Event category: Spring 2021

I will describe new methods for spatial transcriptomics and spacial genomics and contrast these methods with previous single cell and longitudinal genomics analysis approaches. I will focus first on methods for determining differential expression for spatial transcriptomic methods. I will then contract these early probabilistic methods with new methods built on variational auto encoders and generative ML approaches. Lastly I will describe bottlenecks, such as integrating imaging and genomic data in these studies. Prospects for building computational pipelines to integrate time, space and genomic coordinate will not be discussed, but will become apparent after deep reflection following the talk (but only if you pay attention).

In the first part of the talk, we discuss the multi-species competition in a spatial domain, particularly the result of A. Hastings and some recent progress on the conjecture by Dockery et al. concerning the evolution of slow dispersal, i.e. when other things are equal, the slowest diffuser can competitively exclude other competitors. We then discuss the effect of adding passive drift and how it changes the evolutionary dynamics so that fast/intermediate diffuser is selected. In the second part, we will discuss the effect of mutation, and the associated moving Dirac solutions in a nonlocal PDE model proposed by Perthame and Souganidis. This latter equation describes a population structured by space and a phenotypic trait, and can be understood as competition of infinitely many species with different rate of dispersal.