Over-shading is critical for inducing a regime shift from heathland to grassland under nitrogen enrichment

• Heathland conversion to grassland is often explained by increased ammonia deposition.
• A two-species competition model is developed with over-shading and multiple limiting resources.
• Over-shading invokes alternative stable states and is critical for the heathland regime shift.

The mass conversion of heathland to grassland in north-western Europe the past decades is a typical example of how tipping points threaten the biodiversity and ecosystem services delivered by biota. Different explanations have been provided for this conversion, with nitrogen enrichment resulting from anthropogenic activities being a commonly supported hypothesis. Here we present a mathematical model to investigate the conditions under which the conversion of heathland to grassland can occur. The model describes indirect competition for light and nitrogen between heather dwarf shrub (Calluna vulgaris) and wavy hair-grass (Deschampsia flexuosa), while both species also over-shade each other. Nutrient co-limitation in the model is described using the Synthesizing Unit concept. Over-shading is found to play a pivotal role in the existence of alternative stable states in the model. Under constant light availability a combination of over-shading and enrichment with ammonia leads to a regime shift from heathland to grassland, while under enrichment with ammonia alone there is coexistence between the two species. These results are supported by experimental findings in the literature.