The poster session is on June 27 (18:00-19:30) at the BioSciences Atrium. Each poster should fit within a 6' x 6' poster board. The suggested poster size is A0 (portrait or landscape). Presenters should use the poster board corresponding to their poster number and set up their posters before the session starts.

Estimating the tick-borne encephalitis (TBE) infection risk under substantial uncertainties of the vector abundance, environmental condition and human-tick interaction is important but challenging since the data we observe, i.e., the human incidence of TBE, is only the final outcome of the tick-host transmission and tick-human contact processes.

We introduce a TBE transmission-human case reporting cascade model that couples a TBE virus transmission dynamics among ticks with multiple development stages, animal hosts and humans, with the stochastic observation process of human TBE reporting given infection. By fitting human incidence data in Hungary to the model, we estimate key parameters relevant to the tick-host interaction and tick-human transmission, calculate the basic reproduction number and inform the contribution of co-feeding transmission.

This is based on a joint work with F. Magpantay, Á. Bede-Fazekas, G. Röst, A. Trájer, X. Wu, X. Zhang and J. Wu

Aakash Pandey^{1}, Nicole Mideo^{2}, Thomas G. Platt^{1}

^{1}Division of Biology, Kansas State University

^{2}Department of Ecology and Evolution, University of Toronto

Various aspects of pathogen life history affect the trajectory of virulence evolution. In addition to infecting hosts, facultative pathogens are able to grow independent of hosts in the environmental reservoirs. These diverse ecological settings could give rise to novel life-history trade-offs altering the course of virulence evolution in these pathogens. Although facultative pathogens cause many human and agricultural diseases, models of virulence evolution often focus on obligate pathogen life-histories. As a result, virulence evolution in the facultative pathogens is under-explored. We used the adaptive dynamics framework to explore the evolution of facultative pathogen virulence. We found that higher carrying capacity in environmental reservoirs can result in higher virulence evolutionary outcomes. Further, increasing the strength of a potential environmental persistence-virulence trade-off leads to lower virulence. We also found that the evolutionary branching is a common phenomenon where pathogens with diverse virulence strategies can co-exist. Our results highlight the need to evaluate whether facultative pathogens have virulence-associated life-history trade-offs and show that the problem of virulence evolution in these systems are a fertile ground for both theoretical and experimental studies.

Keywords: virulence evolution, facultative pathogens, adaptive dynamics, evolutionary branching

The resistance, behavioral and immunological response, has been reported in the biological literature but its impact on tick population dynamics has not been mathematically formulated and analyzed using dynamical models reflecting the full biological stages of ticks. Here we develop and simulate a delay differential equation model, with a particular focus on resistance resulting in grooming behavior. We calculate the basic reproduction number using the spectral analysis of delay differential equations with positive feedback, and establish the existence and uniqueness of a positive equilibrium when the basic reproduction number exceeds unit. We also conduct numerical and sensitivity analysis about the dependence of this positive equilibrium on the the parameter relevant to grooming behavior. We numerically obtain the relationship between grooming behavior and equilibrium value at different stages.

N. Akhavan Kharazian (presenter)^{1}, C. Allotey^{2} and F.M.G. Magpantay^{3}

^{1}Distributed Compute Labs

^{2}Department of Mathematics, University of Manitoba

^{3}Department of Mathematics and Statistics, Queen's University

We present a comparison of five different well-known models of pre-vaccine era measles dynamics and assess their strengths and weaknesses. We compare them with respect to their fit to data and how they perform when extended to the vaccine era. The models studied are based on the standard SEIR models, and include (1) the deterministic and (2) stochastic models with school-term forcing, (3) stochastic model with school-term forcing and disease immigration, and the stochastic model in He et. al. (2010) (4) with and (5) without the cohort effect.

A. Le^{1} and F.M.G. Magpantay^{1}

^{1}Department of Mathematics and Statistics, Queen's University

In the mathematical modeling of infectious diseases, the failure of infection-derived immunity can differ between models, resulting in different implications on the incidence of reinfection and the overall prevalence of the disease. The SEIR (Susceptible-Exposed-Infected-Recovered) model assumes that infection-derived immunity is perfect and perpetual, implying that once an individual recovers from being infected, they are unable to be infected by the same pathogen again. On the opposite end of the spectrum, the SEIS (Susceptible-Exposed-Infected-Susceptible) model assumes that no infection-derived immunity exists and that an individual who has recovered from infection is immediately susceptible to reinfection by the same pathogen at the same level of risk as prior to their initial infection. There is evidence that several infectious diseases have some level of infection-derived immunity but it is neither perfect nor is it perpetual. Hence, there is a continuum of infectious disease models where the level of infection-derived immunity lies somewhere in between that of the SEIS model and the SEIR model. Here, we consider seven different infectious disease models that all contain a varying method of imperfect infection-derived immunity. We then derive the reinfection probability for each respective model by considering each model’s force of infection, which is dependent on the interactions between each disease compartment in an equilibrium state. A disease model’s reinfection probability is precisely the probability that an individual who has recovered from a primary infection is reinfected by the same pathogen during their lifetime. We see that each model has a different corresponding reinfection probability which allows us to compare the impact that each type of immunity failure has on the rate of reinfection as well as the overall long term behaviour of the disease system.

W.S. Hart^{1}, P.K. Maini^{1} and R.N. Thompson^{1,2}

^{1}Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK

^{2}Christ Church, University of Oxford, Oxford OX1 1DP, UK

Epidemiological models are increasingly used for forecasting during epidemics, and for predicting the impacts of interventions. Most commonly used population-scale epidemiological models, such as the SEIR model, assume that the infectiousness of each host remains constant throughout the infectious period. In reality, infectiousness will vary as the infection progresses through the host. Here we develop a new modelling framework, which utilises a compartmental model with multiple infectious compartments, in order to account for time-dependent infectiousness and scale from within-host to population-scale models. In the limit of infinitely many compartments, our method is mathematically equivalent to previous approaches using integro-differential equations (IDEs). However, our framework has the advantage that compartmental models, formulated as systems of ordinary differential equations, are straightforward to solve numerically using standard methods and software packages.

To demonstrate our framework, we suppose that the infectiousness of each host is determined by a within-host viral dynamics model, which has previously been parametrised for influenza infections. We explore the accuracy of our compartmental method as the number of infectious compartments is varied, finding that 50 compartments are sufficient for the epidemic dynamics to be within 5% of those under the IDE model. We also investigate how errors in the assumed within-host dynamics, caused by inadequate or inaccurate within-host data, may lead to error at the population-scale. Finally, we determine how many compartments are required to reduce the error in the population-scale dynamics to below 5%, in the presence of errors at the within-host level. For the wide range of epidemiological systems for which within-host dynamics are already well-characterised, our compartmental framework allows the accuracy of models used for epidemic forecasting and control to be improved, by enabling time-dependent infectiousness to be easily incorporated into these models.

Population stage structure is fundamental to ecology and helps modulate key population, community, and ecosystem dynamics. Hence, pinpointing the mechanisms that drive variation in stage structure carries implications for both basic and applied biology. To date, however, most empirical efforts have focused on the consequences of stage structure rather than the underlying mechanisms that govern shifts in stage structure. Here, we illustrate that parasites with stage-specific virulence may play a crucial, but underappreciated, role in modulating the stage structure of their host populations. Specifically, we use a population experiment where we created experimental epidemics to show that castrating parasites which cause more harm to adults (relative to juveniles), can shift population demography, decouple stage synchronization, increase population stability, decrease the host’s risk of extinction, and increase the genotypic diversity of host populations. Our findings carry general implications for predicting the dynamical population-level consequences of infectious agents with stage-specific virulence.

Structured populations are often described by mathematical models formulated as delay equations, including integral and integro-differential equations. Because of the complexity of such systems, it is fundamental to develop efficient numerical methods for studying their dynamical and bifurcation properties. I will present the main ideas of the pseudospectral discretization approach for delay equations. With this technique, a general nonlinear delay equations is approximated with a system of ordinary differential equations, whose dynamics and bifurcations can be studied with available software packages. I will show several different examples to which the approach has been successfully applied.

Many species facing climate change have complex life cycles, with individuals in different stages differing in their sensitivity to a changing climate and their contribution to population growth. We use a quantitative genetics model to predict the dynamics of adaptation in a stage-structured population confronted with a steadily changing environment. Our model assumes that different optimal phenotypic values maximize different fitness components, consistent with many empirical observations. In a constant environment, the population evolves toward an equilibrium phenotype, which represents the best compromise given the trade-off between vital rates. In a changing environment, however, the mean phenotype in the population will lag behind this optimal compromise. We show that this lag may result in a shift along the trade-off between vital rates, with negative consequences for some fitness components but, less intuitively, improvements in some others. Complex eco-evolutionary dynamics can emerge in our model due to feedbacks between population demography and adaptation. Because of such feedback loops, selection may favor further shifts in life history in the same direction as those caused by maladaptive lags. These shifts in life history could be wrongly interpreted as adaptations to the new environment, while in reality they only reflect the inability of the population to adapt fast enough.

Jane Shaw MacDonald^{1} and Frithjof Lutscher^{2}

^{1}Department of Mathematics and Statistics, University of Ottawa, 150 Louis Pasteur private, Ottawa,
ON, K1N 6N5

^{2}Department of Mathematics and Statistics, and Department of Biology, University of Ottawa, 150 Louis
Pasteur private, Ottawa, ON, K1N 6N5

The earths climate is warming, and as a result, many species habitat ranges are shifting. The shift in habitat ranges threatens the local persistence of these species. Mathematical models that capture this phenomenon of range shift do so by considering a favourable bounded domain that has a time dependent location on the real line (moving-habitat models). In most of these models, density is considered to be continuous across the boundaries. However, it has been shown that many species exhibit particular behaviour at habitat edges, such as biased movement towards the more suitable habitat. We introduce an extension of previous models by generalizing the boundary conditions to capture such individual behaviour. Under these generalized conditions, the density is not continuous across a boundary. We obtain persistence conditions that show that the behaviour at the trailing edge plays a crucial role in the species' ability to persist. A species that can sense the trailing edge, and respond to it, may be able to persist for arbitrarily fast moving habitats. We illustrate our theoretical results with numerical solutions of the system.

Changes in global thermal regimes have prompted population ecologists to consider how key
demographic parameters depend on and interact with temperature. Conventionally, this has been
investigated by assessing an organism’s response to the average thermal condition, and subsequently
implementing those results to make projections at the population-level. This, however, is the crux of the
problem: an organism’s response to average conditions may not reflect the average response to
variable conditions. This property is one that arises from the principle of Jensen’s inequality, which
states that for a nonlinear function, the average of a function is not equal to the function of the average.
Given the ubiquity of nonlinearities in nature (e.g. temperature-performance curves), there has been a
growing appreciation amongst ecologists for the application of Jensen’s inequality in making predictions
on ecological dynamics in an increasingly variable world. Here, we investigate the consequences of
Jensen’s inequality in the context of infectious diseases. Research on Jensen’s inequality and the effect
of temperature variability on host-parasite dynamics has predominantly been at the individual-level, and
has therefore been rarely applied to dynamics at the population-level. As such, we will examine the
effect of thermal variability on host-parasite dynamics using the model system *Daphnia
magna-Ordospora colligata*. Demographic rates for this system have been quantified across
temperature and have been used to parameterize a set of ordinary differential equations that predict the
spread of infection in a host population. Here, we test the hypothesis that as a consequence of
Jensen’s inequality, host-parasite dynamics will differ in temporally variable thermal regimes relative to
temporally constant thermal regimes, and that predictions on the net outcome of host-parasite
dynamics can be made using a combination of ODEs and nonlinear averaging. Since this system is
amenable to experimental tests, theoretical predictions generated will eventually be tested in a
laboratory environment. This work may contribute to a theoretical framework for making reliable
predictions on the effect of variability on population dynamics and species interactions, and may have
practical implications for conservation and management.

Abstract will be posted here when available.

We describe the behaviour of solutions of a scalar Delay Differential Equation (DDE) with delay that periodically switches between two constant values. Such an equation arises naturally from structured vector populations involved in a range of vector-borne disease spreads in a periodically varying environment. We examine if and how the two different time lags and the switching time influence the existence and patterns of periodic solutions. We pay particular attention to the patterns involving multi-cycles within the prime period of the periodic solutions

Many different techniques have been used to account for the duration of the infectious period in mathematical models of the spread of an infectious disease. These models include the well-known SIR and SEIR models, where the duration of the infectious period is assumed to be exponential distributed, or models where the time spend in each stage of the infection is constant. We propose a mathematical model that explicitly includes infectious age. By assuming that the duration of the infectious stage is a positive random variable, we show how to create a mathematical model with an arbitrary distribution of infectious stage duration. This model formulation naturally allows for decreasing infectivity as infectious age progresses and can incorporate the effects of treatment by altering the rate at which individuals progress through the infected stage. As an example, we show how our formulation recaptures the common SIR and SEIR formulations for specific choices of infection duration.

Dutch Elm Disease (DED) is a fungal disease caused by *Ophiostoma novo-ulmi* and transmitted by a beetle (*Hylurgopinus rufipes*).
The disease transmission cycle uses the relationship between the fungus and the beetle, which are known to be symbiotic partners.
In this work, we model the spread of the disease among elms in a city using a metapopulation in which elms are the patches and beetles live within and move between patches.
Since beetles behave differently depending on their life stage, we use a matrix population model to represent the development of the beetles in trees.
Further, beetles are attracted to different types of elms at different times of their life and are able to move toward them.
We thus consider trees in different states, as a function of their contamination status: Healthy (*H*), Weak Susceptible (*S _{W}*),
Weak Infected (

*I*), Dead Susceptible (

_{W}*S*) and Dead Infected (

_{D}*I*). Tree states are ruled by a stochastic process dependent on the number of beetles that carried the pathogen during a certain amount of time. Using data from the city of Winnipeg on the exact location of elms in the city, we observe how the disease spreads in the city and we compare different scenarios (bad, normal or good years) as a function of temperatures. We also investigate different control strategies.

_{D}Integrodifference equations (IDEs) are often used for discrete-time continuous-space models in mathematical biology. The model includes two stages: the reproduction stage, and the dispersal stage. The output of the model is the population density of a species for the next generation across the landscape, given the current population density. Most previous models for dispersal in a heterogeneous landscape approximate the landscape by a set of homogeneous patches, and allow for different demographic and dispersal rates within each patch. Some work has been done designing and analyzing models which also include a patch preference at the boundaries, which is commonly referred to as the degree of bias. Individuals dispersing across a patchy landscape can detect the changes in habitat at a neighborhood of a patch boundary, and as a result, they might change the direction of their movement if they are approaching a bad patch.

In our work, we derive a generalization of the classic Laplace kernel, which includes different dispersal rates in each patch as well as different degrees of bias at the patch boundaries. The simple Laplace kernel and the truncated Laplace kernel most often used in classical work appear as special cases of this general kernel. The form of this general kernel is the sum of two different terms: the classic truncated Laplace kernel within each patch, and a correction accounting for the bias at patch boundaries.

We create and analyze an extension to the classic Competitive Lotka Volterra (CLV)
model. The goal being to model competition between species, with a response from the
environment. This response is a function of the population of each species and can represent
numerous physical phenomena including resource limitation and immune response of a host
due to infection. We name this new system a Functional Competitive Lotka Volterra (FCLV)
model. We use a number of techniques, most notably the construction of contraction metrics
to determine global properties of the model. The main result is a method to reduce systems
that are a mixture of competitive and cooperative dynamics to a monotone systems. This
method applied to FCLV shows that the system is eventually a monotone competitive system.
We use this result to analyze the competition between *Plasmodium* sp. and genetically
engineered bacteria within the midgut of a mosquito. We find that the effect of the immune
response of the mosquito to invaders has a significant effect on whether *Plasmodium* sp. or
the genetically engineered bacteria dominates the interaction in the model.

Keywords — ODE, Dynamical Systems, Modelling, Contraction Analysis, Competitive Lotka Volterra, Monotone Dynamical Systems

Joany Mariño^{1}, Suzanne Dufour^{1} and Amy Hurford^{1,2}

^{1}Department of Biology, Memorial University of Newfoundland, St. John's A1B 3X9, Canada

^{2}Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's A1C 5S7, Canada

Physiologically structured population models (PSPMs) provide a link between individual-level processes and population dynamics. PSPMs are formulated using functions that represent the life history of individuals as demographic rates. Here, we formulate a PSPM deriving the demographic rates from a dynamic energy budget (DEB) model, which takes into account energy acquisition and allocation at different stages of an organisms' life cycle. The demographic rates in the DEB-PSPM offer a mechanistic representation based on individual energy storage, structural biomass, and maturity.

We use our DEB-PSPM approach to model symbiosis using thyasirid bivalves as a case study.
Thyasirids are particulate feeders, obtaining nutrients from free-living chemosynthetic bacteria.
However, some species are symbiotic and harbour bacteria in enlarged gills. Symbiotic thyasirids are
mixotrophs, digesting symbiotic bacteria as an additional resource. We compare two closely related
species that co-occur in a seasonal environment: *Thyasira* cf. *gouldi*, which is symbiotic, and
*Parathyasira* sp., which is asymbiotic. We hypothesize that, under environmental forcing, harbouring
symbionts results in stable population sizes, while the asymbiotic species' populations fluctuate over
time. Our findings highlight how the symbiotic association is likely to change the energy budget of a
mixotrophic bivalve and thereby determine its population dynamics, which is of interest in a wide
range of trophic symbioses.

Amelia R. Cox, Raleigh J. Robertson, Wallace B. Rendell, Frances Bonier

Many populations of birds that forage on the wing for flying insects are declining precipitously, but it is unclear why. For most of these aerial insectivores, we simply lack the long-term demographic data necessary to identify a cause. Fortunately, at the Queen’s University Biological Station, we have monitored a box-nesting population of tree swallows since 1975 and have collected a wealth of data along the way. Using demographic data collected from 1975-2017, we performed a life-stage simulation analysis, based on stage structured population projection model with three life-stages (egg, one-year-old female, older female) and nine vital rates (number of nests laid, clutch size, hatching success, fledging success, juvenile recruitment, one-year-old survival, older female survival). Accounting for correlation between vital rates, we found that fledging success, juvenile recruitment, and adult survival has the most influence on overall population dynamics. While adult survival has not changed over time, declines in fledging success and juvenile recruitment parallel declines in the population. Poor fledging success is associated with cool and rainy spring weather, likely because the insects that aerial insectivores rely on to feed their young are inactive under these conditions. Similarly, nestling body mass has declined, suggesting that nestlings no longer get enough to eat. As climate change alters precipitation patterns, spring rainfall is increasing in this region and insects are becoming a less predictable food source for tree swallows, and likely other avian aerial insectivores.

Modern coexistence theory is accredited for creating a fundamental shift for community ecology, bringing generalizable principles to an otherwise highly contingent and system specific "mess" (Fukami et al. 2015). However, coexistence theory has largely failed to address evidence that the effects of order and timing of species arrival plays a critical role in shaping communities via priority effects (Chase 2003, Drake 1991, Petraitis and Latham 1999, Fukami et al 2015/2016). We have developed theory and analytically solved for the conditions when alternate stable states produced by priority effects should arise in communities, using a two species Lotka-Volterra competition model with an Allee effect. This first step in advancing coexistence theory that we will present now needs to be 'scaled up', so that species coexistence is measured on a scale where the area’s dynamics are not affected by migration across its boundary (Chesson 2000). This is problematic because rarely are landscapes contiguous at the scale at which migration is irrelevant, meaning Chesson's framework needs to be extended to understand metacommunities, or patchily distributed communities, to be meaningful to most natural systems. The work that we will present provides two challenges we aim to address in scaling up local priority affects. First, it will require addressing a fundamental challenge in the seminal work of Ovaskainen and Hanski (1998), whereby no species with an Allee effect can invade any given patch nor the network, even in the absence of competition. A spatially realistic metapopulation model constitutes a stage structured population model in space rather than time, and we therefore propose to draw on theory of stage structured population models to create a spatially realistic metapopulation model incorporating Allee effects to investigate when invasion should be possible. Second, we will need to extend this basic model to a two-species model, such that competition and spatially mediated encounter rates may alter coexistence outcomes locally and regionally. By combining these goals, we aim to develop a general model of how alternate stable states may arise and persist at the regional scale, and under influence of local and regional dynamics.

Empirical results and theoretical analyses reveal that fear alters the behaviours of prey then influence its population size. In most cases, animals are observed to reduce activities to avoid being captured by predators at the cost of growth, which also results in the reduction of movement. We formulate a patch model incorporated with dispersal. Using adaptive dynamical methods to study the evolution of anti-predation strategy, we show that in an isolated patch there may exist a non-zero optimal strategy which is both an evolutionary stable strategy (ESS) and a convergence stable strategy (CSS). Numerical simulations are given for the full model, implying that anti-predation strategy plays an important role in the long-term population dynamics of prey and an optimal strategy may exist, which is stable in evolutionary sense.

Mari Kawakatsu (presenter)^{1},
Christopher K. Tokita^{2},
Yuko Ulrich^{3,4},
Vikram Chandra^{4},
Jonathan Saragosti^{4},
Daniel J. C. Kronauer^{4} and
Corina E. Tarnita^{2}

^{1}Program in Applied and Computational Mathematics, Princeton University, NJ, USA

^{2}Department of Ecology and Evolutionary Biology, Princeton University, NJ, USA

^{3}Department of Ecology and Evolution, University of Lausanne, Lausanne, Switzerland

^{4}Laboratory of Social Evolution and Behavior, The Rockefeller University, NY, USA

From microbes to humans, social groups at different biological scales divide tasks among specialized individuals. The emergence of such division of labor is a major transition in the evolution of social organization and considered a key to the ecological success of many social groups, especially social insect colonies. Theory suggests that interindividual variability in response thresholds among workers that are otherwise identical can generate specialized behavior. However, few studies consider interactions between individuals with distinct behavioral tendencies that are genetically or developmentally determined. Even fewer directly link theory and experiment.

We combine mathematical modeling with experimental data to investigate fixed thresholds, the simplest form of response thresholds, as a mechanism for the emergence of specialized behavior in genetically or developmentally heterogeneous groups.
These groups exhibit different behavioral types that differ in the efficiency with which they perform tasks and in the ability to meet the needs of the colony.
Counterintuitively, in the fixed threshold model, we find that mixing two types of individuals that differ in task performance efficiency results in behavioral contagion,
whereby the types become behaviorally more similar to each other when mixed.
Moreover, this contagion exhibits asymmetry that depends on how well each type can keep up with the demands of the colony. We then compare our theoretical results with experimental data from camera tracking experiments in colonies of the
clonal raider ant, *Ooceraea biroi*, with controlled variations in genetic, demographic, and morphological types. We find that the fixed threshold model can capture the
range of behavioral patterns observed in these colonies.
Finally, we extend the model to predict the average behavior of colonies with varying ratios of behavioral types.
This work demonstrates that fixed thresholds, despite their simplicity, offer a powerful mechanism to capture and predict the emergence of social organization in heterogeneous groups.

R. A. Smith^{1} (presenter), T. Yamanaka^{2}, O. N. Bjornstad^{3} and W. A. Nelson^{1}

^{1} Department of Biology, Queen’s University, Canada

^{2} Research Center for Agricultural Information Technology, NARO, Japan

^{3} Department of Biology, Penn State University, USA

Temperature is the primary driver of ectotherm growth rates in temperate regions. For organisms
that can only overwinter in a specific life stage, it is critical that developmental phenology matches
seasonality. Two hypotheses for how ectotherms respond to seasonal temperature change are (1)
evolution of a reaction norm to temperature only, and (2) evolution of a reaction norm dependent on
both temperature and other variables. Here we use high resolution records of densities of the smaller
tea tortrix (*Adoxophyes honmai*) over multiple decades across 15 locations in Japan to characterize
changes in the developmental reaction norm to temperature in both time and space. The insect
displays regular single-generation limit cycles, which provides a unique opportunity to infer changes
in the developmental reaction norm directly from natural populations. We find evidence that a
fixed relationship between temperature and development rate is insufficient to explain observed
population dynamics. Effect size can be as large as a 20% reduction in development rate, which is
enough to maintain the same number of cycles per year in the face of climate change. Growth rates
measured from common garden experiments indicate that this effect is not due to evolutionary
change; plasticity in the developmental reaction norm is the most parsimonious explanation for the
observed population dynamics.

Integro-differential equations often arise in the study of mathematical ecology in areas such as population dynamics, forestry, and invasive species management. We present a new approach to solving nonlinear integrodifferential boundary value problems via the sinc-method of interpolation. The new approach is based upon derivative interpolation, which has been shown to exhibit higher accuracy than the standard approach of direct interpolation. A general method for nonlinear, finite integro-differential boundary value problems is developed which is capable of solving Fredholm-Volterra type problems. The method is tested on different types of problems and compared against published results for the standard method of interpolation. The new method shows higher accuracy with less computational requirements.

Amy Forsythe^{1}, Troy Day^{1,2} and William A. Nelson^{1}

^{1}Department of Biology, Queen’s University

^{2}Department of Mathematics and Statistics, Queen’s University

Demographic heterogeneity refers to among-individual variation in vital rates that cannot be attributed to distinct class type (age, stage or sex), nor to demographic or environmental stochasticity. At one extreme, demographic heterogeneity may be structured as persistent heterogeneity, in which individual vital rates are set at birth and maintained for life. Temporary heterogeneity lies at the other extreme, occurring when an individual can transition to any vital rate phenotype in the population at any time.

Here, we use population projection matrices to compare the ecological and evolutionary consequences of non-genetic persistent and temporary heterogeneity. Our model is density-independent and considers two stages of individuals, juveniles and adults, within simulated clonal populations. All non-genetic demographic heterogeneity is generated from variation in three vital rates that characterize an individual’s phenotype: survival rate, birth rate and development rate. We find that, regardless of the genetic and non-genetic covariance structure between the three vital rates, populations under persistent heterogeneity experience slower rates of evolution by natural selection than populations under temporary heterogeneity.

Reductions in body size has been suggested as a universal response to global warming for many species.
Here, we investigate the population level consequence of changes in body size and size-dependent life history characteristics using size-structured matrix projection models.
Analyzing experimental data from 412 isolated *Daphnia magna* individuals raised under varying temperature and food levels, we show that temperature and food availability interact in a complex fashion in shaping *Daphnia* population size structure and the asymptotic population growth rate.
We find food abundance determines the direction of population growth and temperature affects the magnitude of demographic variability, mediated through simultaneous limitation on size-dependent growth, survival and reproduction.
Given the evidence for the synergistic interaction between temperature and food abundance on *Daphnia* individual fitness and population demography, we argue that accounting for the variation in food availability is crucial in understanding how populations might respond to rapid climate change.

Jake M. Alexander^{1} and Robert I. Colautti^{2}

^{1} Institute of Integrative Biology, ETH Zurich

^{2} Biology Department, Queen’s University

Traditional niche theory tends to consider species as homogenous units with fundamental and realized niches described as a single function of one or more environmental gradients. This classic model neglects the fact that populations within species can adapt to local environmental conditions. Consequently, a species does not have a single, static niche, but rather a collection of evolutionarily labile, population-specific niches that together determine the species-wide ‘meta-niche’. We explore the evolutionary ecology of niche dynamics by modelling parameters of classic Lotka-Volterra models as simple environment-dependent quadratic functions with genetic trade-offs. These parameters are sufficient to produce a number of phenomena observed in nature, including the apparent maintenance of conditionally neutral alleles, evolution of the fundamental niche, and time lags in range expansion. Are model also suggests genetic links between the fundamental and realized niche with implications for predicting range shifts under global change.

John Fryxell, Xueqi Wang, and Gustavo Betini

Anthropogenic processes are rapidly changing key parameters that shape food web dynamics. We combined bench-top measurement of size-dependent variation in vital rates under a realistic range of food densities to parameterize a structured population model for the zooplankton species Daphnia magna. We then linked this size-structured Daphnia demographic model with a dynamic model of green algal-nutrient dynamics to predict the impact of changes in nutrient loading and temperature change on food chain dynamics. These predictions were then evaluated against outcomes of replicated experimental trials in a set of large controlled mesocosms.