DIVERSITY:

THEORY PREDICTS THE UNEVEN DISTRIBUTION OF GENETIC DIVERSITY WITHIN SPECIES

Below is a one-page summary of the work. An extended informal presentation is also available.

We studied genealogical trees and discovered that they have quite general properties that imply that a population will have small groups that are very distinct from all the rest. These small groups are like diversity hotspots that we have been trying to protect in conservation efforts. Since we need to protect biodiversity to ensure species survival, we should identify these small groups and protect them from going extinct.

Key points:

What? We studied diversity of populations, how individuals in a population are different from each other and the degree to which they are different from each other. If we look at the whole population we can quantify how diverse the population is. We studied how individuals contriubte to that diversity: If you lose one or more individuals how much of the diversity do you lose. The exciting result was that there are individuals or small groups that contribute much of the diversity, they are very different from the others, and therefore if they are lost, then much of the diversity is lost.

Why? The importance of diversity: Biodiversity is important to survival of species in general. Having diversity allows a population to successfully respond to changes in environment new diseases, and so on. The diversity is a key property of systems in general. It is a key to survival. If a population is homogeneous, a new disease may kill the entire population, if the climate changes the population may also go extinct.

How? We studied the properties of genealogical trees. The more an individual doesn't have other close living relatives, the more unique he or she is. If the only living relatives are very remote, then the individual is very unique. Studying a particular genealogy can give an idea about the genealogical properties, but we also studied analytically the universal properties of genealogies based upon "scaling arguments" that tell how the structure of a genealogy works in general.

One of the key results is that there are remarkably unique individuals and groups. Much of the diversity is found in a few individuals.

This is characteristic of what are called power law distributions, which are often found in complex systems. For example, cities are not all the same size --- there are some cities that have many more people than other cities. Similarly, in a population some individuals have many more distinct parts of their DNA than others.

Experimental verification: After we performed the theoretical study, we were able to find data that was obtained on genetic comparisons within a bacterial species whose samples were taken from around the world, and these data are consistent with our predictions.

Implications? The main lesson from this study is that just as it is important to identify endangered species, it is important to identify the endangered individuals and groups that comprise a species. Even just after an extinction event, if we identify unique individuals we can preserve much of the diversity. This is clearly relevant right now because of the human impact on the environment.

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