Modeling tree species migration in the Alps during the Holocene: What creates complexity?

Abstract

The tree migration model TreeMig is presented as an example for modeling a complex ecological system. The model was derived from a forest gap model, reducing the gap models’ complexity by model aggregation and includes elements for showing complex behavior: many state variables, non-linear process functions, feedbacks and spatial interactions. Additionally, the model depends on external variables, namely climate. In a case study, the tree migration in the highly structured environment of the region of Valais in the Swiss Alps during the Holocene was simulated. The simulations were run on a grid with 1 km × 1 km resolution with a yearly time step. A scenario of temperature-anomalies in the Holocene, spatially interpolated climate data and times of species immigration into the simulation area was used as input. The simulation results were evaluated with regard to the spatio-temporal species composition and complexity, i.e. species diversity and spatio-temporal unevenness. Two indices of complexity were calculated from the simulated species biomasses in space and time: the Shannon–Weaver index for species diversity and an index of spatio-temporal complexity (unevenness) of total biomass. Both indices depended on climate, but in different ways. Tree species diversity was positively related to degree day sum, i.e. was high at low and smaller at high altitudes. Spatio-temporal complexity in turn was high at the alpine timberline, but very low at lower elevations. Increased complexity independent from climate occurred during migration waves into the simulation area. Spatio-temporal complexity was high when the first species colonized the region. Tree species diversity changed during the immigration wave of each immigrating species, particularly that of the dominant species Picea abies. At the fronts of the immigration waves in particular, spots of increased diversity appeared. However, no formation of stable patchy patterns was observed at the studied scale. The standard simulation, reflecting climate patterns and endogenous processes such as local dispersal, long-range migration and succession was compared to simulations, where single or all endogenous processes were excluded. The dissimilarities between the species compositions of these simulations indicated that after immigration of dominant species succession and migration strongly influence the species pattern, succession over centuries and migration over millennia. I conclude that the species pattern and its complexity, as shown by the model simulations, were to a great extent determined by external factors and their complexity. After changes in the boundary conditions, succession and migration had a strong influence.