This paper is concerned with spreading phenomena of the classical two-species Lotka-Volterra reaction-diffusion system in the weak competition case. More precisely, some new sufficient conditions on the linear or nonlinear speed selection of the minimal wave speed of travelling wave fronts, which connect one half-positive equilibrium and one positive equilibrium, have been given via constructing types of super-sub solutions. Moreover, these conditions for the linear or nonlinear determinacy are quite different from that of the minimal wave speeds of travelling wave fronts connecting other equilibria of Lotka-Volterra competition model. In addition, based on the weighted energy method, we give the global exponential stability of such solutions with large speed $c$. Specially, when the competition rate exerted on one species converges to zero, then for any $c>c_0$, where $c_0$ is the critical speed, the travelling wave front with the speed $c$ is globally exponentially stable.

The concept of a rapid spread of self-replicating interstellar probes (SRPs) throughout the Milky Way adds considerable strength to Fermi's Paradox. A single civilization creating a single SRP is sufficient for a fleet of SRPs to grow and explore the entire Galaxy on timescales much shorter than the age of the Earth – so why do we see no signs of such probes? One solution to this Paradox suggests that self-replicating probes eventually undergo replication errors and evolve into predator-prey populations, reducing the total number of probes and removing them from our view.

I apply Lotka-Volterra models of predator-prey competition to interstellar probes navigating a network of stars in the Galactic Habitable Zone to investigate this scenario. I find that depending on the local growth mode of both populations and the flow of predators/prey between stars, there are many stable solutions with relatively large numbers of prey probes inhabiting the Milky Way. The solutions can exhibit the classic oscillatory pattern of Lotka-Volterra systems, but this depends sensitively on the input parameters. Typically, local and global equilibria are established with prey sometimes outnumbering the predators. Accordingly, we find this solution to Fermi's Paradox does not reduce the probe population sufficiently to be viable.

Predator-prey models are often applied to the interactions between host immunity and parasite growth. A key component of these models is the immune system's functional response, the relationship between immune activity and parasite load. Typically, models assume a simple, linear functional response. However, based on the mechanistic interactions between parasites and immunity we argue that alternative forms are more likely, resulting in very different predictions, ranging from parasite exclusion to chronic infection. By extending this framework to consider multiple infections we show that combinations of parasites eliciting different functional responses greatly affect community stability. Indeed, some parasites may stabilize other species that would be unstable if infecting alone. Therefore hosts' immune systems may have adapted to tolerate certain parasites, rather than clear them and risk erratic parasite dynamics. We urge for more detailed empirical information relating immune activity to parasite load to enable better predictions of the dynamic consequences of immune-mediated interspecific interactions within parasite communities.