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====== Diversity analysis ====== | ====== Diversity analysis ====== | ||
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+ | ===== Theory ===== | ||
In general, diversity is a measure quantifying number of different states in a system. In case of ecological communities these states are usually species, but could be also genera, families, OTU’s or functional types. Many important ecological theories predict number of species in a community (e.g. island biogeography, | In general, diversity is a measure quantifying number of different states in a system. In case of ecological communities these states are usually species, but could be also genera, families, OTU’s or functional types. Many important ecological theories predict number of species in a community (e.g. island biogeography, | ||
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Diversity has two components: **species richness** (number of species in a community), and **evenness** (or shape of species abundance distribution (SAD) – the fact that some species are common and other are rare). | Diversity has two components: **species richness** (number of species in a community), and **evenness** (or shape of species abundance distribution (SAD) – the fact that some species are common and other are rare). | ||
- | To understand why differences in abundances between species matter for the diversity, let’s take a walk through two forests (example adapted from Gotelli & Chao 2013). Both communities have the same species richness of 20 different tree species. Note that here, richness refers to number of species in the whole community, and we are surveying the community by sampling limited number of individuals (it is unlikely that we would be able to survey the whole community, i.e. all individuals in it). The first forest (community A) is perfectly even, i.e. each species is represented by the same number of individuals. The second forest (community B) is highly uneven, i.e. one species | + | To understand why differences in abundances between species matter for the diversity, let’s take a walk through two forests (example adapted from Gotelli & Chao 2013). Both communities have the same species richness of 20 different tree species. Note that here, richness refers to the number of species in the whole community, and we are surveying the community by sampling |
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- | As you can see from the figure above, in the even community A we have high probability that each new individual will be a new species, while in the highly uneven community B we keep meeting still the same species, while rarely observing the other. In the forest A, during the first walk we observed 15 species, which means that 5 species remain undetected, and during the second walk we observed 13 species (7 undetected). In forest B, first walk brings 3 species (17 undetected), | + | As you can see from the figure above, in the even community A we have a high probability that each new individual will be a new species, while in the highly uneven community B we keep meeting still the same species, while rarely observing the other. In the forest A, during the first walk we observed 15 species, which means that 5 species remain undetected, and during the second walk, we observed 13 species (7 undetected). In forest B, the first walk brings 3 species (17 undetected), |
- | The shape of species abundance distribution (SAD) has been for rather long time considered as an important indicator of underlying community assembly processes. R.A. Fisher was perhaps the first to plot the SAD plot in which x-axis represents number of individuals per species and y-axis represents number of species, and fitted the data by logseries, which was that time considered empirically as the most common shape of species abundance distribution and predicted that singletons (species with only one detected individuals) are always the most common. Fisher’s alpha, one of the oldest diversity measures considering both species richness and evenness, is derived from this empirical relationship. Preston modified this diagram and showed that if community is sampled more completely and the x-axis is transformed into octaves (numbers of species are binned into groups of 1, 2, 4, 8, 16, 32 etc. species), the resulting shape of SAD resembles symmetric bell shape of Gaussian distribution (more intensive sampling will make singletons less common or completely absent, since it’s a matter of time to find another one or more individuals for each species original represented by singletons). Robert H. Whittaker introduced “rank abundance curve”, called also diversity-dominance or Whittaker’s curve, where x-axis represents species ranked according to their relative abundance (from commonest at the left to rarest at the right), and y-axis represents | + | The shape of species abundance distribution (SAD) has been for a rather long time considered as an important indicator of underlying community assembly processes. R.A. Fisher was perhaps the first to plot the SAD plot in which x-axis represents number of individuals per species and y-axis represents number of species, and fitted the data by log series, which was that time considered empirically as the most common shape of species abundance distribution and predicted that singletons (species with only one detected individuals) are always the most common. Fisher’s alpha, one of the oldest diversity measures considering both species richness and evenness, is derived from this empirical relationship. Preston modified this diagram and showed that if community is sampled more completely and the x-axis is transformed into octaves (numbers of species are binned into groups of 1, 2, 4, 8, 16, 32 etc. species), the resulting shape of SAD resembles symmetric bell shape of Gaussian distribution (more intensive sampling will make singletons less common or completely absent, since it’s a matter of time to find another one or more individuals for each species original represented by singletons). Robert H. Whittaker introduced “rank abundance curve”, called also diversity-dominance or Whittaker’s curve, where the x-axis represents species ranked according to their relative abundance (from commonest at the left to rarest at the right), and the y-axis represents relative species abundances (often log-transformed). The shape (the steepness and the length of the tail) indicates the relative proportion of dominant and rare species in a community. |
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- | There are several diversity indices differing by the degree in which they consider richness and evenness (species richness, Shannon entropy and Simpson concentration index in this order putting the weight on evenness from //no// in case of species richness to //high// in case of Simpson), and also several indices of evenness itself. [[references|Mark O. Hill (1973)]] showed that all three diversity indices can be summarized using so called **Hill numbers** of order **//q//**, which represent effective numbers of species (increasing //q// puts less weight on rare species and more weight on abundant species). Hill numbers can be used to draw diversity profiles, which allow for elegant comparison of diversity among communities considering both richness and evenness. | + | There are several diversity indices differing by the degree in which they consider richness and evenness (species richness, Shannon entropy and Simpson concentration index in this order putting the weight on evenness from //no// in case of species richness to //high// in case of Simpson), and also several indices of evenness itself. [[references|Mark O. Hill (1973)]] showed that all three diversity indices can be summarized using so-called **Hill numbers** of order **//q//**, which represent effective numbers of species (increasing //q// puts less weight on rare species and more weight on abundant species). Hill numbers can be used to draw diversity profiles, which allow for an elegant comparison of diversity among communities considering both richness and evenness. |
- | Since Earth is finite, each community has theoretically countable number of species and their evenness. However, these theoretical numbers are usually not readily available, since we **estimate diversity of a community by sampling it**, and sampling is always incomplete. Diversity estimated from sampled data is dependent on sampling effort, and if diversity (alpha, beta, gamma) should be compared among different communities, | + | Since Earth is finite, each community has theoretically |
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- | There are several concepts which aim to specify different | + | There are several concepts which aim to specify different |
- | **Beta diversity** is a concept fundamentally different from alpha or gamma diversity, and itself represents a complex topic. Beta diversity can be seen as **species turnover** (directional exchange of species among pair of samples or along spatial, temporal or environmental gradient) or as **variation in species composition** (non-directional description of heterogeneity in species composition within the dataset)(e.g. [[references|Anderson et al. 2011]]). Alternatively (sensu [[references|Jurasinsky et al. 2009]]), beta diversity can be seen as either differential diversity (considering differences in species composition) or as proportional diversity (proportion of species on regional and local level, gamma vs alpha diversity). | + | **Beta diversity** is a concept fundamentally different from alpha or gamma diversity, and itself represents a complex topic. Beta diversity can be seen as **species turnover** (directional exchange of species among pair of samples or along spatial, temporal or environmental gradient) or as **variation in species composition** (non-directional description of heterogeneity in species composition within the dataset)(e.g. [[references|Anderson et al. 2011]]). Alternatively (sensu [[references|Jurasinsky et al. 2009]]), beta diversity can be seen as either differential diversity (considering differences in species composition) or as proportional diversity (proportion of species on a regional and local level, gamma vs alpha diversity). |