Traveling vegetation-herbivore waves can sustain ecosystems threatened by droughts and population growth

Dryland vegetation forms spatial patterns as an adaptation to water stress, driven by the uneven distribution of resources. While these patterns aid plant survival, herbivore grazing adds pressure, increasing desertification risks through vegetation loss and soil erosion. We present a novel model integrating vegetation patterning and herbivore grazing dynamics to explore their feedback loops over time. The model accounts for herbivore behaviors, including foraging, movement, and vegetation preferences. Using numerical continuation methods, we analyze solutions such as uniform and patterned vegetation-herbivore dynamics. A key finding is the emergence of traveling waves, where vegetation and herbivores propagate across the landscape. Herbivore distribution within these waves is asymmetric, causing uneven grazing stress. Surprisingly, this dynamic reduces overall grazing impact, enhancing vegetation sustainability compared to uniform grazing. Understanding these dynamics is vital for food security in drylands. By balancing herbivore populations and preserving vegetation, these interactions help mitigate drought and population growth challenges.