Three-dimensional random walk models of individual animal movement and their application to trap counts modelling.

BACKGROUND: Random walks (RWs) have proved to be a powerful modelling tool in ecology, particularly in the study of animal movement. An application of RW concerns trapping which is the predominant sampling method to date in insect ecology and agricultural pest management. A lot of research effort has been directed towards modelling ground-dwelling insects by simulating their movement in 2D, and computing pitfall trap counts, but comparatively very little for flying insects with 3D elevated traps. METHODS: We introduce the mathematics behind 3D RWs and present key metrics such as the mean squared displacement (MSD) and path sinuosity, which are already well known in 2D. We develop the mathematical theory behind the 3D correlated random walk (CRW) which involves short-term directional persistence and the 3D Biased random walk (BRW) which introduces a long-term directional bias in the movement so that there is an overall preferred movement direction. In this study, we focus on the geometrical aspects of the 3D trap and thus consider three types of shape; a spheroidal trap, a cylindrical trap and a rectangular cuboidal trap. By simulating movement in 3D space, we investigated the effect of 3D trap shapes and sizes and of movement diffusion on trapping efficiency. RESULTS: We found that there is a non-linear dependence of trap counts on the trap surface area or volume, but the effect of volume appeared to be a simple consequence of changes in area. Nevertheless, there is a slight but clear hierarchy of trap shapes in terms of capture efficiency, with the spheroidal trap retaining more counts than a cylinder, followed by the cuboidal type for a given area. We also showed that there is no effect of short-term persistence when diffusion is kept constant, but trap counts significantly decrease with increasing diffusion. CONCLUSION: Our results provide a better understanding of the interplay between the movement pattern, trap geometry and impacts on trapping efficiency, which leads to improved trap count interpretations, and more broadly, has implications for spatial ecology and population dynamics.

Preventing intrusive memories after trauma via a brief intervention involving Tetris computer game play in the emergency department: a proof-of-concept randomized controlled trial.

After psychological trauma, recurrent intrusive visual memories may be distressing and disruptive. Preventive interventions post trauma are lacking. Here we test a behavioural intervention after real-life trauma derived from cognitive neuroscience. We hypothesized that intrusive memories would be significantly reduced in number by an intervention involving a computer game with high visuospatial demands (Tetris), via disrupting consolidation of sensory elements of trauma memory. The Tetris-based intervention (trauma memory reminder cue plus c. 20 min game play) vs attention-placebo control (written activity log for same duration) were both delivered in an emergency department within 6 h of a motor vehicle accident. The randomized controlled trial compared the impact on the number of intrusive trauma memories in the subsequent week (primary outcome). Results vindicated the efficacy of the Tetris-based intervention compared with the control condition: there were fewer intrusive memories overall, and time-series analyses showed that intrusion incidence declined more quickly. There were convergent findings on a measure of clinical post-trauma intrusion symptoms at 1 week, but not on other symptom clusters or at 1 month. Results of this proof-of-concept study suggest that a larger trial, powered to detect differences at 1 month, is warranted. Participants found the intervention easy, helpful and minimally distressing. By translating emerging neuroscientific insights and experimental research into the real world, we offer a promising new low-intensity psychiatric intervention that could prevent debilitating intrusive memories following trauma.

Applications of time-series analysis to mood fluctuations in bipolar disorder to promote treatment innovation: a case series.

Treatment innovation for bipolar disorder has been hampered by a lack of techniques to capture a hallmark symptom: ongoing mood instability. Mood swings persist during remission from acute mood episodes and impair daily functioning. The last significant treatment advance remains Lithium (in the 1970s), which aids only the minority of patients. There is no accepted way to establish proof of concept for a new mood-stabilizing treatment. We suggest that combining insights from mood measurement with applied mathematics may provide a step change: repeated daily mood measurement (depression) over a short time frame (1 month) can create individual bipolar mood instability profiles. A time-series approach allows comparison of mood instability pre- and post-treatment. We test a new imagery-focused cognitive therapy treatment approach (MAPP; Mood Action Psychology Programme) targeting a driver of mood instability, and apply these measurement methods in a non-concurrent multiple baseline design case series of 14 patients with bipolar disorder. Weekly mood monitoring and treatment target data improved for the whole sample combined. Time-series analyses of daily mood data, sampled remotely (mobile phone/Internet) for 28 days pre- and post-treatment, demonstrated improvements in individuals' mood stability for 11 of 14 patients. Thus the findings offer preliminary support for a new imagery-focused treatment approach. They also indicate a step in treatment innovation without the requirement for trials in illness episodes or relapse prevention. Importantly, daily measurement offers a description of mood instability at the individual patient level in a clinically meaningful time frame. This costly, chronic and disabling mental illness demands innovation in both treatment approaches (whether pharmacological or psychological) and measurement tool: this work indicates that daily measurements can be used to detect improvement in individual mood stability for treatment innovation (MAPP).

Nonlinear time-series approaches in characterizing mood stability and mood instability in bipolar disorder.

Bipolar disorder is a psychiatric condition characterized by episodes of elevated mood interspersed with episodes of depression. While treatment developments and understanding the disruptive nature of this illness have focused on these episodes, it is also evident that some patients may have chronic week-to-week mood instability. This is also a major morbidity. The longitudinal pattern of this mood instability is poorly understood as it has, until recently, been difficult to quantify. We propose that understanding this mood variability is critical for the development of cognitive neuroscience-based treatments. In this study, we develop a time-series approach to capture mood variability in two groups of patients with bipolar disorder who appear on the basis of clinical judgement to show relatively stable or unstable illness courses. Using weekly mood scores based on a self-rated scale (quick inventory of depressive symptomatology-self-rated; QIDS-SR) from 23 patients over a 220-week period, we show that the observed mood variability is nonlinear and that the stable and unstable patient groups are described by different nonlinear time-series processes. We emphasize the necessity in combining both appropriate measures of the underlying deterministic processes (the QIDS-SR score) and noise (uncharacterized temporal variation) in understanding dynamical patterns of mood variability associated with bipolar disorder.

Survival costs of reproduction predict age-dependent variation in maternal investment.

Life-history theory predicts that older females will increase reproductive effort through increased fecundity. Unless offspring survival is density dependent or female size constrains offspring size, theory does not predict variation in offspring size. However, empirical data suggest that females of differing age or condition produce offspring of different sizes. We used a dynamic state-variable model to determine when variable offspring sizes can be explained by an interaction between female age, female state and survival costs of reproduction. We found that when costs depend on fecundity, young females with surplus state increase offspring size and reduce number to minimize fitness penalties. When costs depend on total reproductive effort, only older females increase offspring size. Young females produce small offspring, because decreasing offspring size is less expensive than number, as fitness from offspring investment is nonlinear. Finally, allocation patterns are relatively stable when older females are better at acquiring food and are therefore in better condition. Our approach revealed an interaction between female state, age and survival costs, providing a novel explanation for observed variation in reproductive traits.

Effects of among-offspring relatedness on the origins and evolution of parental care and filial cannibalism.

Parental care is expected to increase the likelihood of offspring survival at the cost of investment in future reproductive success. However, alternative parental behaviours, such as filial cannibalism, can decrease current reproductive success and consequently individual fitness. We evaluate the role of among-offspring relatedness on the evolution of parental care and filial cannibalism. Building on our previous work, we show how the evolution of care is influenced by the effect of among-offspring relatedness on both the strength of competition and filial cannibalism. When there is a positive relationship between among-offspring competition and relatedness, parental care will be favoured when among-offspring relatedness is relatively low, and the maintenance of both care and no-care strategies is expected. If the relationship between among-offspring competition and relatedness is negative, parental care is most strongly favoured when broods contain highly related offspring. Further, we highlight the range of conditions over which the level of this among-offspring relatedness can affect the co-occurrence of different care/no care and cannibalism/no cannibalism strategies. Coexistence of multiple strategies is independent of the effects of among-offspring relatedness on cannibalism but more likely when among-offspring relatedness and competition are positively associated.

The evolution of parental care in stochastic environments.

Parental care is of fundamental importance to understanding reproductive strategies and allocation decisions. Here, we explore how parental care strategies evolve in variable environments. Using a set of life-history trait trade-offs, we explore the relative costs and benefits of parental care in stochastic environments. Specifically, we consider the cases in which environmental variability results in varying adult death rates, egg death rates, reproductive rate and carrying capacity. Using a measure of fitness appropriate for stochastic environments, we find that parental care has the potential to evolve over a wide range of life-history characteristics when the environment is variable. A variable environment that affects adult or egg death rates can either increase or decrease the fitness of care relative to that in a constant environment, depending on the specific costs of care. Variability that affects carrying capacity or adult reproductive rate has negligible effects on the fitness associated with care. Increasing parental care across different life-history stages can increase fitness gains in variable environments. Costly investment in care is expected to affect the overall fitness benefits, the fitness optimum and rate of evolution of parental care. In general, we find that environmental variability, the life-history traits affected by such variability and the specific costs of care interact to determine whether care will be favoured in a variable environment and what levels of care will be selected.

Measuring biodiversity to explain community assembly: a unified approach.

One of the oldest challenges in ecology is to understand the processes that underpin the composition of communities. Historically, an obvious way in which to describe community compositions has been diversity in terms of the number and abundances of species. However, the failure to reject contradictory models has led to communities now being characterized by trait and phylogenetic diversities. Our objective here is to demonstrate how species, trait and phylogenetic diversity can be combined together from large to local spatial scales to reveal the historical, deterministic and stochastic processes that impact the compositions of local communities. Research in this area has recently been advanced by the development of mathematical measures that incorporate trait dissimilarities and phylogenetic relatedness between species. However, measures of trait diversity have been developed independently of phylogenetic measures and conversely most of the phylogenetic diversity measures have been developed independently of trait diversity measures. This has led to semantic confusions particularly when classical ecological and evolutionary approaches are integrated so closely together. Consequently, we propose a unified semantic framework and demonstrate the importance of the links among species, phylogenetic and trait diversity indices. Furthermore, species, trait and phylogenetic diversity indices differ in the ways they can be used across different spatial scales. The connections between large-scale, regional and local processes allow the consideration of historical factors in addition to local ecological deterministic or stochastic processes. Phylogenetic and trait diversity have been used in large-scale analyses to determine how historical and/or environmental factors affect both the formation of species assemblages and patterns in species richness across latitude or elevation gradients. Both phylogenetic and trait diversity have been used at different spatial scales to identify the relative impacts of ecological deterministic processes such as environmental filtering and limiting similarity from alternative processes such as random speciation and extinction, random dispersal and ecological drift. Measures of phylogenetic diversity combine phenotypic and genetic diversity and have the potential to reveal both the ecological and historical factors that impact local communities. Consequently, we demonstrate that, when used in a comparative way, species, trait and phylogenetic structures have the potential to reveal essential details that might act simultaneously in the assembly of species communities. We highlight potential directions for future research. These might include how variation in trait and phylogenetic diversity alters with spatial distances, the role of trait and phylogenetic diversity in global-scale gradients, the connections between traits and phylogeny, the importance of trait rarity and independent evolutionary history in community assembly, the loss of trait and phylogenetic diversity due to human impacts, and the mathematical developments of biodiversity indices including within-species variations.

Effects of host plant and genetic background on the fitness costs of resistance to Bacillus thuringiensis.

Novel resistance to pathogens and pesticides is commonly associated with a fitness cost. However, measurements of the fitness costs of insecticide resistance have used diverse methods to control for genetic background and rarely assess the effects of environmental variation. Here, we explored how genetic background interacts with resource quality to affect the expression of the fitness costs associated with resistance. We used a serially backcrossed line of the diamondback moth, Plutella xylostella, resistant to the biopesticide Bacillus thuringiensis, to estimate the costs of resistance for insects feeding on two Brassica species. We found that fitness costs increased on the better-defended Brassica oleracea cultivars. These data were included in two meta-analyses of fitness cost experiments that used standardized protocols (and a common resistant insect stock) but which varied in the methodology used to control for the effects of genetic background. The meta-analysis confirmed that fitness costs were higher on the low-quality host (B. oleracea); and experimental methodology did not influence estimates of fitness costs on that plant species. In contrast, fitness costs were heterogeneous in the Brassica pekinensis studies: fitness costs in genetically homogenized lines were significantly higher than in studies using revertant insects. We hypothesize that fitness modifiers can moderate fitness costs on high-quality plants but may not affect fitness when resource quality is low.

The form of host density-dependence and the likelihood of host-pathogen cycles in forest-insect systems.

Forest-insect systems frequently show cyclic dynamics which has been of considerable interest to both experimental and theoretical ecologists. One important issue has been the manner in which density-dependence acting on the host population through resource competition influences the likelihood of population cycles. Existing models make contradictory predictions. Here, we explore two models that allow different forms of density-dependence to be examined. We find that host density-dependence can influence the persistence of the host-pathogen interaction, the likelihood of population cycles and the stability of the host-pathogen interaction. In particular, over-compensatory density-dependence is likely to lead to host-pathogen cycles while under-compensatory density-dependence can promote stability. We discuss these differences with reference to the different forms of intraspecific competition and recent developments in insect population ecology.

Pathogen responses to host immunity: the impact of time delays and memory on the evolution of virulence.

Current analytical models of the mammalian immune system typically assume a specialist predator-prey relationship between invading pathogens and the active components of the immune response. However, in reality, the specific immune system is not immediately effective following invasion by a novel pathogen. First, there may be an explicit time delay between infection and immune initiation and, second, there may be a gradual build-up in immune efficacy (for instance, during the period of B-cell affinity maturation) during which the immune response develops, before reaching maximal specificity to the pathogen. Here, we use a novel theoretical approach to show that these processes, together with the presence of long-lived immune memory, decouple the immune response from current pathogen levels, greatly changing the dynamics of the pathogen-immune system interaction and the ability of the immune response to eliminate the pathogen. Furthermore, we use this model to show how distributed primary immune responses combine with immune memory to greatly affect the optimal virulence of the pathogen, potentially resulting in the evolution of highly virulent pathogens.

Persistence and coexistence of engineered baculoviruses.

Baculoviruses, and in particular, the nucleopolyhedroviruses infect a wide range of arthropod hosts and have the potential to be used as biopesticides. However, one of the major drawbacks with these pathogens as biocontrol agents is that they have a slow response time. Alterations to the speed of kill and pathogen life history characteristics can influence the competitive outcome and persistence between wildtype and modified strains. Here, we explore, theoretically, how life-history modifications of pathogens can affect the epidemiology and ecology of strain coexistence. In particular, we show how under simple mass action disease transmission, life-history difference between strains are insufficient to allow coexistence. Additional heterogeneities in transmission are shown to be necessary to facilitate coexistence of wildtype and modified pathogen strains. We also illustrate how the patterns of infectivity of wildtype and modified strains can also affect long-term coexistence, and argue that appropriate assessment of genetic modifications must be presented in terms of relevant ecological theory.

Contrasting dynamics in the same plant-herbivore interaction.

Long-term studies of two-species interactions under field conditions are unusual; most long-term field studies are of single species dynamics (1-6). Concurrent long-term studies on the dynamics of the same two interacting species in different locations are very rare. This result has led to the tacit assumption that different cases of the same two-species interaction would involve essentially quantitative differences (e.g., context-specific differences in the numeric values of demographic parameters like fecundity or death rates). Here, we show that for one of the best-known two-species systems (ragwort and cinnabar moth), this finding does not hold. The interaction between the plant and its herbivore is fundamentally different in coastal dunes in The Netherlands and in grasslands in Southeast England. In the first case, the dynamics are cyclic and the interaction involves both direct and delayed density dependence; in the second case, the insect has little impact on plant dynamics and there are no time lags in density dependence. The difference is caused by differences in the importance of seed-limitation in plant recruitment in the two locations.

The effects of metapopulation structure on indirect interactions in host-parasitoid assemblages.

The interaction between two species that do not compete for resources but share a common natural enemy is known as apparent competition. In the absence of other limiting factors, such three-species interactions are impermanent, with one species being excluded from the assemblage by the natural enemy. Here, the effects of metapopulation structure are explored in a system of two hosts that experience apparent competition through a shared parasitoid. A coupled-map lattice model is developed and used to explore species coexistence and patterns of patch occupancy at the metapopulation scale. Linking local and regional dynamics favours coexistence by uncoupling the dynamics of the three species in space. Coexistence is promoted by the inferior species being either a fugitive or a sedentary species. The occurrence of these two mutually exclusive mechanisms of coexistence is influenced by the relative dispersal of the inferior apparent competitor.

Population dynamics of apparent competition in a host-parasitoid assemblage.

The population dynamics of two moth species, Plodia interpunctella (Hübner) and Ephestia kuehniella Zeller in the presence of their shared parasitoid, Venturia canescens (Gravenhorst), were studied in well replicated time series experiments. Moths were prevented from competing for resources and could therefore only interact via the shared parasitoid. This study examines the consequences of apparent competition on the population dynamics of a simple laboratory insect assemblage. Ephestia kuehniella suffers severly in the presence of the shared parasitoid. In all eight replicates, this moth species is eliminated. Time series analysis reveals that the E. kuehniella populations show divergent oscillations. Plodia interpunctella and V. canescens populations show persistent populations. Time series analysis reveals that there is a delayed density dependence acting on these populations and the dynamics are either stable equilibrium or damped oscillations. Repeated-measures analysis of the strength of the indirect interaction reveals that the effects of apparent competition before E. kuehniella is lost are amensal. The indirect interaction between E. kuehniella and P. interpunctella is [-, 0] rather than [-, -].