Invasive species must adapt to a suite of novel selective pressures as they colonise new territory. For example, theory predicts that selective forces at an invasion front will favour traits that enhance rates of dispersal and population growth, whereas selective forces in the range-core will favour traits that enhance competitive ability. To explore this idea, I conducted competition trials on three life stages of the invasive cane toad (Rhinella marina) from invasion-front and range-core populations in tropical Australia. For larval and early terrestrial-stage animals, I conducted experiments whereby the offspring of invasion-front and range-core adults were placed into mesocosms to compete for limited resources. To enable such experiments, I developed a simple method to mark each cohort of tadpoles, with minimal observed effects on growth or survival. Range-core larvae proved to be better competitors than invasion-front larvae, as predicted by evolutionary theory. Contrary to expectations, invasion-front metamorphs outcompeted range-core metamorphs, growing larger and winning more food. For adults, I focused on the trade-off between rapid dispersal versus success in male-male rivalry. Longer arms reduced the force required to displace an amplecting male from a female. When competing for a female, males with longer arms had lower likelihoods of retaining amplexus. I also explored how visual and acoustic cues influence the behaviour of sexually active males. Male toads used the presence of a chorus to increase their activity levels and as a cue to initiate amplexus. Males also used movement to identify potential mates, with increased rates of amplexus when a target was moving. My thesis presents empirical evidence that the evolutionary forces unleashed by a biological invasion can modify traits important in intraspecific competition at each life stage. My results are relevant to evolutionary theory and are directly translatable into proposed management strategies.