Homogenization techniques for population dynamics in strongly heterogeneous landscapes

An important problem in spatial ecology is to understand how population-scale patterns emerge from individual-level birth, death, and movement processes. These processes, which depend on local landscape characteristics, vary spatially and may exhibit sharp transitions through behavioural responses to habitat edges, leading to discontinuous population densities. Such systems can be modelled using reaction–diffusion equations with interface conditions that capture local behaviour at patch boundaries. In this work we develop a novel homogenization technique to approximate the large-scale dynamics of the system. We illustrate our approach, which also generalizes to multiple species, with an example of logistic growth within a periodic environment. We find that population persistence and the large-scale population carrying capacity is influenced by patch residence times that depend on patch preference, as well as movement rates in adjacent patches. The forms of the homogenized coefficients yield key theoretical insights into how large-scale dynamics arise from the small-scale features

Diffusion-driven instabilities and emerging spatial patterns in patchy landscapes

Spatial variation in population densities across a landscape is a feature of many ecological systems, from self-organised patterns on mussel beds to spatially restricted insect outbreaks. It occurs as a result of environmental variation in abiotic factors and/or biotic factors structuring the spatial distribution of populations. However the ways in which abiotic and biotic factors interact to determine the existence and nature of spatial patterns in population density remain poorly understood. Here we present a new approach to studying this question by analysing a predator–prey patch-model in a heterogenous landscape. We use analytical and numerical methods originally developed for studying nearest- neighbour (juxtacrine) signalling in epithelia to explore whether and under which conditions patterns emerge. We find that abiotic and biotic factors interact to promote pattern formation. In fact, we find a rich and highly complex array of coexisting stable patterns, located within an enormous number of unstable patterns. Our simulation results indicate that many of the stable patterns have appreciable basins of attraction, making them significant in applications. We are able to identify mechanisms for these patterns based on the classical ideas of long-range inhibition and short-range activation, whereby landscape heterogeneity can modulate the spatial scales at which these processes operate to structure the populations

Should I stay or should I go: partially sedentary populations can outperform fully dispersing populations in response to climate-induced range shifts

Global mean temperatures have increased by 0.72 ∘C since the 1950s, and climate warming is resulting in geographical shifts in the range limits of many species. Climate velocity is estimated to be 0.42 km/year, and if a species fails to adapt to the new climate, it must track the location of its climatically constrained niche in order to survive. Dispersal has an important role to play in enabling a population to shift is geographical range limits, but many species are partially sedentary, with only a fraction of the population dispersing each year. We ask, can partially sedentary populations keep pace with climate or will such populations be more vulnerable to extinction? Through the development of a moving-habitat integrodifference equation model, we show that, provided climate velocity is not too large, partially sedentary populations can outperform fully dispersing populations in one of two ways: (i) by persisting at climate speeds where a fully dispersing population cannot, and (ii) exhibiting higher population densities. Moreover, we find that positive density-dependent dispersal can further improve the likelihood a population can persist. Our results highlight the positive role that non-dispersers may play in mitigating the effects of overdispersal and facilitating population persistence in a warming world

Skewed temperature dependence affects range and abundance in a warming world

Population growth metrics such as R0 are usually asymmetric functions of temperature, with cold-skewed curves arising when the positive effects of a temperature increase outweigh the negative effects, and warm-skewed curves arising in the opposite case. Classically, cold-skewed curves are interpreted as more beneficial to a species under climate warming, because cold-skewness implies increased population growth over a larger proportion of the species's fundamental thermal niche than warm-skewness. However, inference based on the shape of the fitness curve alone, and without considering the synergistic effects of net reproduction, density and dispersal, may yield an incomplete understanding of climate change impacts. We formulate a moving-habitat integrodifference equation model to evaluate how fitness curve skewness affects species’ range size and abundance during climate warming. In contrast to classic interpretations, we find that climate warming adversely affects populations with cold-skewed fitness curves, positively affects populations with warm-skewed curves and has relatively little or mixed effects on populations with symmetric curves. Our results highlight the synergistic effects of fitness curve skewness, spatially heterogeneous densities and dispersal in climate change impact analyses, and that the common approach of mapping changes only in R0 may be misleading

Changing environments and genetic variation: natural variation in inbreeding does not compromise short-term physiological responses

Selfing plant lineages are surprisingly widespread and successful in a broad range of environments, despite showing reduced genetic diversity, which is predicted to reduce their long-term evolutionary potential. However, appropriate short-term plastic responses to new environmental conditions might not require high levels of standing genetic variation. In this study, we tested whether mating system variation among populations, and associated changes in genetic variability, affected short-term responses to environmental challenges. We compared relative fitness and metabolome profiles of naturally outbreeding (genetically diverse) and inbreeding (genetically depauperate) populations of a perennial plant, Arabidopsis lyrata, under constant growth chamber conditions and an outdoor common garden environment outside its native range. We found no effect of inbreeding on survival, flowering phenology or short-term physiological responses. Specifically, naturally occurring inbreeding had no significant effects on the plasticity of metabolome profiles, using either multivariate approaches or analysis of variation in individual metabolites, with inbreeding populations showing similar physiological responses to outbreeding populations over time in both growing environments. We conclude that low genetic diversity in naturally inbred populations may not always compromise fitness or short-term physiological capacity to respond to environmental change, which could help to explain the global success of selfing mating strategies

Changing environments and genetic variation: natural variation in inbreeding does not compromise short-term physiological responses

Selfing plant lineages are surprisingly widespread and successful in a broad range of environments, despite showing reduced genetic diversity, which is predicted to reduce their long-term evolutionary potential. However, appropriate short-term plastic responses to new environmental conditions might not require high levels of standing genetic variation. In this study, we tested whether mating system variation among populations, and associated changes in genetic variability, affected short-term responses to environmental challenges. We compared relative fitness and metabolome profiles of naturally outbreeding (genetically diverse) and inbreeding (genetically depauperate) populations of a perennial plant, Arabidopsis lyrata, under constant growth chamber conditions and an outdoor common garden environment outside its native range. We found no effect of inbreeding on survival, flowering phenology or short-term physiological responses. Specifically, naturally occurring inbreeding had no significant effects on the plasticity of metabolome profiles, using either multivariate approaches or analysis of variation in individual metabolites, with inbreeding populations showing similar physiological responses to outbreeding populations over time in both growing environments. We conclude that low genetic diversity in naturally inbred populations may not always compromise fitness or short-term physiological capacity to respond to environmental change, which could help to explain the global success of selfing mating strategies

Feral populations of Brassica oleracea along Atlantic coasts in western Europe

EAM was funded by a University of Glasgow Lord Kelvin Adam Smith PhD studentship; UZI was funded by a NERC Independent Research Fellowship (NE/L011956); CAC is supported by the BBSRC (BB/P004202/1); KAM utilized equipment funded by the Wellcome Trust Institutional Strategic Support Fund (WT097835MF), Wellcome Trust Multi‐User Equipment Award (WT101650MA), and BBSRC LOLA award (BB/K003240/1). Part of the work was supported by a British Society for Plant Pathology summer studentship, and grants from the Botanical Research Fund, and the Blodwen Lloyd Bins trust funded through the Glasgow Natural History Society.There has been growing emphasis on the role that crop wild relatives might play in supporting highly selected agriculturally valuable species in the face of climate change. In species that were domesticated many thousands of years ago, distinguishing wild populations from escaped feral forms can be challenging, but reintroducing variation from either source could supplement current cultivated forms. For economically important cabbages (Brassicaceae: Brassica oleracea), “wild” populations occur throughout Europe but little is known about their genetic variation or potential as resources for breeding more resilient crop varieties. The main aim of this study was to characterize the population structure of geographically isolated wild cabbage populations along the coasts of the UK and Spain, including the Atlantic range edges. Double-digest restriction-site-associated DNA sequencing was used to sample individual cabbage genomes, assess the similarity of plants from 20 populations, and explore environment–genotype associations across varying climatic conditions. Interestingly, there were no indications of isolation by distance; several geographically close populations were genetically more distinct from each other than to distant populations. Furthermore, several distant populations shared genetic ancestry, which could indicate that they were established by escapees of similar source cultivars. However, there were signals of local adaptation to different environments, including a possible relationship between genetic diversity and soil pH. Overall, these results highlight wild cabbages in the Atlantic region as an important genetic resource worthy of further research into their relationship with existing crop varieties.Publisher PDFPeer reviewe

Dynamic virtual ecosystems as a tool for detecting large-scale responses of biodiversity to environmental and land-use change

In the face of biodiversity loss, we rely upon measures of diversity to describe the health of ecosystems and to direct policymakers and conservation efforts. However, there are many complexities in natural systems that can easily confound biodiversity measures, giving misleading interpretations of the system status and, as a result, there is yet to be a consistent framework by which to measure this biodiversity loss. Ecosystems are governed by dynamic processes, such as reproduction, dispersal and competition for resources, that both shape their biodiversity and how the system responds to change. Here, we incorporate these processes into simulations of habitat and environmental change, in order to understand how well we can identify signals of biodiversity loss against the background inherent variability these processes introduce. We developed a tool for Ecosystem Simulation through Integrated Species Trait-Environment Modelling (EcoSISTEM), which models on the species-level for several sizes of ecosystem, from small islands and patches through to entire regions, and several different types of habitat. We tested a suite of traditionally-used and new biodiversity measures on simulated ecosystems against a range of different scenarios of population decline, invasion and habitat loss. We found that the response of biodiversity measures was generally stronger in larger, more heterogeneous habitats than in smaller or homogeneous habitats. We were also able to detect signals of increasing homogenisation in climate change scenarios, which contradicted the signal of increased heterogeneity and distinctiveness through habitat loss

A novel approach for predicting risk of vector-borne disease establishment in marginal temperate environments under climate change: West Nile virus in the UK

Vector-borne diseases (VBDs), such as dengue, Zika, West Nile virus (WNV) and tick-borne encephalitis, account for substantial human morbidity worldwide and have expanded their range into temperate regions in recent decades. Climate change has been proposed as a likely driver of past and future expansion, however, the complex ecology of host and vector populations and their interactions with each other, environmental variables and land-use changes makes understanding the likely impacts of climate change on VBDs challenging. We present an environmentally driven, stage-structured, host–vector mathematical modelling framework to address this challenge. We apply our framework to predict the risk of WNV outbreaks in current and future UK climates. WNV is a mosquito-borne arbovirus which has expanded its range in mainland Europe in recent years. We predict that, while risks will remain low in the coming two to three decades, the risk of WNV outbreaks in the UK will increase with projected temperature rises and outbreaks appear plausible in the latter half of this century. This risk will increase substantially if increased temperatures lead to increases in the length of the mosquito biting season or if European strains show higher replication at lower temperatures than North American strains

Moving forward in circles: challenges and opportunities in modelling population cycles

Population cycling is a widespread phenomenon, observed across a multitude of taxa in both laboratory and natural conditions. Historically, the theory associated with population cycles was tightly linked to pairwise consumer–resource interactions and studied via deterministic models, but current empirical and theoretical research reveals a much richer basis for ecological cycles. Stochasticity and seasonality can modulate or create cyclic behaviour in non-intuitive ways, the high-dimensionality in ecological systems can profoundly influence cycling, and so can demographic structure and eco-evolutionary dynamics. An inclusive theory for population cycles, ranging from ecosystem-level to demographic modelling, grounded in observational or experimental data, is therefore necessary to better understand observed cyclical patterns. In turn, by gaining better insight into the drivers of population cycles, we can begin to understand the causes of cycle gain and loss, how biodiversity interacts with population cycling, and how to effectively manage wildly fluctuating populations, all of which are growing domains of ecological research