@article{calsbeek_lavergne_patel_molofsky_2011, title={Comparing the genetic architecture and potential response to selection of invasive and native populations of reed canary grass}, volume={4}, ISSN={["1752-4571"]}, DOI={10.1111/j.1752-4571.2011.00195.x}, abstractNote={AbstractEvolutionary processes such as migration, genetic drift, and natural selection are thought to play a prominent role in species invasions into novel environments. However, few empirical studies have explored the mechanistic basis of invasion in an evolutionary framework. One promising tool for inferring evolutionarily important changes in introduced populations is the genetic variance–covariance matrix (G matrix). G matrix comparisons allow for the inference of changes in the genetic architecture of introduced populations relative to their native counterparts that may facilitate invasion. Here, we compare the G matrices of reed canary grass (Phalaris arundinacea L.) populations across native and invasive ranges, and between populations along a latitudinal gradient within each range. We find that the major differences in genetic architecture occur between populations at the Northern and Southern margins within each range, not between native and invasive populations. Previous studies have found that multiple introductions in introduced populations caused an increase in genetic variance on which selection could act. In addition, we find that differences in the evolutionary potential of Phalaris populations are driven by differences in latitude, suggesting that selection also shapes the evolutionary trajectory of invasive populations.}, number={6}, journal={EVOLUTIONARY APPLICATIONS}, author={Calsbeek, Brittny and Lavergne, Sebastien and Patel, Manisha and Molofsky, Jane}, year={2011}, month={Nov}, pages={726–735} }
 @article{calsbeek_2012, title={EXPLORING VARIATION IN FITNESS SURFACES OVER TIME OR SPACE}, volume={66}, ISSN={["1558-5646"]}, DOI={10.1111/j.1558-5646.2011.01503.x}, abstractNote={As the number of studies estimating selection on multiple traits has increased in recent years, fitness surfaces have become a fundamental tool for understanding multivariate selection and evolution. However, rigorous statistical comparisons of multivariate selection surfaces over time or space have been limited to parametric analyses of selection coefficients estimated using a quadratic regression model. Although parametric comparisons are useful when selection is approximately linear or quadratic in nature, they are limited when confronting the complex nature of rugged fitness surfaces. Here, I present a novel solution to comparing nonparametric fitness surfaces over time or space. Using a Tucker3 tensor decomposition, which is essentially a higher order principal components analysis, I show how major features of fitness surfaces can be compared statistically. Combined with a bootstrap algorithm, I develop three statistical tests that identify (1) differences in the shape of nonparametric fitness surfaces, (2) differences in the contribution of each surface to variation in fitness across time or space, and (3) specific areas of the surfaces (trait combinations) that vary significantly over time or space. I illustrate the tensor decomposition and statistical analyses using idealized fitness surfaces.}, number={4}, journal={EVOLUTION}, author={Calsbeek, Brittny}, year={2012}, month={Apr}, pages={1126–1137} }