​​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 do 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), on his expeditions around the world found that mountain slopes in different parts of the world show similar turnover patterns of plant communities, which were deterministically predictable by temperature. This was one of the first studies that established the role of climate in determining distribution patterns of organisms, which was later mathematically formalized by Hutchinson (1957) using the niche concept.
Hutchinson proposed that the biogeographic limits of an organism can be described using an abstract n-dimensional space, or the niche space, where niche axes are characterized by environmental attributes that are necessary for the survival of an organism. biogeographic limits of an organism can be obtained by projecting niche space onto physical world can reveal the potential places were an organism can persist. Wide used to understand distribution patterns of ​indivisual species to biomes- highest organisational unit of vegetation, and form the theoretical basis of most models in the clangin world.
 A species can persistence outside its niche if the migration rate from the source habitat (big circle) is more than the negative growth rates in the sink habitat (small circle). 
Even though the niche concept is central to modern biogeography, Hutchinson's concept of the niche is not always a reliable predictor of the occurrence of an organism. huthinson argued that the niche space if two species   when distribution of organisms are proceted reciprocal projection from the physical to niche space should yield non-overlapping hypervolumes characteristic of each species "realized niche". from For instance, an organism can persist outside its climatic niche if there is sufficient influx of population from source habitats (inside its niche) to sink habitats (outside its niche). Therefore, in addition to climatic factors, dispersal of organisms might also be an important driver of biogeographic patterns.
My research aims at understanding how dispersal affects the distribution pattern and resilience 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?