Download abstracts

Keynotes
Sisson, Scott. School of Mathematics and Statistics. University of New South Wales.
Approximate Bayesian computation methods for biological models
Approximate Bayesian computation (ABC) refers to a class of statistical methods that allow the
practitioner to perform an approximate Bayesian inference for models that are computationally
intractable, or are difficult to numerically evaluate. Initially developed in the population genetics
literature, the simplicity and accessibility of ABC methods has resulted in their subsequent
contributions to research in a diverse range of disciplines over the past 15 years. In this talk I will
introduce the ideas and concepts behind ABC methods, and provide several illustrative analyses. The
aim here is to convey a sense of the potential utility of ABC methods for biological models, and to
enable members of the audience to be able to implement their own ABC analyses in the future.
Allesina, Stefano. Department of Ecology & Evolution, Computation Institute. University of
Chicago.
The stability of large ecological systems
I review the theory of local stability analysis for models of ecological communities composed of one,
two, and many populations. I then introduce basic tools of Random Matrix Theory (RMT), describing
the distribution of eigenvalues of large random matrices, and show how these can help solve
problems in ecology. With these tools at hand, I present recent results using RMT to assess the
stability of food webs and the persistence of metapopulations. I conclude by enumerating the main
challenges that need to be solved in the next decade to further our understanding of ecological
dynamical systems.
Presentations (Talks and Posters)
Binzer, Amrei. Dept. of Physics, Chemistry and Biology (IFM) Linköping University; Max Planck
Institute for Evolutionary Biology, Plön, Germany; Department of Ecosystem Biology, Faculty of
Science, University of South Bohemia, České Budějovice, Czech Republic
Temperature induced body mass change: implications for species dynamics and survival (Talk, w.
Arnaud Sentis)
Body size and temperature affect species biological rates, their interactions and ultimately their
ability to survive. Recently it has been recognized that climate change can trigger body size changes.
However, the magnitude and direction of these temperature-size responses are debated and likely to
differ depending on the trophic position of the species. Here, we use a nonlinear bioenergetic
population-dynamic model that accounts for temperature and body-mass dependencies of biological
rates to explore the effects of temperature induced body-size changes on species dynamics and
survival in a three species food chain. We investigate the impact of different temperature-size
responses on species survival in three different scenarios: i) all species display the same size response
to climate change, ii) one species changes its size with temperature, the other are unaffected, and iii)
two species show changing body-sizes with temperature, one is not affected. Our findings contribute
to the ongoing debate over species reactions to climate change and shed light on their repercussions
for species communities and food web persistence.
Brännström, Åke. Institutionen för matematik och matematisk statistik, Umeå universitet.
Geometrically saturated growth and the pipe model of tree form (Poster, w.Lars Hellström and
Linus Carlsson)
The availability of carbon and other nutrients are traditionally seen as the major limiting factors for
plant growth. However, for sufficiently large plants the geometry of space itself may become a more
important limitation, in that the resources the plant has available to grow new branches and leaves
exceed what it can usefully benefit from growing. When this happens, we say that the growth has
reached geometric saturation, and one would expect that the surplus production is instead directed
towards activities other than growth, such as reproduction. We derive a self-thinning model of plants
by combining the idea of geometric saturation with the self-similarity observation that branches of a
given size tend to look pretty much the same regardless of the size of the full plant. This model
predicts how the number of metamers of a certain age changes over time, therefore how many must
be lost as dead wood, and it also gives many details on what the expected branching structure in a
tree should look like. Our self-thinning model is then combined with the pipe model of Shinozaki et
al. (1964a, 1964b). This reduces the number of free variables considerably and we are able to extract
far more information on the growth of plants from the combined model than from either model by
itself.
Brännström, Åke. Institutionen för matematik och matematisk statistik, Umeå universitet.
On the convergence of the Escalator Boxcar Train (Poster, w. Daniel Simpson, and Linus Carlsson)
The Escalator Boxcar Train (EBT) is a numerical method that is widely used in theoretical biology to
investigate the dynamics of physiologically structured population models, i.e., models in which
individuals differ by size or other physiological characteristics. The method was developed more than
two decades ago, but has so far resisted attempts to give a formal proof of convergence. Using a
modern framework of measure-valued solutions, we investigate the EBT method and show that the
sequence of approximating solution measures generated by the EBT method converges weakly to the
true solution measure under weak conditions on the growth rate, birth rate, and mortality rate. In
rigorously establishing the convergence of the EBT method, our results pave the way for wider
acceptance of the EBT method beyond theoretical biology and constitutes an important step towards
integration with established numerical schemes. The poster gives an overview of the proof; for full
details see SINUM 51(6): 3213-3231, 2013.
Curtsdotter, Alva. Department of Physics, Chemistry and Biology. Linköping University.
The strength of interspecific competition modulates the eco-evolutionary response to global
warming (Talk)
Climate change is predicted to have major implications for global biodiversity. Dispersal and
evolution may become crucial for species survival, as species must either adapt or migrate to track
the changing climate. However, migration and evolution do not occur in vacuum – the biotic
community in which these processes play out may modulate their effect on biodiversity. Here, we
use an eco-evolutionary, spatially explicit, multi-species model that allows us to examine the
interactive effects of competition, adaptation and dispersal on species richness in plant communities
under global warming. We find that there is a larger decline in global species richness when
interspecific competition is strong. Furthermore, there is a three-way interaction between
interspecific competition, evolution and dispersal that creates a complex pattern of biodiversity
responses, in which both evolution and dispersal can either increase or decrease the magnitude of
species loss. This interaction arises for at least two reasons: 1) different levels of dispersal, evolution
and competition creates differences in local and global community structure before climate change,
and 2) competitive interactions determine whether the benefits of dispersal and/or evolution
(climate tracking and adaptation) outweighs the risks (competitive exclusion) associated with the
same processes in a community context.
Fransson, Peter. Umeå University.
A simple rule for light-dependent biomass allocation in trees. (Poster, w. Åke Brännström, Oskar
Franklin)
Allocation of biomass to different organs of a tree depends on the surrounding environment (the
availability of resources and the competition with neighboring trees, etc.). If future changes in the
environment are known, one can determine the optimal allocation using methods from optimal
control theory. Light conditions are arguably the most important environmental factor for trees. In
our project we are looking for the possibility of using a heuristic method to approximate these
optimal allocation patterns; when only the present condition of the surrounding light is known. The
heuristic method uses two alternative allocation strategies which it changes between depending on
an associated switching function. The two allocation strategies are suited for different types of light
conditions; one for below canopy level, shaded conditions, the other for close to above canopy, full
light conditions. The switching function determines which of the strategies is used; switching,
between strategies, is triggered when a sufficient level of light is reached.
The heuristic method is used to simulate continuous growth of a tree in a variety of light conditions.
To assess the accuracy, the heuristic method is compared to the optimal allocation pattern across the
full range of light environments.
Gerlee, Philip. Mathematical Sciences, Chalmers och Göteborgs Universitet.
The evolution of carrying capacity in constrained and expanding tumour cell populations. (Talk)
Cancer cells are known to modify their micro-environment such that it can sustain a larger
population, or, in ecological terms, they construct a niche which increases the carrying capacity of
the population. It has however been argued that niche construction, which benefits all cells in the
tumour, would be selected against since cheaters could reap the benefits without paying the cost.
We have investigated the impact of niche specificity on tumour evolution using an individual based
model of breast tumour growth, in which the carrying capacity of each cell consists of two
components: an intrinsic, subclone-specific part and a contribution from all neighbouring cells.
Analysis of the model shows that the ability of a mutant to invade a resident population depends
strongly on the specificity. When specificity is low selection is mostly on growth rate, while high
specificity shifts selection towards increased carrying capacity. Further, we show that the long-term
evolution of the system can be predicted using adaptive dynamics. By comparing the results from a
spatially structured vs. well-mixed population we show that spatial structure restores selection for
carrying capacity even at zero specificity, which poses a possible solution to the niche construction
dilemma. Lastly, we show that an expanding population exhibits spatially variable selection pressure,
where cells at the leading edge exhibit higher growth rate and lower carrying capacity than those at
the centre of the tumour.
Gosh, Arpan. Department of Mathematics. Linköping University
A two dimensional asymptotic model of the wall of a blood vessel
We derive a two dimensional model of the wall of a blood vessel having a circular cross section of a
fixed radius all along its length while having a general curvature and torsion. The wall consists of
three elastic, anisotropic layers, called intima, media and adventia, which except intima are formed
of bundles of collagen fibres. We start by formulating a suitable orthonormal moving frame of
reference in order to have relatively simpler expressions. Constitutive relations of elasticity and
Newton's second law provide us with the partial differential equation system for the displacement of
the wall material. A dynamic boundary condition and a kinematic no-slip boundary condition are
assumed on the inner surface of the wall which help in coupling the equations with the Navier-Stokes
equation governing the blood flow within the vessel. We assume the thickness of the wall of the
vessel to be very small compared to the radius and the length of the vessel. Under such an
assumption, we use asymptotic expansions to obtain a model which essentially describes the wall of
the vessel as a two dimensional surface.
Leach, Clint. Colorado State University.
The role of size-structured food webs in the changing structure of the Scotian Shelf fish
community. (Talk)
The collapse of the cod fishery on the Scotian Shelf in the early 1990s led to a dramatic and
persistent decline in the abundance and body size of predator fish over the last two decades.
Hypotheses for the inability of these large predators to recover include predator-prey role reversal,
wherein numerically dominant fish at lower trophic levels (forage fish) prey upon the early life stages
of large predator fish, and intensified competition between these forage fish and small-bodied
predators . Though there is correlative evidence for these hypotheses, here we explore their role
more explicitly through the use of mechanistic, size-structured partial differential equation models.
These models account for intraspecific variability in body size and diet by using species traits and
individual physiology to track the flow of biomass through time and along a size spectrum (i.e. from
small prey to larger predators). In order to evaluate the role of the above mechanisms in preventing
the recovery of large predators, we develop a statistical framework around the mechanistic model
that allows us to estimate the interaction matrix from 33 years of abundance-at-length estimates
from the Scotian Shelf.
Lindh, Magnus. Umeå University.
Evolution of shoot and root: How droughts influence plant diversity. (Talk)
Deep rootedness is a very common strategy for plants to survive droughts. Despite this there are
large gaps in our knowledge of how plant deep roots interact with deep soil water, partly because of
measuring deep roots in large scale is very difficult. There is no simple relation between precipitation
and deep-rootedness. The deepest roots in the world are found in deserts, but surprisingly,
evergreen tropical forests have the deepest roots of all forests.
We present a two dimensional size-structured model where both shoot and root are growing. We
assume that there is asymmetric competition for light and water, and evolve the allocation to shoot
and root, which is clearly a trait with a trade-off since trees cannot survive with either or.
Our main questions are:
1)
How does light and soil water distribution affect shoot-root allocation?
2)
How does fine root distribution affects shoot-root allocation?
3)
How can we use our model to predict root mass from aboveground biomass?
Radosavljevic, Sonja. Department of Mathematics. Linköping University.
Logistic age-structured population model in a changing environment (Talk)
We present an age-structured logistic population model derived from the classical McKendrick-von
Foerster model by including the intra-species competition for resources or overcrowding effects.
These effects are incorporated in the model through an additional term in the balance equation.
Under assumptions that the birth and the death rates and the carrying capacity are functions of age
and time, we prove that the model has a unique nonnegative bounded solution. Moreover, we
investigate asymptotic behavior of the number of newborns and of the total population in a variable
environment. We use the model to describe asymptotic behavior of four different populations in
special case when the birth rate is a periodic and the death rate is a time-independent function.
Rani, Raffaele. Department of Mathematics and Mathematical Statistics, Umeå University
Influence of Morphological Traits on Wood Litter Production. (Poster)
Wood-litterfall is among the principal factors determining carbon accumulation in soil.
Understanding the mechanisms that give rise to this process is therefore an important task for the
estimation of carbon balances of forests and to develop management practices which balance timber
production with carbon sequestration (Franklin et al. 2012). In fire-prone areas, wood litterfall is an
important facilitator of forest fires, but a predictive theory of fire risk based on the rate of wood
litterfall, branch diameter distributions have yet to be developed. In this study, we investigate how
morphological traits (e.g. branching angle, metamer length and branching frequency) affect the
wood litter production. Similar questions have been studied theoretically using continuous
population dynamics models, e.g., Falster et al. (2011) and the dependence of ecosystem processes
on traits has long been investigated (Eviner 2004). We use an L-systems (Lindenmayer &
Prusinkiewicz 1990) based model introduced by Sterck & Schieving (2007). The model follows the
fundamental physiological principles of plant growth and accounts for the age and weight of a plant’s
constituent parts. The model provided promising results when investigating the effects of size,
shading, carbon economy, meristem population and reproductive allocation on the ontogenetic
patterns in 3-D growth and structure. The project aims to elucidate how differences in architectural
and physiological traits between species affect the rate of biomass loss due to branch turnover. In
addition, as various architectural strategies show different patterns in the size-dependence of
biomass loss, we hypothesize that growth efficiency (fraction of biomass lost due to branch turnover)
is inversely proportional to crown width.
Ripa, Jörgen. ThePEG, Dept. of Biology. Lund University.
Will the radiation of a superior competitor cause mass extinctions in coevolved communities?
(Poster, w. Jacob Jahoansson)
The well known extinctions events seen in the fossil record have been given various exogenous and
endogenous explanations, such as asteroid impacts, changes in the sea level, or a competitive
displacement of one taxon by another. A competitive displacement can be described as a radiation
into already occupied niches. How does such a 'secondary' radiation affect the community of the
replaced species? Will the inferior species go extinct all at once or over a prolonged period of time?
What happens to other trophic levels? We used an adaptive dynamics model, based on standard
community ecology, to study the evolutionary displacement of a competitive community. We found
no mass extinctions, rather the inferior species were replaced one by one by the radiating superior
invaders, keeping the total number of species more or less constant. More surprisingly, trophic levels
above or below were hardly affected at all. In our model, a predator community only shows very
little evolutionary response to a displacement of its whole resource base. According to our results,
the evolutionary replacement of a whole taxon can take place without causing any significant
changes in the embedding food web.
Rüffler, Claus. Department of Animal Ecology, Evolutionary Biology Centre, Uppsala University
A general condition for adaptive genetic polymorphism in temporally and spatially heterogeneous
environments. (Talk)
Both evolution and ecology have long been concerned with the impact of variable environmental
conditions on observed levels of genetic diversity within and between species. We model the
evolution of a quantitative trait under selection that fluctuates in space and time, and derive an
analytical condition for when these fluctuations promote genetic diversification. As ecological
scenario we use a generalized island model with soft selection within patches in which we
incorporate generation overlap. We allow for arbitrary fluctuations in the environment including
spatio-temporal correlations and any functional form of selection on the trait. Using the concepts of
invasion fitness and evolutionary branching, we derive a simple and transparent condition for the
adaptive evolution and maintenance of genetic diversity. This condition relates the strength of
selection within patches to expectations and variances in the environmental conditions across space
and time. Our results unify, clarify, and extend a number of previous results on the evolution and
maintenance of genetic variation under fluctuating selection. Individual-based simulations show that
our results are independent of the details of the genetic architecture and on whether reproduction is
clonal or sexual. The onset of increased genetic variance is predicted accurately also in small
populations in which alleles can go extinct due to environmental stochasticity.
Sasaki, Tatsuya. Faculty of Mathematics, University of Vienna, Austria
How the combined sequential use of rewards and punishments promotes cooperation. (Talk)
Rewards and penalties are frequently employed by social institutions, from parents to governments,
to promote cooperation. As the provisioning of incentives is costly, it is important to develop
strategies for the efficient implementation of incentives. We show for the first time that the
combined sequential use of rewards and penalties, called ‘first carrot, then stick’, achieve 100%
cooperation more effectively and efficiently than either rewards or penalties alone. The novel
incentive policy is so straightforward, and yet so potent, that it is highly surprising that it has as yet
remained unexplored in the literature on the evolution of cooperation.
Säterberg, Torbjörn. Department of Physics, Chemistry and Biology. Linköping University.
Functional extinctions in ecological networks (Talk)
Intensified exploitation of natural populations and habitats has led to increased mortality rates and
decreased abundances of many species. There is a growing concern that this might cause critical
abundance thresholds of species to be crossed, with extinction cascades and state shifts in
ecosystems as a consequence. When increased mortality rate and decreased abundance of a given
species lead to extinction of other species, this species can be characterized as functionally extinct
even though it still exists. Although such functional extinctions have been observed in some
ecosystems, their frequency is largely unknown. Here we use a new modelling approach to explore
the frequency and pattern of functional extinctions in ecological networks. We find that the species
most likely to go extinct first is not the one whose mortality rate is increased but instead another
species.
Trapman, Pieter. Department of Mathematics, Stockholm University.
End of an SIR epidemic on a random network. (Talk, w. Ana Serafimovic)
We consider an SIR (Susceptible-Infective-Recovered) epidemic on a static (configuration model)
random network. We describe the final stages of the epidemic and analyse the time until extinction
of the epidemic. Furthermore we consider the effect of control measures, such as vaccination on the
duration of the epidemic. The analysis heavily relies on theory on branching processes.
We show that the epidemic is always exponentially declining in the final stages, even if the degree
distribution of the network has infinite variance. Furthermore, we show that control measures,
although decreasing the size of the epidemic, might well increase the duration of the epidemic,
which might have serious public health and economic implications.
Wennergren, Uno. Department of Biology, Chemistry and Biology. Linköping University.
TBA (Talk)
TBA
Wickman, Jonas. Department of Mathematics and Mathematical Statistics, Umeå University
Methods for investigating evolution in spatially structured ecological systems. (Talk)
The ecological dynamics of a spatially structured ensemble of species can be modeled by a set of
partial differential equations. In order to study the evolutionary outcomes of such systems, a traitbased approach to phenotypic evolution can be applied, where the effects of an evolvable functional
trait (such as size, or propensity for a specific resource) are studied. We combine ideas from adaptive
dynamics, in which evolution is studied through the invasion of rare mutants with the perturbation
theory of differential operators. These are used to derive an expression for the strength and direction
of selection on a trait for a spatially structured population, as well as when such directional selection
ceases. We demonstrate one important application of the result by applying the developed methods
to evolutionary community assembly of dispersing consumers in an environment with
heterogeneously distributed resources.
Zhang, Lai. Department of Mathematics and Mathematical Statistics, Umeå University
Loss of species diversity through speciation collapse. (Talk)
TBA