When: 3 February 2021, kl. 13-14

Where: This seminar is given online. E-mail Dan Hedlin if you want to attend.

### Abstract

Co-adaptation is key to understanding species evolution. Different traits have to function together so that the organism can work as a whole. Hence, all changes to environmental pressures have to be coordinated. Recently, we (with G. Asimomitis, V. Mitov, T. Stadler) have developed R packages that are able to handle general, multivariate Gaussian processes realized over a phylogenetic tree. The modelling framework is centred around the so-called GLInv (Gaussian, mean depending linearly on the ancestral value and variance Invariant with respect to ancestral value) family of models [3, the PCMFit GitHub package can do inference for this class of models]. More formally a stochastic process evolving on a tree belongs to this family if

* after branching the traits evolve independently

* the distribution of the trait at time t, X(t), conditional on the ancestral value, X(s), at time s<t, is Gaussian with

** E[X(t) | X(s)] = w(s,t) + F(s,t)X(s)

** Var[X(t) | X(s) ] = V(s,t),

where neither w(s,t), F(s,t), nor V(s,t) can depend on X(.) but may be further parametrized. Using the likelihood computational engine PCMBase [2, available on CRAN] the new version of mvSLOUCH [1] is able to (relatively) quickly do inference for multivariate Ornstein-Uhlenbeck (OU) models evolving on a phylogenetic tree. The user is able to propose specific model parametrizations that correspond to particular hypotheses about relationships between traits. Interactions between traits can be understood as magnitudes and signs of off-diagonal entries of F(s,t) or V(s,t). In the talk I will discuss how one can setup different hypotheses concerning relationships between the traits in terms of model parameters and how one can view the long and short term evolutionary dynamics. The software's possibilities will be illustrated by considering the evolution of fruit in the Ferula genus. I will also discuss some limit results that are amongst others, useful for setting initial seeds of the numerical estimation procedures and different inference algorithms.

[1] K. Bartoszek, J. Pienaar, P. Mostad, S. Andersson, and T. F. Hansen. A phylogenetic comparative method for studying multivariate adaptation. J. Theor. Biol. 314:204-215, 2012.

[2] V. Mitov, K. Bartoszek, G. Asimomitis, T. Stadler. Fast likelihood calculation for multivariate phylogenetic comparative methods: The PCMBase R package. arXiv:1809.09014, 2018.

[3] V. Mitov, K. Bartoszek, T. Stadler. Automatic generation of evolutionary hypotheses using mixed Gaussian phylogenetic models. PNAS, 201813823, 2019.