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Abstract

Self-organized periodic vegetation patterns in arid grasslands are thought to originate from a local positive feedback whereby vegetation density increases infiltration coupled with a long-distance negative feedback whereby vegetation patches deplete water from surrounding areas, leaving these bare. Studies show that this patterning could indicate approaching catastrophic ecosystem collapse. Previous models have described the dynamics of vegetation coupled with soil and surface water. However, several other positive feedbacks may occur, including one between vegetation density and local surface temperature. At our field site, it was observed that surface temperatures are cooler in vegetation patches (~35ºC) and hotter in areas of bare ground (>50ºC) due to evapotranspiration. This feedback indicates that the presence of vegetation further supports plant growth by cooling the surface to a temperature suitable for vegetation growth and has not been previously modeled or studied for its impact on vegetation pattern formation. This study analyzes the effect of adding the temperature feedback to the HilleRisLambers model on vegetation patterning. To do this, we multiplied the vegetation growth term by a temperature-dependent term P/(h+P) where P represents plant density and h determines the model’s temperature dependence. We then ran the model at different h values and levels of rainfall to understand how the dynamics of the model were changed by this modification. The simulations run with our modified model indicate a temperature feedback might affect vegetation patterning. The inclusion of a temperature feedback appears to widen the area of bistability when vegetation biomass (P.mean) is plotted against rainfall (R). Without the temperature feedback (h=0), the area of bistability is within the range of R=0.875 and R=0.995. Including the temperature feedback (h=0.05), this range became from R=0.9375 to R=1.5 and expanded further as h increased. Our results created new questions about pattern formation approaching the catastrophic bifurcation switch point and at higher rainfall levels. Literature suggests that patterning increases as the system approaches desertification. While our model was able to recreate patterns observed in nature and in previous studies, specifically labyrinth and fairy rings, at higher values of h (and hence higher temperature dependence of plant growth), we also observed decreased patterning approaching catastrophic bifurcation, contradicting previous studies. Additionally, our model produced patterns resembling patterns formed in Belousov-Zhabotinsky reactions. While this has not been observed in previous studies or in nature, further exploration into the mathematics behind these results would be interesting.

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