• How are groupings of species distributed in nature? (e.g., diversity)

• How are these groupings explained by the environment and the interactions between and among species?

• Species diversity
• Genetic diversity
• Ecosystem diversity

Impossible to count all species

Need to estimate based on sampling (quadrats, plots, transects, traps, etc.)

Richness depends on number of samples collected

More samples → more species

Use extrapolation to predict richness

• Want to predict the asymptote
• Try to collect as few samples as possible

Individual-based and sample-based
Procedures of individual-based rarefaction
Use rarefaction to compare diversity between two sites with different sampling effort

• underlying community is constant over time (no immigration or emigration of species)

• well-mixed community (spatial distribution of each species is random)

• individuals are sampled at random (brighter colored individuals aren't sampled more often than others)

• sampling with identical methods (if used to compare two communities)

$$E\left(S_m\right)\approx S-\sum _{i=1}^S(1-p_i{)}^m$$

where $S$ is the number of species, $m$ is the total number of individuals in the sample, and $p_i$ is the proportion of species $i$ in the original sample.

$$S_{est}=S_{obs}+\left(\frac{(f_1{)}^2}{2f_2}\right)$$

Which community is more diverse??

Richness is an uninformative descriptor: equal weight given to rare and abundant species

• Moth data from England
• x-axis on log2 scale;
• Partial bell-shaped curve -- log-normal distribution
• Very common pattern in nature

Balancing Richness and Abundance/Evenness

$$H^{\prime }=-\sum _{i=1}^S{p}_i\ln p_i$$ Where: $p_i$ = proportion of the total sample represented by species $i$, $\ln$ = log base $e$, $S$ = the number of species in the community

$H^{\prime }=-{\sum }_{i=1}^S{p}_i\ln p_i$

What is the Shannon Index of Diversity for the following community?
A. 0
B. 1
C. 2.83
D. 17

Weakness

• Can’t tell if differences in measurements are due to richness or evenness (or can you?)

• Difference between 0.58 & 1.39. What does it mean?

When all species are equally abundant: $H^{\prime }=\ln \left(4\right)=1.39$: Community B has max diversity

Evenness E = H'/H'max

Slope ≈ evenness; Length ≈ richness.
Most species are moderately abundant; few are very abundant or extremely rare

Jaccard similarity:

$$J(A,B)=\frac{|A\cap B|}{|A\cup B|}$$

$|A\cap B|$ is the shared species between communities $A$ and $B$, while $|A\cup B|$ is the total number of shared and non-shared species.

Measuring beta diversity for presence–absence data

It reviewed 24 such measures!

A common observation: communities which are farther apart tend to be more dissimilar than two communities which are close together

Assemblage Time Series Reveal Biodiversity Change but Not Systematic Loss

Community composition describes the diversity and identity of species within a given community

keystone species is a species that has a large impact on community structure relative to it's abundance / biomass in the community (e.g., top predator)

foundation species is a species that can play a substantial role in determining what species can exist within the community (e.g., beavers, earthworms). Usually, this is a species that defines much of the structure of a community through e.g., habitat-forming

Succession – directional change in community composition at a site (as opposed to simple fluctuations), initiated by natural or anthropogenic disturbance, stress, or the creation of a new site

Some biologists restrict the definition to directional replacement of species after disturbance

Disturbance – a discrete event that damages or kills residents on a site (and potentially creates opportunities for other individuals to grow or reproduce); either catastrophic or non-catastrophic (Platt & Connell 2003 Ecological Monographs)

Stress – factor that reduces growth, reproduction, or survival of individuals (and potentially creates opportunities for other individuals)