Rainfall and river networks prove accurate predictors of fish biodiversity

“The authors have combined sophisticated ecological theory and sophisticated hydrological theory,” said Simon Levin, the George M. Moffett Professor of Biology at Princeton. “This is work not only of practical importance, but [it] also stretches the boundaries of biogeography.”

Biodiversity characterizes the number of species within an ecosystem. Biogeography is the study of how biodiversity changes across space and over time.

“If because of climate change you have an increase in rainfall, our model can tell you how that will affect biodiversity,” said Rodríguez-Iturbe. “Or if you have a change in the connectivity of rivers due to human activity -- for example, the building of a dam -- our model can also measure how that will affect the numbers and distributions of species.”

River networks act as ecological corridors and as such the model will be useful not just for understanding the biodiversity of fish in rivers but also for understanding such things as the dispersal of seeds or even the spread of cholera. Rodríguez-Iturbe, Bertuzzo and Rinaldo also collaborated on a paper that recently appeared in an American Geophysical Union publication on how river networks affect the spread of cholera epidemics.

“Seeds and bacteria are different from fish -- obviously they can’t swim upstream,” said Rodríguez-Iturbe. “But like fish, their distribution is dramatically impacted and controlled by the river network.”

In order to construct the model, the researchers created a mathematical representation of river systems that went far beyond simple volume calculations. They drew upon an advanced area of geometry known as fractals.

River networks are examples of fractals, fragmented geometric shapes whose parts are, mathematically speaking, smaller versions of the whole. Fractals occur widely in nature. For example, the branching structure of trees -- from trunk to branch to twig -- are fractals, as are clouds and lightning bolts and snowflakes.

Unlike in a savannah, where wildlife move across an open plain, in a river basin fish have to move through the fragmented space of river networks, which like all fractals follow a predicable set of mathematical rules.

River networks have “a universal type of structure independent of scale,” said Rodríguez-Iturbe. “Some may be big or small, elongated or round, but they all follow some basic features regardless of their scale, regardless of their size, regardless of where they are located in the world.”

This research was supported by the James S. McDonnell Foundation.