Spatio-temporal dynamics of a model for the effect of variable ages at reproduction

Some species may have totally different ages at successful reproduction (ages at maturity) in population growth. For example, Ixodes ticks, a vector species responsible for many tick-borne diseases, may suspend development and undergo diapause during maturation process, which naturally introduce distinct ages at reproduction. Although the age at reproduction is a key demographic trait that is probably under high selective pressure, it is highly variable and the effect of this variability on spatial establishment and invasion is not well understood. In this study, a spatial mechanistic model, in the form of reaction diffusion equations with nonlocal terms incorporating two different ages at reproduction, is formulated and mathematically analyzed from a dynamical system point of view. Specifically, the persistence of the species in a bounded domain can be predicted by the net reproduction number and the spreading property in an unbounded domain in terms of spreading speed and traveling waves is characterized. Numerical simulations are conducted to further illustrate the impact of ages at reproduction on the net reproduction number and the spreading speed of the species, in particular for various scenarios of fitness tradeoffs of the premature survival and early reproduction.