A model for optimal mycorrhizal colonization along altitudinal gradients

Mycorrhizal associations are generally favourable for vascular plants in nutrient-poor conditions. Still, non-mycorrhizal plants are common in high arctic and alpine areas, which are often poor in nitrogen and phosphorus. The relative proportion of mycorrhizal plants has been found to decrease along with increasing altitude, suggesting that the advantage of the mycorrhizal symbiosis may change along an altitudinal gradient. This may be related to the environmental factors that possibly constrain the amount of photosynthesized carbon to be shared with mycorrhizal fungi. We propose a simple optimization model for root colonization by fungal symbionts and analyze the advantages of mycorrhizas in relation to the nutrient use efficiency of photosynthesis (PNUE), the kinetics of nutrient uptake and the soil nutrient levels. Our model suggests that mycorrhizas are not usually favoured at low PNUE values. At low nutrient levels, mycorrhizas may be advantageous if they have a lower threshold concentration of nutrient uptake (xmin) compared to non-mycorrhizal roots. If mycorrhizal roots have a higher maximum capacity of nutrient uptake (Vmax), mycorrhizas can be favourable for the host plant even at relatively low nutrient concentrations and at relatively low PNUE. Consequently, the possible patterns along altitudinal gradients essentially depend on PNUE. If the soil nutrient concentration is constant and PNUE decreases, the advantage of mycorrhizal symbiosis declines independently of the nutrient uptake kinetics. If PNUE remains constant and the soil nutrient concentration decreases along with increasing altitude, the emerging colonization pattern (either increasing, decreasing or intermediate) depends on the nutrient uptake kinetics. Additionally, if both PNUE and the soil nutrient concentration decrease, several patterns may emerge, depending on the nutrient uptake kinetics.