Heterogeneity in Behaviour and Movement can Influence the Stability of Predator-Prey Periodic Travelling Waves.

Cyclic predator-prey systems are often observed in nature. In a spatial setting, these can manifest as periodic traveling waves (PTW). Environmental change and direct human activity are known to, among other effects, increase the heterogeneity of the physical environment, which prey and predator inhabit. Aiming to understand the effects of heterogeneity on predator-prey PTWs, we consider a one-dimensional infinite landscape Rosenzweig-MacArthur reaction-diffusion model, with alternating patch types, and study the PTWs in this system. Applying the method of homogenisation, we show how heterogeneity can affect the stability of PTW solutions. We illustrate how the effects of heterogeneity can be understood and interpreted using Turchin's concept of residence index (encapsuling diffusion rate and patch preference). In particular, our results show that prey heterogeneity acts to modulate the effects of predator heterogeneity, by this we mean that as prey increasingly spend more time in one patch type over another the stability of the PTWs becomes more sensitive to heterogeneity in predator movement and behaviour.

Phenotypic plasticity as a cause and consequence of population dynamics.

Predicting complex species-environment interactions is crucial for guiding conservation and mitigation strategies in a dynamically changing world. Phenotypic plasticity is a mechanism of trait variation that determines how individuals and populations adapt to changing and novel environments. For individuals, the effects of phenotypic plasticity can be quantified by measuring environment-trait relationships, but it is often difficult to predict how phenotypic plasticity affects populations. The assumption that environment-trait relationships validated for individuals indicate how populations respond to environmental change is commonly made without sufficient justification. Here we derive a novel general mathematical framework linking trait variation due to phenotypic plasticity to population dynamics. Applying the framework to the classical example of Nicholson's blowflies, we show how seemingly sensible predictions made from environment-trait relationships do not generalise to population responses. As a consequence, trait-based analyses that do not incorporate population feedbacks risk mischaracterising the effect of environmental change on 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 [Formula: see text]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.

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.

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.

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.

Effects of forest spatial structure on insect outbreaks: insights from a host-parasitoid model.

Understanding how cycles of forest-defoliating insects are affected by forest destruction is of major importance for forest management. Achieving such an understanding with data alone is difficult, however, because population cycles are typically driven by species interactions that are highly nonlinear. We therefore constructed a mathematical model to investigate the effects of forest destruction on defoliator cycles, focusing on defoliator cycles driven by parasitoids. Our model shows that forest destruction can increase defoliator density when parasitoids disperse much farther than defoliators because the benefits of reduced defoliator mortality due to increased parasitoid dispersal mortality exceed the costs of increased defoliator dispersal mortality. This novel result can explain observations of increased outbreak duration with increasing forest fragmentation in forest tent caterpillar populations. Our model also shows that larger habitat patches can mitigate habitat loss, with clear implications for forest management. To better understand our results, we developed an approximate model that shows that defoliator spatial dynamics can be predicted from the proportion of dispersing animals that land in suitable habitat. This approximate model is practically useful because its parameters can be estimated from widely available data. Our model thus suggests that forest destruction may exacerbate defoliator outbreaks but that management practices could mitigate such effects.

High levels of somatic DNA diversity at the myotonic dystrophy type 1 locus are driven by ultra-frequent expansion and contraction mutations.

Several human genetic diseases are associated with inheriting an abnormally large unstable DNA simple sequence repeat. These sequences mutate, by changing the number of repeats, many times during the lifetime of those affected, with a bias towards expansion. These somatic changes lead not only to the presence of cells with different numbers of repeats in the same tissue, but also produce increasingly longer repeats, contributing towards the progressive nature of the symptoms. Modelling the progression of repeat length throughout the lifetime of individuals has potential for improving prognostic information as well as providing a deeper understanding of the underlying biological process. A large data set comprising blood DNA samples from individuals with one such disease, myotonic dystrophy type 1, provides an opportunity to parameterize a mathematical model for repeat length evolution that we can use to infer biological parameters of interest. We developed new mathematical models by modifying a proposed stochastic birth process to incorporate possible contraction. A hierarchical Bayesian approach was used as the basis for inference, and we estimated the distribution of mutation rates in the population. We used model comparison analysis to reveal, for the first time, that the expansion bias observed in the distributions of repeat lengths is likely to be the cumulative effect of many expansion and contraction events. We predict that mutation events can occur as frequently as every other day, which matches the timing of regular cell activities such as DNA repair and transcription but not DNA replication.

Revisiting the diffusion approximation to estimate evolutionary rates of gene family diversification.

Genetic diversity in multigene families is shaped by multiple processes, including gene conversion and point mutation. Because multi-gene families are involved in crucial traits of organisms, quantifying the rates of their genetic diversification is important. With increasing availability of genomic data, there is a growing need for quantitative approaches that integrate the molecular evolution of gene families with their higher-scale function. In this study, we integrate a stochastic simulation framework with population genetics theory, namely the diffusion approximation, to investigate the dynamics of genetic diversification in a gene family. Duplicated genes can diverge and encode new functions as a result of point mutation, and become more similar through gene conversion. To model the evolution of pairwise identity in a multigene family, we first consider all conversion and mutation events in a discrete manner, keeping track of their details and times of occurrence; second we consider only the infinitesimal effect of these processes on pairwise identity accounting for random sampling of genes and positions. The purely stochastic approach is closer to biological reality and is based on many explicit parameters, such as conversion tract length and family size, but is more challenging analytically. The population genetics approach is an approximation accounting implicitly for point mutation and gene conversion, only in terms of per-site average probabilities. Comparison of these two approaches across a range of parameter combinations reveals that they are not entirely equivalent, but that for certain relevant regimes they do match. As an application of this modelling framework, we consider the distribution of nucleotide identity among VSG genes of African trypanosomes, representing the most prominent example of a multi-gene family mediating parasite antigenic variation and within-host immune evasion.

Mean occupancy time: linking mechanistic movement models, population dynamics and landscape ecology to population persistence.

Reaction-diffusion models for the dynamics of a biological population in a fragmented landscape can incorporate detailed descriptions of movement and behavior, but are difficult to analyze and hard to parameterize. Patch models, on the other hand, are fairly easy to analyze and can be parameterized reasonably well, but miss many details of the movement process within and between patches. We develop a framework to scale up from a reaction-diffusion process to a patch model and, in particular, to determine movement rates between patches based on behavioral rules for individuals. Our approach is based on the mean occupancy time, the mean time that an individuals spends in a certain area of the landscape before it exits that area or dies. We illustrate our approach using several different landscape configurations. We demonstrate that the resulting patch model most closely captures persistence conditions and steady state densities as compared with the reaction-diffusion model.

The impact of mutation and gene conversion on the local diversification of antigen genes in African trypanosomes.

Patterns of genetic diversity in parasite antigen gene families hold important information about their potential to generate antigenic variation within and between hosts. The evolution of such gene families is typically driven by gene duplication, followed by point mutation and gene conversion. There is great interest in estimating the rates of these processes from molecular sequences for understanding the evolution of the pathogen and its significance for infection processes. In this study, a series of models are constructed to investigate hypotheses about the nucleotide diversity patterns between closely related gene sequences from the antigen gene archive of the African trypanosome, the protozoan parasite causative of human sleeping sickness in Equatorial Africa. We use a hidden Markov model approach to identify two scales of diversification: clustering of sequence mismatches, a putative indicator of gene conversion events with other lower-identity donor genes in the archive, and at a sparser scale, isolated mismatches, likely arising from independent point mutations. In addition to quantifying the respective probabilities of occurrence of these two processes, our approach yields estimates for the gene conversion tract length distribution and the average diversity contributed locally by conversion events. Model fitting is conducted using a Bayesian framework. We find that diversifying gene conversion events with lower-identity partners occur at least five times less frequently than point mutations on variant surface glycoprotein (VSG) pairs, and the average imported conversion tract is between 14 and 25 nucleotides long. However, because of the high diversity introduced by gene conversion, the two processes have almost equal impact on the per-nucleotide rate of sequence diversification between VSG subfamily members. We are able to disentangle the most likely locations of point mutations and conversions on each aligned gene pair.

Linking the antigen archive structure to pathogen fitness in African trypanosomes.

Systems that generate antigenic variation enable pathogens to evade host immune responses and are intricately interwoven with major pathogen traits, such as host choice, growth, virulence and transmission. Although much is understood about antigen switching at the molecular level, little is known about the cross-scale links between these molecular processes and the larger-scale within and between host population dynamics that they must ultimately drive. Inspired by the antigenic variation system of African trypanosomes, we apply modelling approaches to our expanding understanding of the organization and expression of antigen repertoires, and explore links across these scales. We predict how pathogen population processes are determined by underlying molecular genetics and infer resulting selective pressures on important emergent repertoire traits.

Effects of plant genotype and insect dispersal rate on the population dynamics of a forest pest.

It has been shown that plant genotype can strongly affect not only individual herbivore performance, but also community composition and ecosystem function. Few studies, however, have addressed how plant genotype affects herbivore population dynamics. In this paper, we used a simulation modeling approach to ask how the genetic composition of a forest influences pest outbreak dynamics, using the example of aspen (Populus tremuloides) and forest tent caterpillars (FTC; Malacosoma disstria). Specifically, we examined how plant genotype, the relative size of genotypic patches, and the rate of insect dispersal between them, affect the frequency, amplitude, and duration of outbreaks. We found that coupling two different genotypes does not necessarily result in an averaging of insect dynamics. Instead, depending on the ratio of patch sizes, when dispersal rates are moderate, outbreaks in the two-genotype case may be more or less severe than in forests of either genotype alone. Thresholds for different dynamic behaviors were similar for all genotypic combinations. Thus, the qualitative behavior of a stand of two different genotypes can be predicted based on the response of the insect to each genotype, the relative sizes of the two patches, and the scale of insect dispersal.

Measuring diversity: the importance of species similarity.

Realistic measures of biodiversity should reflect not only the relative abundances of species, but also the differences between them. We present a natural family of diversity measures taking both factors into account. This is not just another addition to the already long list of diversity indices. Instead, a single formula subsumes many of the most popular indices, including Shannon's, Simpson's, species richness, and Rao's quadratic entropy. These popular indices can then be used and understood in a unified way, and the relationships between them are made plain. The new measures are, moreover, effective numbers, so that percentage changes and ratio comparisons of diversity value are meaningful. We advocate the use of diversity profiles, which provide a faithful graphical representation of the shape of a community; they show how the perceived diversity changes as the emphasis shifts from rare to common species. Communities can usefully be compared by comparing their diversity profiles. We show by example that this is a far more subtle method than any relying on a single statistic. Some ecologists view diversity indices with suspicion, questioning whether they are biologically meaningful. By dropping the naive assumption that distinct species have nothing in common, working with effective numbers, and using diversity profiles, we arrive at a system of diversity measurement that should lay much of this suspicion to rest.

The evolution of developmental timing in natural enemy systems.

Natural parasitoid systems exhibit considerable variation in their life history properties yet little is known about the effects of development time on parasitoid fitness or of the conditions that might select for rapid development at the expense of reduced parasitoid growth. In this study the techniques of adaptive dynamics are applied to a discrete time host-parasitoid model to examine the evolution of parasitoid life history strategies. In particular, we explore the conditions that select for variation in parasitoid traits, such as, the timing of parasitoid attack and emergence from the host. The process of evolutionary branching, leading to dimorphism, can occur when the benefits to reproduction of early parasitoid attack are bought at a cost in terms of mortality of late parasitoid emergence from the host. We also find that trends in parasitoid life history traits depend critically on the nature of the underlying population dynamics. Increases in the strength of host density-dependence acts to select for shorter parasitoid development time and lower searching efficiency when the underlying population dynamics are at equilibrium. This trend is reversed when the underlying population dynamics exhibit fluctuations. Here, fluctuations in host density driven by parasitism become more extreme as the strength of host density-dependence decreases and so the parasitoid selects early emergence to avoid the mortality experienced at outbreak host densities. Our results are consistent with the general principle that parasitoids facing high mortality risk favour short development times over size and high searching efficiency, whereas species facing low mortality risks favour size at the cost of increased development time.

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.

Feral populations of Brassica oleracea along Atlantic coasts in western Europe.

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.

The impact of parasitoid emergence time on host-parasitoid population dynamics.

We investigate the effect of parasitoid phenology on host-parasitoid population cycles. Recent experimental research has shown that parasitized hosts can continue to interact with their unparasitized counterparts through competition. Parasitoid phenology, in particular the timing of emergence from the host, determines the duration of this competition. We construct a discrete-time host-parasitoid model in which within-generation dynamics associated with parasitoid timing is explicitly incorporated. We found that late-emerging parasitoids induce less severe, but more frequent, host outbreaks, independent of the choice of competition model. The competition experienced by the parasitized host reduces the parasitoids' numerical response to changes in host numbers, preventing the 'boom-bust' dynamics associated with more efficient parasitoids. We tested our findings against experimental data for the forest tent caterpillar (Malacosoma disstria Hübner) system, where a large number of consecutive years at a high host density is synonymous with severe forest damage.

Uncovering mechanisms behind mosquito seasonality by integrating mathematical models and daily empirical population data: Culex pipiens in the UK.

BACKGROUND: Many mosquito-borne diseases exhibit substantial seasonality, due to strong links between environmental variables and vector and pathogen life-cycles. Further, a range of density-dependent and density-independent biotic and abiotic processes affect the phenology of mosquito populations, with potentially large knock-on effects for vector dynamics and disease transmission. Whilst it is understood that density-independent and density-dependent processes affect seasonal population levels, it is not clear how these interact temporally to shape the population peaks and troughs. Due to this, the paucity of high-resolution data for validation, and the difficulty of parameterizing density-dependent processes, models of vector dynamics may poorly estimate abundances, which has knock-on effects for our ability predict vector-borne disease outbreaks. RESULTS: We present a rich dataset describing seasonal abundance patterns of each life stage of Culex pipiens, a widespread vector of West Nile virus, at a field site in southern England in 2015. Abundance of immature stages was measured three times per week, whilst adult traps were run four nights each week. This dataset is integrated with an existing delay-differential equation model predicting Cx. pipiens seasonal abundance to improve understanding of observed seasonal abundance patterns. At our field site, the outcome of our model fitting suggests interspecific predation on mosquito larvae and temperature-dependent larval mortality combine to act as the main sources of population regulation throughout the active season, whilst competition for resources is a relatively small source of larval mortality. CONCLUSIONS: The model suggests that density-independent mortality and interspecific predation interact to shape patterns of mosquito seasonal abundance in a permanent aquatic habitat and we propose that competition for resources is likely to be important where periods of high rainfall create transient habitats. Further, we highlight the importance of challenging population abundance models with data from across all life stages of the species of interest if reliable inferences are to be drawn from these models, particularly when considering mosquito control and vector-borne disease transmission.

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.