Speed of invasion of an expanding population by a horizontally transmitted trait

Range expansions are a ubiquitous phenomenon, leading to the spatial spread of genetic, ecological, and cultural traits. While some of these traits are advantageous (and hence selected), other, nonselected traits can also spread by hitchhiking on the wave of population expansion. This requires us to understand how the spread of a hitchhiking trait is coupled to the wave of advance of its host population. Here, we use a system of coupled Fisher-Kolmogorov-Petrovsky-Piskunov (F-KPP) equations to describe the spread of a horizontally transmitted hitchhiking trait within a population as it expands. We extend F-KPP wave theory to the system of coupled equations to predict how the hitchhiking trait spreads as a wave within the expanding population. We show that the speed of this trait wave is controlled by an intricate coupling between the tip of the population and trait waves. Our analysis yields a new speed selection mechanism for coupled waves of advance and reveals the existence of previously unexpected speed transitions.