Individuals differ substantially in fitness components, but such realized variation in lifespan and reproductive success need not be visible to natural selection, because fitness is not a property of individuals but of groups or genotypes. I will present formulas—rooted in Markov Chain theories—to compute exactly the variance in lifespan and in lifetime reproductive success among individuals with identical (genotypic) vital rates. This expected neutral variance is solely driven by individuals transitioning stochastically among stages. I illustrate how the neutral expected variation in fitness components matches those observed in real populations, how ignoring this stochastic variability and labeling it undesired noise can lead to false demographic predictions, and present data from isogenic bacteria that illustrates that the overwhelming amount of variation in fitness components among individuals is neutral and that the amount of variance detected in the lab does not differ much from natural populations.

Hybridization among eukaryotic organisms gives rise to reticulate evolutionary histories, and subsequent potential introgression results in genome mosaics. Consequently, phylogenetic networks have been introduced to model reticulate evolutionary histories. In this talk, I will present our recent work on modeling the evolution of genes and genomes within the branches of phylogenetic networks and the methods we have developed for their inference. Further, I will describe a new comparative genomic method that combines phylogenetic networks with hidden Markov models in order to detect genomic regions with signatures of introgression.

TBA

Epithelial cancers often emerge within genetically altered fields of premalignant cells that appear histologically normal but have a high chance of progression to malignancy. Clinical consequences of this so-called field cancerization are multifocal lesions and high recurrence risks after excision of the primary tumor. We develop a spatiotemporal stochastic model field cancerization, combining evolutionary dynamics at the phenotypic level with a general framework for multi-stage progression to cancer. Based on the model, we derive probabilistic distributions for clinically relevant quantities such as size of the invisible premalignant field at time of cancer diagnosis, and risk of local and distant recurrences. Finally, we discuss how our model can be combined with patient-specific measurements to optimize surgical excision margins and post-operative monitoring.

Marc Ryser is no longer able to attend this workshop. Rick Durrett will be presenting giving this talk instead.

Evolutionary biologists use phylogenetic trees of extant species to study the speciation and extinction patterns of different groups of species. Most inferences are based on methods that use type independent evolutionary rates of speciation and extinction, but recently a number of more type-dependent simulation methods are being used (Maddison et al., Fitzjohnet al., Igic & Goldberg) with important consequences for validity of some previously held beliefs. A fair amount is known about the probability distribution of ancestral trees derived from single type branching processes, while much less is known about the same objects for multi-type branching processes (other than asymptotic results). In this talk I will present a few results in this direction. First, there is an algorithmic way to construct an ancestral tree of the standing population of a multi-type branching process in terms of a Markov chain (of vectors of types and multiplicities). This construction allows one to get explicit formulae for calculating: (a) statistical features that describe the shape of the tree (the law of coalescence times together with types on the ancestral lineages), and (b) statistical features that link types in the standing population with the shape of the tree (the law of same-type coalescence times). Second, explicit calculations can be used to compare the effect that different branching mechanisms have on the distributions of ancestral trees. I will illustrate this in a simple example of two-type process with completely asymmetrical vs symmetrical probabilities of offspring types.

The antibody repertoire of each individual is continuously updated by the evolutionary process of B cell receptor mutation and selection. It has recently become possible to gain detailed information concerning this process through high-throughput sequencing. In this talk I will describe our work on statistical molecular evolution methods for the analysis of B cell sequence data, and their application to a very deep short-read data set of B cell receptors. We find that the mutational process is conserved across individuals but varies significantly across gene regions. We investigate selection on B cell receptors using a novel method that side-steps the difficulties encountered by previous work in differentiating between selection and motif-driven mutation; this is done through stochastic mapping and empirical Bayes estimators that compare the evolution of in frame and out of frame rearrangements. We use this new method to derive a per-residue map of selection, which we find is dominated by purifying selection, though not uniformly so.

Historically, models of quantitative trait evolution have assumed that individual mutations rarely, if ever, produce substantial changes in phenotype. Genome-wide association studies suggest that these infinitesimal models may be appropriate for some traits, like human height. However, experimental manipulations of other traits, such as gene expression, suggests that mutations that drastically alter phenotype may be common. In joint work with Michael Landis at UC Berkeley, we are exploring the development of models of quantitative trait evolution that can handle arbitrary mutational effects. We developed a neutral model using coalescent theory and I will show how this framework can be used to calculate the characteristic function for a sample of individuals from a panmictic population. We also found several scaling limits (as the number of loci controlling the trait increases), including the classical normally distributed limits and a class of alpha-stable limits in which the sampling distribution is fat-tailed. Based on these limits, we conjecture a powerful interpretation of these limits based on de Finetti's theorem. We then applied our models to analyze gene expression data from the fungus Neurospora crassa and found between 20 and 40 genes provide evidence for fat-tailed mutational effects.