Novel spatial analysis methods reveal scale-dependent spread and infer limiting factors of invasion by Sahara mustard

Multiple scale-dependent ecological processes influence species distributions. Uncovering these drivers of dynamic range boundaries can provide fundamental ecological insights and vital knowledge for species management. We develop a transferable methodology that uses widely available data and tools to determine critical scales in range expansion and to infer dominating scale-dependent forces that influence spread. We divide a focal geographic region into different sized square cells, representing different spatial scales. We then used herbarium records to determine the species' occupancy of cells at each spatial scale. We calculated the growth in cell occupancy across scales to infer the scale dependent expansion rate. This is the first time such a 'box-counting' method is used to study range expansion. We coupled this multi-scale analysis with species distribution models to determine the range and spatial scales where suitable climate allows the species to spread, and where other factors may be influencing the expansion. We demonstrate our methodology by assessing the spread of invasive Sahara mustard in North America. We detect critical scales where its spread is limited (100-500 km) or unconstrained (5-50 km) by climatic variables. Using climate-based models to assess the similarity of climate envelopes in its native and invaded range, we find that the climate in the invaded range generally predicts the native distribution, suggesting that either there has been little local adaptation to climate occurring since introduction or the biological interaction experienced in the invaded range has not driven the species to occupy climatic conditions much different from its native range. Our novel method can be broadly utilized in other studies to generate critical insights into the scale dependency of different ecological drivers that influence the spread and distribution limits, as well as to help parameterizing predictions of future spread, and thus inform management decisions.