Exponential Mixing for a Stochastic PDE Driven by Degenerate Noise

We study stochastic partial differential equations of the reaction-diffusion type. We show that, even if the forcing is very degenerate (i.e. has not full rank), one has exponential convergence towards the invariant measure. The convergence takes place in the topology induced by a weighted variation norm and uses a kind of (uniform) Doeblin condition.Comment: 10 pages, 1 figur

Explaining Long-Distance Dispersal: Effects of Dispersal Distance on Survival and Growth in a Stream Salamander

Long-distance dispersal (LDD) may contribute disproportionately to range expansions, the creation of new evolutionary lineages, and species persistence in human-dominated landscapes. However, because data on the individual consequences of dispersal distance are extremely limited, we have little insight on how LDD is maintained in natural populations. I used six years of spatially explicit capture–mark–recapture (CMR) data to test the prediction that individual performance increases with dispersal distance in the stream salamander Gyrinophilus porphyriticus. Dispersal distance was total distance moved along the 1-km study stream, ranging from 0 to 565 m. To quantify individual performance, I used CMR estimates of survival and individual growth rates based on change in body length. Survival and growth rates increased significantly with dispersal distance. These relationships were not confounded by pre-dispersal body condition or by ecological gradients along the stream. Individual benefits of LDD were likely caused by an increase in the upper limit of settlement site quality with dispersal distance. My results do not support the view that the fitness consequences of LDD are unpredictable and instead suggest that consistent evolutionary mechanisms may explain the prevalence of LDD in nature. They also highlight the value of direct CMR data for understanding the individual consequences of variation in dispersal distance and how that variation is maintained in natural populations

Computational and Biological Analogies for Understanding Fine-Tuned Parameters in Physics

In this philosophical paper, we explore computational and biological analogies to address the fine-tuning problem in cosmology. We first clarify what it means for physical constants or initial conditions to be fine-tuned. We review important distinctions such as the dimensionless and dimensional physical constants, and the classification of constants proposed by Levy-Leblond. Then we explore how two great analogies, computational and biological, can give new insights into our problem. This paper includes a preliminary study to examine the two analogies. Importantly, analogies are both useful and fundamental cognitive tools, but can also be misused or misinterpreted. The idea that our universe might be modelled as a computational entity is analysed, and we discuss the distinction between physical laws and initial conditions using algorithmic information theory. Smolin introduced the theory of "Cosmological Natural Selection" with a biological analogy in mind. We examine an extension of this analogy involving intelligent life. We discuss if and how this extension could be legitimated. Keywords: origin of the universe, fine-tuning, physical constants, initial conditions, computational universe, biological universe, role of intelligent life, cosmological natural selection, cosmological artificial selection, artificial cosmogenesis.Comment: 25 pages, Foundations of Science, in pres

Ecological equivalence: a realistic assumption for niche theory as a testable alternative to neutral theory

Hubbell's 2001 neutral theory unifies biodiversity and biogeography by modelling steady-state distributions of species richness and abundances across spatio-temporal scales. Accurate predictions have issued from its core premise that all species have identical vital rates. Yet no ecologist believes that species are identical in reality. Here I explain this paradox in terms of the ecological equivalence that species must achieve at their coexistence equilibrium, defined by zero net fitness for all regardless of intrinsic differences between them. I show that the distinction of realised from intrinsic vital rates is crucial to evaluating community resilience. An analysis of competitive interactions reveals how zero-sum patterns of abundance emerge for species with contrasting life-history traits as for identical species. I develop a stochastic model to simulate community assembly from a random drift of invasions sustaining the dynamics of recruitment following deaths and extinctions. Species are allocated identical intrinsic vital rates for neutral dynamics, or random intrinsic vital rates and competitive abilities for niche dynamics either on a continuous scale or between dominant-fugitive extremes. Resulting communities have steady-state distributions of the same type for more or less extremely differentiated species as for identical species. All produce negatively skewed log-normal distributions of species abundance, zero-sum relationships of total abundance to area, and Arrhenius relationships of species to area. Intrinsically identical species nevertheless support fewer total individuals, because their densities impact as strongly on each other as on themselves. Truly neutral communities have measurably lower abundance/area and higher species/abundance ratios. Neutral scenarios can be parameterized as null hypotheses for testing competitive release, which is a sure signal of niche dynamics. Ignoring the true strength of interactions between and within species risks a substantial misrepresentation of community resilience to habitat los

Predators reduce extinction risk in noisy metapopulations

Background Spatial structure across fragmented landscapes can enhance regional population persistence by promoting local “rescue effects.” In small, vulnerable populations, where chance or random events between individuals may have disproportionately large effects on species interactions, such local processes are particularly important. However, existing theory often only describes the dynamics of metapopulations at regional scales, neglecting the role of multispecies population dynamics within habitat patches. Findings By coupling analysis across spatial scales we quantified the interaction between local scale population regulation, regional dispersal and noise processes in the dynamics of experimental host-parasitoid metapopulations. We find that increasing community complexity increases negative correlation between local population dynamics. A potential mechanism underpinning this finding was explored using a simple population dynamic model. Conclusions Our results suggest a paradox: parasitism, whilst clearly damaging to hosts at the individual level, reduces extinction risk at the population level

Incorporating the geometry of dispersal and migration to understand spatial patterns of species distributions

Dispersal and migration can be important drivers of species distributions. Because the paths followed by individuals of many species are curvilinear, spatial statistical models based on rectilinear coordinates systems would fail to predict population connectivity or the ecological consequences of migration or species invasions. I propose that we view migration/dispersal as if organisms were moving along curvilinear geometrical objects called smooth manifolds. In that view, the curvilinear pathways become the ‘shortest realised paths’ arising from the necessity to minimise mortality risks and energy costs. One can then define curvilinear coordinate systems on such manifolds. I describe a procedure to incorporate manifolds and define appropriate coordinate systems, with focus on trajectories (1D manifolds), as parts of mechanistic ecological models. I show how a statistical method, known as ‘manifold learning’, enables one to define the manifold and the appropriate coordinate systems needed to calculate population connectivity or study the effects of migrations (e.g. in aquatic invertebrates, fish, insects and birds). This approach may help in the design of networks of protected areas, in studying the consequences of invasion, range expansions, or transfer of parasites/diseases. Overall, a geometrical view to animal movement gives a novel perspective to the understanding of the ecological role of dispersal and migration

Evolution of predator dispersal in relation to spatio-temporal prey dynamics : how not to get stuck in the wrong place!

Peer reviewedPublisher PD

Middle and Late Pleistocene environmental history of the Marsworth area, south-central England

To elucidate the Middle and Late Pleistocene environmental history of south-central England, we report the stratigraphy, sedimentology, palaeoecology and geochronology of some deposits near the foot of the Chiltern Hills scarp at Marsworth, Buckinghamshire. The Marsworth site is important because its sedimentary sequences contain a rich record of warm stages and cold stages, and it lies close to the Anglian glacial limit. Critical to its history are the origin and age of a brown pebbly silty clay (diamicton) previously interpreted as weathered till. The deposits described infill a river channel incised into chalk bedrock. They comprise clayey, silty and gravelly sediments, many containing locally derived chalk and some with molluscan, ostracod and vertebrate remains. Most of the deposits are readily attributed to periglacial and fluvial processes, and some are dated by optically stimulated luminescence to Marine Isotope Stage (MIS) 6. Although our sedimentological data do not discriminate between a glacial or periglacial interpretation of the diamicton, amino-acid dating of three molluscan taxa from beneath it indicates that it is younger than MIS 9 and older than MIS 5e. This makes a glacial interpretation unlikely, and we interpret the diamicton as a periglacial slope deposit. The Pleistocene history reconstructed for Marsworth identifies four key elements: (1) Anglian glaciation during MIS 12 closely approached Marsworth, introducing far-travelled pebbles such as Rhaxella chert and possibly some fine sand minerals into the area. (2) Interglacial environments inferred from fluvial sediments during MIS 7 varied from fully interglacial conditions during sub-stages 7e and 7c, cool temperate conditions during sub-stage 7b or 7a, temperate conditions similar to those today in central England towards the end of the interglacial, and cool temperate conditions during sub-stage 7a. (3) Periglacial activity during MIS 6 involved thermal contraction cracking, permafrost development, fracturing of chalk bedrock, fluvial activity, slopewash, mass movement and deposition of loess and coversand. (4) Fully interglacial conditions during sub-stage 5e led to renewed fluvial activity, soil formation and acidic weathering

Threat-sensitive anti-predator defence in precocial wader, the northern lapwing Vanellus vanellus

Birds exhibit various forms of anti-predator behaviours to avoid reproductive failure, with mobbing—observation, approach and usually harassment of a predator—being one of the most commonly observed. Here, we investigate patterns of temporal variation in the mobbing response exhibited by a precocial species, the northern lapwing (Vanellus vanellus). We test whether brood age and self-reliance, or the perceived risk posed by various predators, affect mobbing response of lapwings. We quantified aggressive interactions between lapwings and their natural avian predators and used generalized additive models to test how timing and predator species identity are related to the mobbing response of lapwings. Lapwings diversified mobbing response within the breeding season and depending on predator species. Raven Corvus corax, hooded crow Corvus cornix and harriers evoked the strongest response, while common buzzard Buteo buteo, white stork Ciconia ciconia, black-headed gull Chroicocephalus ridibundus and rook Corvus frugilegus were less frequently attacked. Lapwings increased their mobbing response against raven, common buzzard, white stork and rook throughout the breeding season, while defence against hooded crow, harriers and black-headed gull did not exhibit clear temporal patterns. Mobbing behaviour of lapwings apparently constitutes a flexible anti-predator strategy. The anti-predator response depends on predator species, which may suggest that lapwings distinguish between predator types and match mobbing response to the perceived hazard at different stages of the breeding cycle. We conclude that a single species may exhibit various patterns of temporal variation in anti-predator defence, which may correspond with various hypotheses derived from parental investment theory