These pages are being generated as part of a senior seminar course  directed by Neal Williams 
at Bryn Mawr College during fall semester, 2007. This week's topic is
"Biodiversity and Stability"
Reading to be discussed:
While the insurance hypothesis is an interesting theory that can potentially explain how an increased species richness can decrease community variability and thus increase community stability, so is the portfolio effect. Therefore, I will attempt to explain this concept as understood during our discussion. Unlike the insurance hypothesis, the portfolio effect does not assume that individual species are correlated. On the contrary, it assumes that fluctuations of individual species are not perfectly correlated. However, despite the lack of strong correlation between species that could lead to a more negative covariance, the variability of community is lowered than variability of individual species populations due to averaging of population fluctuations across species. Because this explanation, which is derived from the article discussed from this week, was somewhat confusing, we attempted to understand this concept in our own way.
From our discussion we have understood the insurance hypothesis to be associated with the effects of the covariance of individual populations of species to the variance of the community the populations compose, whereas the portfolio effect is associated with the variance of the individual species rather than the covariance. In other words, the decrease in community stability is due not to the decrease in the covariance of species as a result of increased species richness, but due to the decrease in variances of each species as a result of increased species richness. This makes sense, especially in the case of biomass being the measure of stability, considering that a community has a limited area because if the number of species increase it is inevitable that the area for each species decreases automatically lowering the species variance. However, this can only be true under the assumption that species evenness is high.
Species evenness is an important aspect of this theory because in the presence of a dominant species that will remain the dominant species even with the introduction of new species, the variance will not change for that species and because it makes up a large portion of the community, it will have different effects. In the case that of low species evenness, the stability is mainly influenced by the population fluctuations of dominant species.
For this reading, we approached two statistical principles by which stability in a community can be understood, the insurance hypothesis and the portfolio effect. Here I will attempt to explain the insurance hypothesis, as I understood it from our discussion. The idea behind stability is that a community is stable when its components do not vary. Therefore, to quantify stability in a community, we measure the amount of variability in the community’s species, recognizing that there is a negative relationship between the two (high stability means low variability, and low stability means high variability). However, because species can interact with one another, variability in one species (such as a predator or competitor) can directly cause variability in another (such as its prey or competitor). For species that are not related in such a way, there is also the possibility that a change in the environment will cause different responses in different species, so that if a few species cannot handle the change, there will still be others that can take over their role in the system.
To mathematically describe the variability in this system, we have two components: a term that increases the variability of the system, and a term that decreases the variability of the system. The term that increases variability represents how much the individual species vary independently of each other and is given by the sum of the variance of the individual species. For two species it would be the variance of species A plus the variance of species B: var(a) + var(b). The term that decreases variability represents the variability associated with a relationship between the species, that is, if the species directly influence each other (the article gives competition as an example) or indirectly respond differently to change. This component represents the covariance of species A’s effects on species B, and species B’s effects on species A, and is given by: 2cov(a,b). To describe the variability of a community of two species, A and B, we put the two terms together and get: variance(a + b) = var(a) + var(b) +2cov(a,b).
The more species you add the mix, the greater the chance that some are related to each other or respond differently to change, increasing the chance that the covariant term will play a role in the equation, decreasing variability and increasing stability. Therefore, the insurance hypothesis suggests that stability will increase with increasing biodiversity.