Importance of individual and environmental variation for invasive species spread: a spatial integral projection model.

Plant survival, growth, and flowering are size dependent in many plant populations but also vary among individuals of the same size. This individual variation, along with variation in dispersal caused by differences in, e.g., seed release height, seed characteristics, and wind speed, is a key determinant of the spread rate of species through homogeneous landscapes. Here we develop spatial integral projection models (SIPMs) that include both demography and dispersal with continuous state variables. The advantage of this novel approach over discrete-stage spread models is that the effect of variation in plant size and size-dependent vital rates can be studied at much higher resolution. Comparing Neubert-Caswell matrix models to SIPMs allowed us to assess the importance of including individual variation in the models. As a test case we parameterized a SIPM with previously published data on the invasive monocarpic thistle Carduus nutans in New Zealand. Spread rate (c*) estimates were 34% lower than for standard spatial matrix models and stabilized with as few as seven evenly distributed size classes. The SIPM allowed us to calculate spread rate elasticities over the range of plant sizes, showing the size range of seedlings that contributed most to c* through their survival, growth and reproduction. The annual transitions of these seedlings were also the most important ones for local population growth (lambda). However, seedlings that reproduced within a year contributed relatively more to c* than to lambda. In contrast, plants that grow over several years to reach a large size and produce many more seeds, contributed relatively more to lambda than to c*. We show that matrix models pick up some of these details, while other details disappear within wide size classes. Our results show that SIPMs integrate various sources of variation much better than discrete-stage matrix models. Simpler, heuristic models, however, remain very valuable in studies where the main goal is to investigate the general impact of a life history stage on population dynamics. We conclude with a discussion of future extensions of SIPMs, including incorporation of continuous time and environmental drivers.