​​Theoretical Biogeography: The mathematics of when and where
Drawings of plant communities on the slopes of Anders, Teneriffe, and the Himalayas by Alexander von Humbolt (Essay on the Geography of Plants 1807).
Earth is home to millions of organisms that live in a wide range of habitats, from arid and cold regions near the poles to humid and warm tropics. Each of these habitats offers a unique challenge for the survival of an organism. Over two centuries, biogeographers have been interested in understanding why organisms occur where they do. What makes this endeavor so fascinating is that no one organism occurs everywhere on the planet. Instead, organisms are distributed in predictably repeatable ways. For instance,  Alexander von Humbolt (1807) argued that mountain slopes in different parts of the world show similar turnover patterns of plant communities which are deterministically predictable by temperature. 
Extending this idea, Whittaker (1970) argued that the spatial limits of global biomes—the highest organizational unit of plants—are also deterministically predictable by climate. Recent empirical works, however, show that biomes, such as tropical savanna and forest, are not always predictable by climate. Although forests are more common in high rainfall areas and savannas in low rainfall areas, the boundary between these biomes occurs over a wide range of rainfall values . Explaining variations in the spatial limits of savanna and forest biomes with respect to climate remains an open challenge. 
Whittaker's (1970) biome classification map based on climatic niches.
Current biome theories neglect spatial interactions when savanna and forest occur side-by-side. Long-term observational studies show deforested grasslands can repopulate from adjacent forest patches if left alone. Thus, dispersive interactions could be an important driver of biome limits.
Savanna-forest boundary in Western Ghats, India
My research aims at understanding how dispersal affects the distribution of savanna and forest biomes at continental scales, using a combination of theoretical (continuous- and discrete-diffusion models) and empirical (paleo and remote sensing data) approaches.
Some of the questions I am currently pursuing are:

  • How does the boundary between savanna and forest form?
  • What determines the position of the boundary?
  • Is the boundary stable to anthropogenic disturbances and climate change?
The position of the savanna-forest boundary (brown line) and its relationship to rainfall. 
Contrary to Whittaker's biome theory, the savanna-forest boundary is not solely predictable by a particular rainfall contour PM (grey line; commonly known as Maxwell precipitation), but also by source-sink dynamics. When PM is curved, the boundary deviates from PM (left) because of the imbalance between influx and outflux of seeds, resulting in the nondeterministic relationship between rainfall and tree cover (right).