EVOP Subgroup Contributed Talks

Renee Dale

Donald Danforth Plant Science Center

"Describing root structural traits using characteristics of the multivariate normal distribution"

The structure of plant roots has a large impact on the environment through ground nutrient usage and underground carbon fixation. Crop plants can be improved to reduce fertilizer usage and combat climate change through identification of the genes controlling root structural traits. However, this remains challenging due to the highly variable and responsive nature of root growth. I derive new traits using characteristics of matrices and multivariate normal distributions (MVN) of roots from a diversity panel. The Sorghum diversity panel consists of 600 unique genotypes from around the world. The genotypes were grown in controlled conditions and X-ray imaged. From these images I obtain square matrices of root locations as a function of depth. The matrices are then analyzed and MVN distributions estimated to obtain root distribution information of each Z-slice. The resulting features include entropy, eccentricity, and the two largest eigenvalues of the covariance matrix. The ability of these characteristics to measure root structural traits are benchmarked against existing highly heritable traits, such as root depth and mass. Finally, after applying dimension reduction techniques, we can identify significant changes over depth and the genetic loci controlling highly heritable structural traits.

Thomas Tunstall

Living Systems Institute and Physics and Astronomy, University of Exeter, Exeter, United Kingdom

"Two subcritical processes combine into a supercritical process during range expansion into a heterogeneous environment"

We investigate the role of landscape structure on a range expansion with mutation and selection, using a generalised Eden model. In this lattice model, sites are occupied by wild type or mutant, or empty until infected by a neighbouring site. A phase transition between long-term mutant domination of the population front and coexistence has been characterised in a homogeneous environment for slower-growing mutants in the absence of back mutations [Kuhr et al., NJP, 2011].We here investigate the effect of randomly distributed circular patches that can only be invaded by the mutant - reminiscent of pesticide-treated areas that can only be invaded by resistant pests. Our simulations show that at surprisingly low patch density, mutants can dominate even at fitness lower than which is required in a homogeneous environment. Patches bestow a spatial advantage upon the mutants, enlarging mutant domains that can then overlap with downstream patches, leading to a cascade of patch to patch infection by the mutant domain. This argument can be quantified by combining geometrical arguments for domain boundaries with percolation theory.Our results provide an indication for the long-term dynamics of an expanding population frontier in an inhomogeneous medium, under the effects of mutation and selection.

Jody Reimer

University of Utah

"Beyond the mean: incorporating small scale heterogeneity into algal bloom models using generalized polynomial chaos"

When parameterizing dynamical systems models of biological processes, we often use summary statistics (e.g., the mean) reported in experimental or observational studies. However, these summary statistics are abstractions, concealing variation occurring over space, time, or among individuals. Further, we know that the behavior of a nonlinear model using mean parameter values will differ from the mean model behavior if the parameter is instead treated as a random variable. Algae growing within polar sea ice provides an example of a system where extreme local heterogeneity in environmental conditions results in local heterogeneity in algal growth rates. Ignoring this and using a fixed, mean growth parameter to approximate regional dynamics can result in incorrect predictions of bloom timing and magnitude. Instead, algal growth rates at a given location should be treated as a random variable capturing the known heterogeneity. In this talk, I will provide an introduction to generalized polynomial chaos as an elegant, computationally efficient method for incorporating heterogeneous growth rates into standard algal bloom models, resulting in improved predictions of bloom dynamics. This method is broadly applicable for any system where local heterogeneity needs to be accounted for when considering aggregate dynamics over larger scales.

Olivia Chu

Princeton University

"Opinion dynamics in heterogeneous environments"

In human social systems, it is natural to assume that individuals' opinions influence and are influenced by their interactions. Mathematically, it is common to represent such systems as networks, where nodes are individuals and edges between them denote a connection. Adaptive network models explore the dynamic relationship between node properties and network topology. In the context of opinion dynamics, these models often take the form of adaptive voter models, where there are two mechanisms through which network changes can take place. Through homophily, an edge forms between two individuals who already agree. Through social learning, an individual adopts a neighbor's opinion. In these models, individuals are more frequently attached to those who share their opinion, seen through the formation of sub-communities of like-minded individuals. However, it is not always the case that individuals want to cluster into homogeneous groups. Instead, they might attempt to surround themselves with those who both agree and disagree with them to attain a balance of inclusion and distinctiveness in their social environments. In this work, we explore the effects that such heterogeneous preferences have on the dynamics of the adaptive voter model.