Anomalous invasion dynamics due to dispersal polymorphism and dispersal-reproduction trade-offs.

Dispersal polymorphism and mutation play significant roles during biological invasions, potentially leading to evolution and complex behaviour such as accelerating or decelerating invasion fronts. However, life-history theory predicts that reproductive fitness-another key determinant of invasion dynamics-may be lower for more dispersive strains. Here, we use a mathematical model to show that unexpected invasion dynamics emerge from the combination of heritable dispersal polymorphism, dispersal-fitness trade-offs, and mutation between strains. We show that the invasion dynamics are determined by the trade-off relationship between dispersal and population growth rates of the constituent strains. We find that invasion dynamics can be 'anomalous' (i.e. faster than any of the strains in isolation), but that the ultimate invasion speed is determined by the traits of, at most, two strains. The model is simple but generic, so we expect the predictions to apply to a wide range of ecological, evolutionary, or epidemiological invasions.

Mate-finding Allee effects can be exacerbated or relieved by sexual cannibalism.

Allee effects occur when individual or population survival decreases due to populations being small or sparse. A key mechanism underlying Allee effects is difficulty in finding mates at low densities. Species may be particularly vulnerable to mate-finding Allee effects if females rely on an abundance of males to reproduce successfully. In sexually cannibalistic species, females may consume males before or after copulation, potentially reducing the supply of males to the point where a mate-finding Allee effect occurs. In this study, we investigate the extent to which sexual cannibalism can modulate mate-finding Allee effects, and the conditions under which sexual cannibalism is likely to be particularly detrimental to population viability. We created an individual-based model that tracked specific females throughout the breeding season and used extinction risk and per capita growth rate to measure the strength of the Allee effects. We varied both founder population size and mate encounter rate independently of each other to expose the mechanism driving the Allee effects. We also analysed how cannibalism-derived female fecundity benefits affected extinction risk. We found that sexual cannibalism could lead to high extinction risk, particularly when cannibalism occurred before copulation, founder population size was small and mate encounter rates were low. However, post-copulatory cannibalism reduced extinction risk, if cannibalism increased female fecundity enough. We found that there were strong threshold effects, in which small changes in encounter rate could strongly alter population extinction risk. We find that sexual cannibalism is likely to negatively impact population survival as population size and mate encounter rate decrease. This may be exacerbated if male quality declines and female hunger increases in declining populations. As many top invertebrate predators, such as spiders and mantises, are sexually cannibalistic, this may have ecosystem-wide impacts. We also suggest that other reproductive behaviours, such as rejecting all but high-quality mates or requiring multiple mates to ensure fertility, are also likely to cause mate-finding Allee effects when habitat quality degrades.

Controlling invasive rodents via synthetic gene drive and the role of polyandry.

House mice are a major ecosystem pest, particularly threatening island ecosystems as a non-native invasive species. Rapid advances in synthetic biology offer new avenues to control pest species for biodiversity conservation. Recently, a synthetic sperm-killing gene drive construct called t-Sry has been proposed as a means to eradicate target mouse populations owing to a lack of females. A factor that has received little attention in the discussion surrounding such drive applications is polyandry. Previous research has demonstrated that sperm-killing drivers are extremely damaging to a male's sperm competitive ability. Here, we examine the importance of this effect on the t-Sry system using a theoretical model. We find that polyandry substantially hampers the spread of t-Sry such that release efforts have to be increased three- to sixfold for successful eradication. We discuss the implications of our finding for potential pest control programmes, the risk of drive spread beyond the target population, and the emergence of drive resistance. Our work highlights that a solid understanding of the forces that determine drive dynamics in a natural setting is key for successful drive application, and that exploring the natural diversity of gene drives may inform effective gene drive design.

The evolution of variance in sequential defences.

The defences used by organisms against predators display a great degree of variability. Defence phenotypes can differ substantially among individuals of the same species, and a single individual can itself deploy a variety of defences. Here, we use a mathematical model that includes mutation and selection to understand the evolutionary origin of this variability in a population of a species that deploys defences sequentially ("first" and "second" defences). Typically, the first defence evolves to have lower variance, i.e. appears more closely accumulated around the ideal phenotype, than the second defence (even when the breaching the first defence incurs more fitness loss than breaching the second defence with the other parameters the same for both defences). However, if the first defence is much less effective in repelling predators, or is much less tolerant of deviation from the ideal phenotype, then the first defence can evolve to have higher variance than the second. Other factors like mutation strength and the losses in the fitness when each defence fails also influence the defence variance. Larger mutation rate incurs larger equilibrium variances, and when the comparative importance in fitness of one defence increases, then the ratio between the variances of this defence and the other defence decreases. Sequentially acting defences are found in many organisms, so we encourage empirical research to test our theoretical predictions.

A theory for investment across defences triggered at different stages of a predator-prey encounter.

We introduce a general theoretical description of a combination of defences acting sequentially at different stages in the predatory sequence in order to make predictions about how animal prey should best allocate investment across different defensive stages. We predict that defensive investment will often be concentrated at stages early in the interaction between a predator individual and the prey (especially if investment is concentrated in only one defence, then it will be in the first defence). Key to making this prediction is the assumption that there is a cost to a prey when it has a defence tested by an enemy, for example because this incurs costs of deployment or tested costs as a defence is exposed to the enemies; and the assumption that the investment functions are the same among defences. But if investment functions are different across defences (e.g. the investment efficiency in making resources into defences is higher in later defences than in earlier defences), then the contrary could happen. The framework we propose can be applied to other victim-exploiter systems, such as insect herbivores feeding on plant tissues. This leads us to propose a novel explanation for the observation that herbivory damage is often not well explained by variation in concentrations of toxic plant secondary metabolites. We compare our general theoretical structure with related examples in the literature, and conclude that coevolutionary approaches will be profitable in future work.

When can species abundance data reveal non-neutrality?

Species abundance distributions (SAD) are probably ecology's most well-known empirical pattern, and over the last decades many models have been proposed to explain their shape. There is no consensus over which model is correct, because the degree to which different processes can be discerned from SAD patterns has not yet been rigorously quantified. We present a power calculation to quantify our ability to detect deviations from neutrality using species abundance data. We study non-neutral stochastic community models, and show that the presence of non-neutral processes is detectable if sample size is large enough and/or the amplitude of the effect is strong enough. Our framework can be used for any candidate community model that can be simulated on a computer, and determines both the sampling effort required to distinguish between alternative processes, and a range for the strength of non-neutral processes in communities whose patterns are statistically consistent with neutral theory. We find that even data sets of the scale of the 50 Ha forest plot on Barro Colorado Island, Panama, are unlikely to be large enough to detect deviations from neutrality caused by competitive interactions alone, though the presence of multiple non-neutral processes with contrasting effects on abundance distributions may be detectable.

Offspring Provisioning Explains Clone-Specific Maternal Age Effects on Life History and Life Span in the Water Flea, Daphnia pulex.

Genetic inheritance underpins evolutionary theories of aging, but the role that nongenetic inheritance plays is unclear. Parental age reduces the life span of offspring in a diverse array of taxa but has not been explained from an evolutionary perspective. We quantified the effect that maternal age had on the growth and maturation decisions, life history, rates of senescence, and life span of offspring from three Daphnia pulex clones collected from different populations. We then used those data to test general hypotheses proposed to explain maternal age effects on offspring life span. Three generations of breeding from young or old mothers produced dramatic differences in the life histories of fourth-generation offspring, including significant reductions in life span. The magnitude of the effect differed between clones, which suggests that genetic and nongenetic factors ultimately underpin trait inheritance and shape patterns of aging. Older parents did not transmit a senescent state to their offspring. Instead, offspring from older ancestors had increased early-life reproductive effort, which resulted in an earlier onset of reproductive senescence, and an increased rate of actuarial senescence, which shortened their life span. Our results provide a clear example of the need to consider multiple inheritance mechanisms when studying trait evolution.

Predictive systems ecology.

Human societies, and their well-being, depend to a significant extent on the state of the ecosystems that surround them. These ecosystems are changing rapidly usually in response to anthropogenic changes in the environment. To determine the likely impact of environmental change on ecosystems and the best ways to manage them, it would be desirable to be able to predict their future states. We present a proposal to develop the paradigm of predictive systems ecology, explicitly to understand and predict the properties and behaviour of ecological systems. We discuss the necessary and desirable features of predictive systems ecology models. There are places where predictive systems ecology is already being practised and we summarize a range of terrestrial and marine examples. Significant challenges remain but we suggest that ecology would benefit both as a scientific discipline and increase its impact in society if it were to embrace the need to become more predictive.

Downscaling species occupancy from coarse spatial scales.

The measurement and prediction of species' populations at different spatial scales is crucial to spatial ecology as well as conservation biology. An efficient yet challenging goal to achieve such population estimates consists of recording empirical species' presence and absence at a specific regional scale and then trying to predict occupancies at finer scales. So far the majority of the methods have been based on particular species' distributional features deemed to be crucial for downscaling occupancy. However, only a minority of them have dealt explicitly with specific spatial features. Here we employ a wide class of spatial point processes, the shot noise Cox processes (SNCP), to model species occupancies at different spatial scales and show that species' spatial aggregation is crucial for predicting population estimates at fine scales starting from coarser ones. These models are formulated in continuous space and locate points regardless of the arbitrary resolution that one employs to study the spatial pattern. We compare the performances of nine models, calibrated at regional scales and demonstrate that a very simple class of SNCP, the Thomas process, is able to outperform other published models in predicting occupancies down to areas four orders of magnitude smaller than the ones employed for the parameterization. We conclude by explaining the ability of the approach to infer spatially explicit information from spatially implicit measures, the potential of the framework to combine niche and spatial models, and the possibility of reversing the method to allow upscaling.

Partner intrinsic characteristics influence foraging trip duration, but not coordination of care in wandering albatrosses Diomedea exulans.

Long-lived monogamous species gain long-term fitness benefits by equalizing effort during biparental care. For example, many seabird species coordinate care by matching foraging trip durations within pairs. Age affects coordination in some seabird species; however, the impact of other intrinsic traits, including personality, on potential intraspecific variation in coordination strength is less well understood. The impacts of pair members' intrinsic traits on trip duration and coordination strength were investigated using data from saltwater immersion loggers deployed on 71 pairs of wandering albatrosses Diomedea exulans. These were modeled against pair members' age, boldness, and their partner's previous trip duration. At the population level, the birds exhibited some coordination of parental care that was of equal strength during incubation and chick-brooding. However, there was low variation in coordination between pairs and coordination strength was unaffected by the birds' boldness or age in either breeding stage. Surprisingly, during incubation, foraging trip duration was mainly driven by partner traits, as birds which were paired to older and bolder partners took shorter trips. During chick-brooding, shorter foraging trips were associated with greater boldness in focal birds and their partners, but age had no effect. These results suggest that an individual's assessment of their partner's capacity or willingness to provide care may be a major driver of trip duration, thereby highlighting the importance of accounting for pair behavior when studying parental care strategies.

Analytical approximation for invasion and endemic thresholds, and the optimal control of epidemics in spatially explicit individual-based models.

Computer simulations of individual-based models are frequently used to compare strategies for the control of epidemics spreading through spatially distributed populations. However, computer simulations can be slow to implement for newly emerging epidemics, delaying rapid exploration of different intervention scenarios, and do not immediately give general insights, for example, to identify the control strategy with a minimal socio-economic cost. Here, we resolve this problem by applying an analytical approximation to a general epidemiological, stochastic, spatially explicit SIR(S) model where the infection is dispersed according to a finite-ranged dispersal kernel. We derive analytical conditions for a pathogen to invade a spatially explicit host population and to become endemic. To derive general insights about the likely impact of optimal control strategies on invasion and persistence: first, we distinguish between 'spatial' and 'non-spatial' control measures, based on their impact on the dispersal kernel; second, we quantify the relative impact of control interventions on the epidemic; third, we consider the relative socio-economic cost of control interventions. Overall, our study shows a trade-off between the two types of control interventions and a vaccination strategy. We identify the optimal strategy to control invading and endemic diseases with minimal socio-economic cost across all possible parameter combinations. We also demonstrate the necessary characteristics of exit strategies from control interventions. The modelling framework presented here can be applied to a wide class of diseases in populations of humans, animals and plants.

Coevolution of group-living and aposematism in caterpillars: warning colouration may facilitate the evolution from group-living to solitary habits.

BACKGROUND: Animals use diverse antipredator mechanisms, including visual signalling of aversive chemical defence (aposematism). However, the initial evolution of aposematism poses the problem that the first aposematic individuals are conspicuous to predators who have not learned the significance of the warning colouration. In one scenario, aposematism evolves in group-living species and originally persisted due to kin selection or positive frequency-dependent selection in groups. Alternatively, group-living might evolve after aposematism because grouping can amplify the warning signal. However, our current understanding of the evolutionary dynamics of these traits is limited, leaving the relative merit of these scenarios unresolved. RESULTS: We used a phylogenetic comparative approach to estimate phenotypic evolutionary models to enable inferences regarding ancestral states and trait dynamics of grouping and aposematic colouration in a classic model system (caterpillars). We find strong support for aposematism at the root of the clade, and some (but weaker) support for ancestral solitary habits. Transition rates between aposematism and crypsis are generally higher than those between group-living and solitary-living, suggesting that colouration is more evolutionarily labile than aggregation. We also find that the transition from group-living to solitary-living states can only happen in aposematic lineage, suggesting that aposematism facilitates the evolution of solitary caterpillars, perhaps due to the additional protection offered when the benefits of grouping are lost. We also find that the high frequency of solitary, cryptic caterpillars is because this state is particularly stable, in that the transition rates moving towards this state are substantially higher than those moving away from it, favouring its accumulation in the clade over evolutionary time. CONCLUSIONS: Our results provide new insights into the coevolution of colour and aggregation in caterpillars. We find support for an aposematic caterpillar at the root of this major clade, and for the signal augmentation hypothesis as an explanation of the evolution of aposematic, group-living caterpillars. We find that colouration is more labile than aggregation behaviour, but that the combination of solitary and cryptic habits is particularly stable. Finally, our results reveal that the transitions from group-living to solitary-living could be facilitated by aposematism, providing a new link between these well-studied traits.

Protracted speciation revitalizes the neutral theory of biodiversity.

Understanding the maintenance and origin of biodiversity is a formidable task, yet many ubiquitous ecological patterns are predicted by a surprisingly simple and widely studied neutral model that ignores functional differences between species. However, this model assumes that new species arise instantaneously as singletons and consequently makes unrealistic predictions about species lifetimes, speciation rates and number of rare species. Here, we resolve these anomalies - without compromising any of the original model's existing achievements and retaining computational and analytical tractability - by modelling speciation as a gradual, protracted, process rather than an instantaneous event. Our model also makes new predictions about the diversity of 'incipient' species and rare species in the metacommunity. We show that it is both necessary and straightforward to incorporate protracted speciation in future studies of neutral models, and argue that non-neutral models should also model speciation as a gradual process rather than an instantaneous one.

Modelling stochastic transmission processes in helminth infections.

The number of helminths within a host can only increase by the host encountering additional infectious stages, so it is important to consider not only whether a host is infected, but also the severity of its infection. Stochastic models consider explicitly the number of parasites within the host and treat infection, death and other demographic events as random processes. I discuss stochastic helminth population models of increasing degrees of complexity, starting with the infection dynamics within a single host and finishing with the full parasite lifecycle among a population of hosts. I demonstrate the mathematical techniques that can help to analyse these models and discuss the insights into parasite population biology that these methods can bring.

A new framework for growth curve fitting based on the von Bertalanffy Growth Function.

All organisms grow. Numerous growth functions have been applied to a wide taxonomic range of organisms, yet some of these models have poor fits to empirical data and lack of flexibility in capturing variation in growth rate. We propose a new VBGF framework that broadens the applicability and increases flexibility of fitting growth curves. This framework offers a curve-fitting procedure for five parameterisations of the VBGF: these allow for different body-size scaling exponents for anabolism (biosynthesis potential), besides the commonly assumed 2/3 power scaling, and allow for supra-exponential growth, which is at times observed. This procedure is applied to twelve species of diverse aquatic invertebrates, including both pelagic and benthic organisms. We reveal widespread variation in the body-size scaling of biosynthesis potential and consequently growth rate, ranging from isomorphic to supra-exponential growth. This curve-fitting methodology offers improved growth predictions and applies the VBGF to a wider range of taxa that exhibit variation in the scaling of biosynthesis potential. Applying this framework results in reliable growth predictions that are important for assessing individual growth, population production and ecosystem functioning, including in the assessment of sustainability of fisheries and aquaculture.

Species-area curves, neutral models, and long-distance dispersal.

We simulate species-area curves (SACs) using a spatially explicit neutral model. These display three distinct phases with the central phase being well approximated by a "power law" where species richness (S) is related to area (A) by S = cA(z). If seeds are normally distributed in space about their parent, the power law phase of the SAC is unrealistically narrow, and implausibly large speciation rates are required to fit empirical data. However, if dispersal follows a more realistic "fat-tailed" distribution (where long-distance dispersal events are more likely) the SACs fit the empirical data better, have a power law that holds for a much broader range of areas, and require a dramatically smaller speciation rate than when dispersal is normally distributed. Neutral models with biologically plausible dispersal parameters and speciation rates lead to empirically realistic SACs.

Intracellular demography and the dynamics of Salmonella enterica infections.

An understanding of within-host dynamics of pathogen interactions with eukaryotic cells can shape the development of effective preventive measures and drug regimes. Such investigations have been hampered by the difficulty of identifying and observing directly, within live tissues, the multiple key variables that underlay infection processes. Fluorescence microscopy data on intracellular distributions of Salmonella enterica serovar Typhimurium (S. Typhimurium) show that, while the number of infected cells increases with time, the distribution of bacteria between cells is stationary (though highly skewed). Here, we report a simple model framework for the intensity of intracellular infection that links the quasi-stationary distribution of bacteria to bacterial and cellular demography. This enables us to reject the hypothesis that the skewed distribution is generated by intrinsic cellular heterogeneities, and to derive specific predictions on the within-cell dynamics of Salmonella division and host-cell lysis. For within-cell pathogens in general, we show that within-cell dynamics have implications across pathogen dynamics, evolution, and control, and we develop novel generic guidelines for the design of antibacterial combination therapies and the management of antibiotic resistance.

Interactions between harvesting, noise and territoriality in a model of red grouse population cycles.

1. Population cycles are mostly thought to arise through extrinsic rather than intrinsic processes. However, in red grouse (Lagopus lagopus scoticus), intrinsic male territoriality has been proposed as a driver of the cycles, possibly in conjunction with an extrinsic interaction with specialist parasitic worms. Here we examine how harvesting and environmental noise may also interact with territoriality to determine how grouse populations cycle. 2. A stochastic model of grouse dynamics based on the territoriality hypothesis is developed, including harvesting and the effects of nonterritorial birds on aggressiveness. Cycles are detected in 97% of populations simulated over realistic parameter ranges, and these exhibit similar statistical properties to those reported in studies of multiple grouse populations. As observed, cycle periods are shorter at higher breeding productivities. 3. The model demonstrates the destabilizing influence of delayed density-dependent territorial aggressiveness. Cycle amplitudes are higher when annual changes in aggression are larger and when nonterritorial males provoke greater aggression. Intriguingly, the model suggests how an interaction between aggressiveness and parasites may operate. It is known that males with high worm burdens show dramatic decreases in aggressiveness in the year following a peak in territoriality. When this is included in the model, via larger crashes in aggression, amplitudes are higher, despite a reduction in overall aggressiveness. 4. Environmental stochasticity interacts with territoriality to determine the form of the cycles, but this is mediated through its 'colour' or temporal autocorrelation. For example, uncorrelated white noise increases amplitudes, while autocorrelated red noise has the opposite effect. However, noise increases cycle periods whatever the colour. 5. Harvesting occurs before territorial competition. This reduces the pool of males competing for territories and so increases recruitment and population densities. However, crashes can then be more extreme so cycle amplitudes are higher. With harvesting at ~150% of current typical levels, which is within observed variation, the dynamics exhibit a sharp transition to a state where cyclicity is reduced, periods are shorter and amplitudes lower. 6. The model suggests that to understand regional variation in red grouse cycles, interactions between territoriality, productivity, harvesting and noise must be considered.

A unified framework for analysis of individual-based models in ecology and beyond.

Individual-based models, 'IBMs', describe naturally the dynamics of interacting organisms or social or financial agents. They are considered too complex for mathematical analysis, but computer simulations of them cannot give the general insights required. Here, we resolve this problem with a general mathematical framework for IBMs containing interactions of an unlimited level of complexity, and derive equations that reliably approximate the effects of space and stochasticity. We provide software, specified in an accessible and intuitive graphical way, so any researcher can obtain analytical and simulation results for any particular IBM without algebraic manipulation. We illustrate the framework with examples from movement ecology, conservation biology, and evolutionary ecology. This framework will provide unprecedented insights into a hitherto intractable panoply of complex models across many scientific fields.

Seasonality, cohort-dependence and the development of immunity in a natural host-nematode system.

Acquired immunity is known to be a key modulator of the dynamics of many helminth parasites in domestic and human host populations, but its relative importance in natural populations is more controversial. A detailed long-term dataset on the gastrointestinal nematode Trichostrongylus retortaeformis in a wild population of European rabbits (Oryctolagus cuniculus) shows clear evidence of seasonal acquired immunity in the age-structured infection profiles. By fitting a hierarchy of demographic infection-immunity models to the observed age-structured infection patterns, we are able to quantify the importance of different components (seasonality, immunity and host age structure) of the parasite dynamics. We find strong evidence that the hosts' immunocompetence waxes and wanes with the seasons, but also contains a lifelong cohort factor, possibly acting through a maternal effect dependent on the host's month of birth. These observations have important and broad implications for the ecology of parasite infection in seasonal natural herbivore systems.