Periodically Varying Externally Imposed Environmental Effects on Population Dynamics

Effects of externally imposed periodic changes in the environment on population dynamics are studied with the help of a simple model. The environmental changes are represented by the temporal and spatial dependence of the competition terms in a standard equation of evolution. Possible applications of the analysis are on the one hand to bacteria in Petri dishes and on the other to rodents in the context of the spread of the Hantavirus epidemic. The analysis shows that spatio-temporal structures emerge, with interesting features which depend on the interplay of separately controllable aspects of the externally imposed environmental changes.Comment: 7 pages, 8 figures, include

Bounding biomass in the Fisher equation

The FKPP equation with a variable growth rate and advection by an incompressible velocity field is considered as a model for plankton dispersed by ocean currents. If the average growth rate is negative then the model has a survival-extinction transition; the location of this transition in the parameter space is constrained using variational arguments and delimited by simulations. The statistical steady state reached when the system is in the survival region of parameter space is characterized by integral constraints and upper and lower bounds on the biomass and productivity that follow from variational arguments and direct inequalities. In the limit of zero-decorrelation time the velocity field is shown to act as Fickian diffusion with an eddy diffusivity much larger than the molecular diffusivity and this allows a one-dimensional model to predict the biomass, productivity and extinction transitions. All results are illustrated with a simple growth and stirring model.Comment: 32 Pages, 13 Figure

Spatial complementarity and the coexistence of species

Coexistence of apparently similar species remains an enduring paradox in ecology. Spatial structure has been predicted to enable coexistence even when population-level models predict competitive exclusion if it causes each species to limit its own population more than that of its competitor. Nevertheless, existing hypotheses conflict with regard to whether clustering favours or precludes coexistence. The spatial segregation hypothesis predicts that in clustered populations the frequency of intra-specific interactions will be increased, causing each species to be self-limiting. Alternatively, individuals of the same species might compete over greater distances, known as heteromyopia, breaking down clusters and opening space for a second species to invade. In this study we create an individual-based model in homogeneous two-dimensional space for two putative sessile species differing only in their demographic rates and the range and strength of their competitive interactions. We fully characterise the parameter space within which coexistence occurs beyond population-level predictions, thereby revealing a region of coexistence generated by a previously-unrecognised process which we term the triadic mechanism. Here coexistence occurs due to the ability of a second generation of offspring of the rarer species to escape competition from their ancestors. We diagnose the conditions under which each of three spatial coexistence mechanisms operates and their characteristic spatial signatures. Deriving insights from a novel metric — ecological pressure — we demonstrate that coexistence is not solely determined by features of the numerically-dominant species. This results in a common framework for predicting, given any pair of species and knowledge of the relevant parameters, whether they will coexist, the mechanism by which they will do so, and the resultant spatial pattern of the community. Spatial coexistence arises from complementary combinations of traits in each species rather than solely through self-limitation

Can a Species Keep Pace with a Shifting Climate?

Consider a patch of favorable habitat surrounded by unfavorable habitat and assume that due to a shifting climate, the patch moves with a fixed speed in a one-dimensional universe. Let the patch be inhabited by a population of individuals that reproduce, disperse, and die. Will the population persist? How does the answer depend on the length of the patch, the speed of movement of the patch, the net population growth rate under constant conditions, and the mobility of the individuals? We will answer these questions in the context of a simple dynamic profile model that incorporates climate shift, population dynamics, and migration. The model takes the form of a growth-diffusion equation. We first consider a special case and derive an explicit condition by glueing phase portraits. Then we establish a strict qualitative dichotomy for a large class of models by way of rigorous PDE methods, in particular the maximum principle. The results show that mobility can both reduce and enhance the ability to track climate change that a narrow range can severely reduce this ability and that population range and total population size can both increase and decrease under a moving climate. It is also shown that range shift may be easier to detect at the expanding front, simply because it is considerably steeper than the retreating back

Evolution of defence portfolios in exploiter-victim systems

Some organisms maintain a battery of defensive strategies against their exploiters (predators, parasites or parasitoids), while others fail to employ a defence that seems obvious. In this paper, we shall investigate the circumstances under which defence strategies might be expected to evolve. Brood parasites and their hosts provide our main motivation, and we shall discuss why the reed warbler Acrocephalus scirpaceus has evolved an egg-rejection but not a chick-rejection strategy as a defence against the common (Eurasian) cuckoo Cuculus canorus, while the superb fairy-wren Malurus cyaneus has evolved a chick-rejection but not an egg-rejection strategy as a defence against Horsfield's bronze-cuckoo Chrysococcyx basalis. We suggest that the answers lie in strategy-blocking, where one strategy (the blocking strategy) prevents the appearance of another (the blocked strategy) that would be adaptive in its absence. This may be common in exploiter-victim systems. © 2006 Springer Science+Business Media, Inc

Structured models of cell migration incorporating molecular binding processes

The dynamic interplay between collective cell movement and the various molecules involved in the accompanying cell signalling mechanisms plays a crucial role in many biological processes including normal tissue development and pathological scenarios such as wound healing and cancer. Information about the various structures embedded within these processes allows a detailed exploration of the binding of molecular species to cell-surface receptors within the evolving cell population. In this paper we establish a general spatio-temporal-structural framework that enables the description of molecular binding to cell membranes coupled with the cell population dynamics. We first provide a general theoretical description for this approach and then illustrate it with two examples arising from cancer invasion

Chalk-Ex—fate of CaCO3 particles in the mixed layer : evolution of patch optical properties

Author Posting. © American Geophysical Union, 2009. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 114 (2009): C07020, doi:10.1029/2008JC004902.The fate of particles in the mixed layer is of great relevance to the global carbon cycle as well as to the propagation of light in the sea. We conducted four manipulative field experiments called “Chalk-Ex” in which known quantities of uniform, calcium carbonate particles were injected into the surface mixed layer. Since the production term for these patches was known to high precision, the experimental design allowed us to focus on terms associated with particle loss. The mass of chalk in the patches was evaluated using the well-calibrated light-scattering properties of the chalk plus measurements from a variety of optical measurements and platforms. Patches were surveyed with a temporal resolution of hours over spatial scales of tens of kilometers. Our results demonstrated exponential loss of the chalk particles with time from the patches. There was little evidence for rapid sinking of the chalk. Instead, horizontal eddy diffusion appeared to be the major factor affecting the dispersion of the chalk to concentrations below the limits of detection. There was unequivocal evidence of subduction of the chalk along isopycnals and subsequent formation of thin layers. Shear dispersion is the most likely mechanism to explain these results. Calculations of horizontal eddy diffusivity were consistent with other mixed layer patch experiments. Our results provide insight into the importance of physics in the formation of subsurface particle maxima in the sea, as well as the importance of rapid coccolith production and critical patch size for maintenance of natural coccolithophore blooms in nature.We would like to thank the Office of Naval Research/Optical and Biological Oceanography Program for their support of Chalk-Ex with awards N000140110042 (WMB) and N00014-01-1-0141 (AJP). Additional funding for this work came from ONR (N00014-05-1- 0111) and NASA (NNG04Gl11G, NNX08AC27G, NNG04HZ25C) to W.M.B

Genome-Wide Identification of Calcium-Response Factor (CaRF) Binding Sites Predicts a Role in Regulation of Neuronal Signaling Pathways

Calcium-Response Factor (CaRF) was first identified as a transcription factor based on its affinity for a neuronal-selective calcium-response element (CaRE1) in the gene encoding Brain-Derived Neurotrophic Factor (BDNF). However, because CaRF shares no homology with other transcription factors, its properties and gene targets have remained unknown. Here we show that the DNA binding domain of CaRF has been highly conserved across evolution and that CaRF binds DNA directly in a sequence-specific manner in the absence of other eukaryotic cofactors. Using a binding site selection screen we identify a high-affinity consensus CaRF response element (cCaRE) that shares significant homology with the CaRE1 element of Bdnf. In a genome-wide chromatin immunoprecipitation analysis (ChIP-Seq), we identified 176 sites of CaRF-specific binding (peaks) in neuronal genomic DNA. 128 of these peaks are within 10kB of an annotated gene, and 60 are within 1kB of an annotated transcriptional start site. At least 138 of the CaRF peaks contain a common 10-bp motif with strong statistical similarity to the cCaRE, and we provide evidence predicting that CaRF can bind independently to at least 64.5% of these motifs in vitro. Analysis of this set of putative CaRF targets suggests the enrichment of genes that regulate intracellular signaling cascades. Finally we demonstrate that expression of a subset of these target genes is altered in the cortex of Carf knockout (KO) mice. Together these data strongly support the characterization of CaRF as a unique transcription factor and provide the first insight into the program of CaRF-regulated transcription in neurons