Vlasov scaling for stochastic dynamics of continuous systems

We describe a general scheme of derivation of the Vlasov-type equations for Markov evolutions of particle systems in continuum. This scheme is based on a proper scaling of corresponding Markov generators and has an algorithmic realization in terms of related hierarchical chains of correlation functions equations. Several examples of the realization of the proposed approach in particular models are presented.Comment: 23 page

Simple guide to starting a research group

Conducting cutting-edge research and scholarship becomes more complicated with each passing year; forming a collaborative research group offers a way to navigate this increasing complexity. Yet many individuals whose work might benefit from the formation of a collaborative team may feel overwhelmed by the prospect of attempting to build and maintain a research group. We propose this simple guide for starting and maintaining such an enterprise

Can hot temperatures limit disease transmission? A test of mechanisms in a zooplankton–fungus system

Thermal ecology theory predicts that transmission of infectious diseases should respond unimodally to temperature, that is be maximized at intermediate temperatures and constrained at extreme low and high temperatures. However, empirical evidence linking hot temperatures to decreased transmission in nature remains limited.We tested the hypothesis that hot temperatures constrain transmission in a zooplankton–fungus (Daphnia dentifera–Metschnikowia bicuspidata) disease system where autumnal epidemics typically start after lakes cool from their peak summer temperatures. This pattern suggested that maximally hot summer temperatures could be inhibiting disease spread.Using a series of laboratory experiments, we examined the effects of high temperatures on five mechanistic components of transmission. We found that (a) high temperatures increased exposure to parasites by speeding up foraging rate but (b) did not alter infection success post‐exposure. (c) High temperatures lowered parasite production (due to faster host death and an inferred delay in parasite growth). (d) Parasites made in hot conditions were less infectious to the next host (instilling a parasite ‘rearing’ or ’trans‐host’ effect of temperature during the prior infection). (e) High temperatures in the free‐living stage also reduce parasite infectivity, either by killing or harming parasites.We then assembled the five mechanisms into an index of disease spread. The resulting unimodal thermal response was most strongly driven by the rearing effect. Transmission peaked at intermediate hot temperatures (25–26°C) and then decreased at maximally hot temperatures (30–32°C). However, transmission at these maximally hot temperatures only trended slightly lower than the baseline control (20°C), which easily sustains epidemics in laboratory conditions and in nature. Overall, we conclude that while exposure to hot epilimnetic temperatures does somewhat constrain disease, we lack evidence that this effect fully explains the lack of summer epidemics in this natural system. This work demonstrates the importance of experimentally testing hypothesized mechanisms of thermal constraints on disease transmission. Furthermore, it cautions against drawing conclusions based on field patterns and theory alone.A free Plain Language Summary can be found within the Supporting Information of this article.A free Plain Language Summary can be found within the Supporting Information of this article.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/151821/1/fec13403-sup-0001-Summary.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151821/2/fec13403_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151821/3/fec13403.pd

Persistence, extinction and spatio-temporal synchronization of SIRS cellular automata models

Spatially explicit models have been widely used in today's mathematical ecology and epidemiology to study persistence and extinction of populations as well as their spatial patterns. Here we extend the earlier work--static dispersal between neighbouring individuals to mobility of individuals as well as multi-patches environment. As is commonly found, the basic reproductive ratio is maximized for the evolutionary stable strategy (ESS) on diseases' persistence in mean-field theory. This has important implications, as it implies that for a wide range of parameters that infection rate will tend maximum. This is opposite with present results obtained in spatial explicit models that infection rate is limited by upper bound. We observe the emergence of trade-offs of extinction and persistence on the parameters of the infection period and infection rate and show the extinction time having a linear relationship with respect to system size. We further find that the higher mobility can pronouncedly promote the persistence of spread of epidemics, i.e., the phase transition occurs from extinction domain to persistence domain, and the spirals' wavelength increases as the mobility increasing and ultimately, it will saturate at a certain value. Furthermore, for multi-patches case, we find that the lower coupling strength leads to anti-phase oscillation of infected fraction, while higher coupling strength corresponds to in-phase oscillation.Comment: 12page

Influence of density and salinity on larval development of salt-adapted and salt-naïve frog populations

Environmental change and habitat fragmentation will affect population densities for many species. For those species that have locally adapted to persist in changed or stressful habitats, it is uncertain how density dependence will affect adaptive responses. Anurans (frogs and toads) are typically freshwater organisms, but some coastal populations of green treefrogs (Hyla cinerea) have adapted to brackish, coastal wetlands. Tadpoles from coastal populations metamorphose sooner and demonstrate faster growth rates than inland populations when reared solitarily. Although saltwater exposure has adaptively reduced the duration of the larval period for coastal populations, increases in densities during larval development typically in-crease time to metamorphosis and reduce rates of growth and survival. We test how combined stressors of density and salinity affect larval development between salt-adapted (“coastal�) and nonsalt-adapted (“inland�) populations by measuring various developmental and metamorphic phenotypes. We found that increased tadpole density strongly affected coastal and inland tadpole populations similarly. In high-density treatments, both coastal and inland populations had reduced growth rates, greater exponential decay of growth, a smaller size at metamorphosis, took longer to reach metamorphosis, and had lower survivorship at metamorphosis. Salinity only exaggerated the effects of density on the time to reach metamorphosis and exponential decay of growth. Location of origin affected length at metamorphosis, with coastal tadpoles metamorphosing slightly longer than inland tadpoles across densities and salinities. These findings confirm that density has a strong and central influence on larval development even across divergent populations and habitat types and may mitigate the expression (and therefore detection) of locally adapted phenotypes

The orbit rigidity matrix of a symmetric framework

A number of recent papers have studied when symmetry causes frameworks on a graph to become infinitesimally flexible, or stressed, and when it has no impact. A number of other recent papers have studied special classes of frameworks on generically rigid graphs which are finite mechanisms. Here we introduce a new tool, the orbit matrix, which connects these two areas and provides a matrix representation for fully symmetric infinitesimal flexes, and fully symmetric stresses of symmetric frameworks. The orbit matrix is a true analog of the standard rigidity matrix for general frameworks, and its analysis gives important insights into questions about the flexibility and rigidity of classes of symmetric frameworks, in all dimensions. With this narrower focus on fully symmetric infinitesimal motions, comes the power to predict symmetry-preserving finite mechanisms - giving a simplified analysis which covers a wide range of the known mechanisms, and generalizes the classes of known mechanisms. This initial exploration of the properties of the orbit matrix also opens up a number of new questions and possible extensions of the previous results, including transfer of symmetry based results from Euclidean space to spherical, hyperbolic, and some other metrics with shared symmetry groups and underlying projective geometry.Comment: 41 pages, 12 figure

The demographic consequences of growing older and bigger in oyster populations

Structured population models, particularly size-or age-structured, have a long history of informing conservation and natural resource management. While size is often easier to measure than age and is the focus of many management strategies, age-structure can have important effects on population dynamics that are not captured in size-only models. However, relatively few studies have included the simultaneous effects of both age-and size-structure. To better understand how population structure, particularly that of age and size, impacts restoration and management decisions, we developed and compared a size-structured integral projection model (IPM) and an age-and size-structured IPM, using a population of Crassostrea gigas oysters in the northeastern Pacific Ocean. We analyzed sensitivity of model results across values of local retention that give populations decreasing in size to populations increasing in size. We found that age-and size-structured models yielded the best fit to the demographic data and provided more reliable results about long-term demography. Elasticity analysis showed that population growth rate was most sensitive to changes in the survival of both large (\u3e175 mm shell length) and small (length) oysters, indicating that a maximum size limit, in addition to a minimum size limit, could be an effective strategy for maintaining a sustainable population. In contrast, the purely size-structured model did not detect the importance of large individuals. Finally, patterns in stable age and stable size distributions differed between populations decreasing in size due to limited local retention and populations increasing in size due to high local retention. These patterns can be used to determine population status and restoration success. The methodology described here provides general insight into the necessity of including both age-and size-structure into modeling frameworks when using population models to inform restoration and management decisions

Modelling collective cell behaviour

The classical mean-field approach to modelling biological systems makes a number of simplifying assumptions which typically lead to coupled systems of reaction-diffusion partial differential equations. While these models have been very useful in allowing us to gain important insights into the behaviour of many biological systems, recent experimental advances in our ability to track and quantify cell behaviour now allow us to build more realistic models which relax some of the assumptions previously made. This brief review aims to illustrate the type of models obtained using this approach

Intense or Spatially Heterogeneous Predation Can Select against Prey Dispersal

Dispersal theory generally predicts kin competition, inbreeding, and temporal variation in habitat quality should select for dispersal, whereas spatial variation in habitat quality should select against dispersal. The effect of predation on the evolution of dispersal is currently not well-known: because predation can be variable in both space and time, it is not clear whether or when predation will promote dispersal within prey. Moreover, the evolution of prey dispersal affects strongly the encounter rate of predator and prey individuals, which greatly determines the ecological dynamics, and in turn changes the selection pressures for prey dispersal, in an eco-evolutionary feedback loop. When taken all together the effect of predation on prey dispersal is rather difficult to predict. We analyze a spatially explicit, individual-based predator-prey model and its mathematical approximation to investigate the evolution of prey dispersal. Competition and predation depend on local, rather than landscape-scale densities, and the spatial pattern of predation corresponds well to that of predators using restricted home ranges (e.g. central-place foragers). Analyses show the balance between the level of competition and predation pressure an individual is expected to experience determines whether prey should disperse or stay close to their parents and siblings, and more predation selects for less prey dispersal. Predators with smaller home ranges also select for less prey dispersal; more prey dispersal is favoured if predators have large home ranges, are very mobile, and/or are evenly distributed across the landscape