheries. However, the use of MPAs in MSP often neglects, or simplifies, the redistribution of fishing and non-fishing activities inside and outside of MPAs following their implementation. This redistribution of effort can have important implications for effective MSP. Using long-term (14 yr) aerial surveys of boats at the California Channel Islands, we examined the spatial redistribution of fishing and non-fishing activities and their drivers following MPA establishment. Our data represent 6 yr of information before the implementation of an MPA network and 8 yr after implementation. Different types of boats responded in different ways to the closures, ranging from behaviors by commercial dive boats that support the hypothesis of fishing-the-line, to behaviors by urchin, sport fishing, and recreational boats that support the theory of ideal free distribution. Additionally, we found that boats engaged in recreational activities targeted areas that are sheltered from large waves and located near their home ports, while boats engaged in fishing activities also avoided high wave areas but were not constrained by the distance to their home ports. We did not observe the expected pattern of effort concentration near MPA borders for some boat types; this can be explained by the habitat preference of certain activities (for some activities, the desired habitat attributes are not inside the MPAs), species’ biology (species such as urchins where the MPA benefit would likely come from larval export rather than adult spillover), or policy-infraction avoidance. The diversity of boat responses reveals variance from the usual simplified assumption that all extractive boats respond similarly to MPA establishment. Our work is the first empirical study to analyze the response of both commercial and recreational boats to closure. Our results will inform MSP in better accounting for effort redistribution by ocean users in response to the implementation of MPAs and other closures

Schwinger Boson Formulation and Solution of the Crow-Kimura and Eigen Models of Quasispecies Theory

We express the Crow-Kimura and Eigen models of quasispecies theory in a functional integral representation. We formulate the spin coherent state functional integrals using the Schwinger Boson method. In this formulation, we are able to deduce the long-time behavior of these models for arbitrary replication and degradation functions. We discuss the phase transitions that occur in these models as a function of mutation rate. We derive for these models the leading order corrections to the infinite genome length limit.Comment: 37 pages; 4 figures; to appear in J. Stat. Phy

Finite-size scaling of the error threshold transition in finite population

The error threshold transition in a stochastic (i.e. finite population) version of the quasispecies model of molecular evolution is studied using finite-size scaling. For the single-sharp-peak replication landscape, the deterministic model exhibits a first-order transition at $Q=Q_c=1/a$, where $Q$ is the probability of exact replication of a molecule of length $L \to \infty$, and $a$ is the selective advantage of the master string. For sufficiently large population size, $N$, we show that in the critical region the characteristic time for the vanishing of the master strings from the population is described very well by the scaling assumption \tau = N^{1/2} f_a \left [ \left (Q - Q_c) N^{1/2} \right ] , where $f_a$ is an $a$-dependent scaling function.Comment: 8 pages, 3 ps figures. submitted to J. Phys.

Optimal discrete stopping times for reliability growth tests

Often, the duration of a reliability growth development test is specified in advance and the decision to terminate or continue testing is conducted at discrete time intervals. These features are normally not captured by reliability growth models. This paper adapts a standard reliability growth model to determine the optimal time for which to plan to terminate testing. The underlying stochastic process is developed from an Order Statistic argument with Bayesian inference used to estimate the number of faults within the design and classical inference procedures used to assess the rate of fault detection. Inference procedures within this framework are explored where it is shown the Maximum Likelihood Estimators possess a small bias and converges to the Minimum Variance Unbiased Estimator after few tests for designs with moderate number of faults. It is shown that the Likelihood function can be bimodal when there is conflict between the observed rate of fault detection and the prior distribution describing the number of faults in the design. An illustrative example is provided

Epoprostenol (PGI2, Prostacyclin) During High‐Risk Hemodialysis: Preventing Further Bleeding Complications

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97231/1/j.1552-4604.1988.tb03222.x.pd

Utterance Selection Model of Language Change

We present a mathematical formulation of a theory of language change. The theory is evolutionary in nature and has close analogies with theories of population genetics. The mathematical structure we construct similarly has correspondences with the Fisher-Wright model of population genetics, but there are significant differences. The continuous time formulation of the model is expressed in terms of a Fokker-Planck equation. This equation is exactly soluble in the case of a single speaker and can be investigated analytically in the case of multiple speakers who communicate equally with all other speakers and give their utterances equal weight. Whilst the stationary properties of this system have much in common with the single-speaker case, time-dependent properties are richer. In the particular case where linguistic forms can become extinct, we find that the presence of many speakers causes a two-stage relaxation, the first being a common marginal distribution that persists for a long time as a consequence of ultimate extinction being due to rare fluctuations.Comment: 21 pages, 17 figure

Anderson Localization, Non-linearity and Stable Genetic Diversity

In many models of genotypic evolution, the vector of genotype populations satisfies a system of linear ordinary differential equations. This system of equations models a competition between differential replication rates (fitness) and mutation. Mutation operates as a generalized diffusion process on genotype space. In the large time asymptotics, the replication term tends to produce a single dominant quasispecies, unless the mutation rate is too high, in which case the populations of different genotypes becomes de-localized. We introduce a more macroscopic picture of genotypic evolution wherein a random replication term in the linear model displays features analogous to Anderson localization. When coupled with non-linearities that limit the population of any given genotype, we obtain a model whose large time asymptotics display stable genotypic diversityComment: 25 pages, 8 Figure

Analytical study of the effect of recombination on evolution via DNA shuffling

We investigate a multi-locus evolutionary model which is based on the DNA shuffling protocol widely applied in \textit{in vitro} directed evolution. This model incorporates selection, recombination and point mutations. The simplicity of the model allows us to obtain a full analytical treatment of both its dynamical and equilibrium properties, for the case of an infinite population. We also briefly discuss finite population size corrections

Large Fluctuations and Fixation in Evolutionary Games

We study large fluctuations in evolutionary games belonging to the coordination and anti-coordination classes. The dynamics of these games, modeling cooperation dilemmas, is characterized by a coexistence fixed point separating two absorbing states. We are particularly interested in the problem of fixation that refers to the possibility that a few mutants take over the entire population. Here, the fixation phenomenon is induced by large fluctuations and is investigated by a semi-classical WKB (Wentzel-Kramers-Brillouin) theory generalized to treat stochastic systems possessing multiple absorbing states. Importantly, this method allows us to analyze the combined influence of selection and random fluctuations on the evolutionary dynamics \textit{beyond} the weak selection limit often considered in previous works. We accurately compute, including pre-exponential factors, the probability distribution function in the long-lived coexistence state and the mean fixation time necessary for a few mutants to take over the entire population in anti-coordination games, and also the fixation probability in the coordination class. Our analytical results compare excellently with extensive numerical simulations. Furthermore, we demonstrate that our treatment is superior to the Fokker-Planck approximation when the selection intensity is finite.Comment: 17 pages, 10 figures, to appear in JSTA

The statistical mechanics of a polygenic characterunder stabilizing selection, mutation and drift

By exploiting an analogy between population genetics and statistical mechanics, we study the evolution of a polygenic trait under stabilizing selection, mutation, and genetic drift. This requires us to track only four macroscopic variables, instead of the distribution of all the allele frequencies that influence the trait. These macroscopic variables are the expectations of: the trait mean and its square, the genetic variance, and of a measure of heterozygosity, and are derived from a generating function that is in turn derived by maximizing an entropy measure. These four macroscopics are enough to accurately describe the dynamics of the trait mean and of its genetic variance (and in principle of any other quantity). Unlike previous approaches that were based on an infinite series of moments or cumulants, which had to be truncated arbitrarily, our calculations provide a well-defined approximation procedure. We apply the framework to abrupt and gradual changes in the optimum, as well as to changes in the strength of stabilizing selection. Our approximations are surprisingly accurate, even for systems with as few as 5 loci. We find that when the effects of drift are included, the expected genetic variance is hardly altered by directional selection, even though it fluctuates in any particular instance. We also find hysteresis, showing that even after averaging over the microscopic variables, the macroscopic trajectories retain a memory of the underlying genetic states.Comment: 35 pages, 8 figure