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Species Diversity Concepts

Species RichnessSpecies-Area CurvesRarefactionDiversity Indices

- Simpson's Index- Shannon-Weiner Index- Brillouin Index

Species Abundance Models

Describing Communities

There are two important descriptors of a community:

1) its physiognomy(physical structure), as described in the previous lecture, and

2) the number of speciespresent and their relative abundances (species richness and diversity).

Species Richness

The simplest way to describe a community is to list the species in it.

Species richness (S) is the number of species on that list, and is most often used as the first pass estimate of diversity for acommunity.

How would one generate such a list? A simple and widely used method is to define the boundaries of the community and then walk through it seasonally, noting all the species you encounter. This is what we call a flora.

Species Richness

While simply finding and listing the species is useful, this method has many limitations.

If we wish to compare two or more communities, we need comparable samples, otherwise we might just find a difference because one was sampled more intensively than the other.

This begs the question, how much sampling should we do in order to be confident that we have found most of the species in each community?

Species-Area Curve

One way to make this interpretation is through the use of a species-area curve.

A graph of the total number of species found as the number of quadrats increases explains the relationship. We know that we have sampled sufficiently when the curve begins to "plateau".

0

5

10

15

20

25

30

1 3 5 7 9 11 13 15

No. of 1m2 quadrats

No

. of

Sp

eci

es

(S

)

Conclusion: 10-12 quadrats would be sufficient to describe the vegetation in this community.

Species-Area Curve

After many years of study, we now realize that the classical perception of the shape of a "typical" species-area curve is an artifact of the type of communities in which the relationship was first described.

Moreover, it is now apparent, that habitat grain, patch size, and equitability will have a substantial influence on the shape of the curve and must be evaluated in that context.

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Species-Area CurveFine-grained; high equitability

(classical condition)

Species-Area CurveFine-grained; low equitability

Species-Area CurveCoarse-grained; equal patch size

Species-Area CurveCoarse-grained; unequal patch size

Grain, Patch Size, Equitability Species Richness

While many studies include S as a descriptive factor associated with the community, it is largely uninformative in as much as it does not reflect relative abundance.

Example: suppose two communities (1 & 2) each contain 100 individuals distributed among five species (A-E):

EDCBA

111196Comm-2

2020202020Comm-1

Are these two communities equivalent?

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Species Richness

There are two ways to overcome this problem:

1) incorporate both species richness and abundance information in to one diversity index.

2) rely on species richness but control for the effects of sample size by a procedure called rarefaction.

We will examine both alternatives as they are widely used in ecology.

Rarefaction

One of the fundamental tenants of diversity is that the number of species found in a given sample is strongly dependent upon the size of that sample.

This makes good intuitive sense in that the more quadrats one samples in a plant community, the more likely you are to pick up more and more rare species.

One method of avoiding incompatibility of measurements resulting from samples of different sizes is called rarefaction.

Rarefaction

Si

i=1

N - N NE(S) = 1 - /

n n

∑

Where E(S) is the expected number of species in the rarefied sample, n is the standardized sample, N is the total number of in the sample to be rarefied, and Ni is the number of individuals in the ith species in the sample to be rarefied, summed over all species counted.

Rarefaction

The term N

n

is a "combination" that is calculated as:

N N! =

n n! N n !

where N! is a "factorial", e.g., 5! = 5×4×3×2×1 = 120

This combination is important, because it allows us to calculate all the possible numbers of unique species combinations...

Rarefaction

For example, if we have four species, A, B, C, D, then we have six species pairs: AB, AC, AD, BC, BD, CD.

Using the combinatorial equation:

4 4! 24 = = 6

2 2! 4 2 ! 4

=

Thus N

n

is the number of unique combinations of N

taken n at a time; i.e., the number of different ways of picking species pairs from four different species.

Rarefaction

Let's look at a fully worked real-world example (taken from Magurran 1988).

Imagine two moth traps that have been set out in a forest to monitor moth diversity. Trap-B was inadvertently left out for only about half the time as Trap-A.

We know this will be a problem because Trap-A "sampled" the environment more (longer period of time) and is likely to pick up more species. To compare S between traps would be misleading and inappropriate.

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Moth light traps are typically suspended above the vegetation and contain a battery powered light. The trap is set to operate only during the evening hours. Moths are drawn to the light and become entrapped in the canister below.

Rarefaction

As expected, Trap-A has more species. The best way to correct for the difference in sampling time is to ask,

How many species would we expect to find in Trap-A if it too contained 13 individuals?

1323N

69S

0112

3111

5010

019

208

117

016

025

044

103

032

191

Trap-BTrap-ASpecies

No. of Individuals

Rarefaction

First, take the number of individuals of each species from Trap-A and insert them into the formula.

For species in Trap-A: N = 23, n = 13, Ni = 9, N-Ni = 14

( )

( )

[ ]{ }

i

N 23! =

n 13! 23 - 13 !

N-N 14! =

n 13! 14 - 13 !

therefore:

14! 23!1 - / 1 14 /1144066 1 0.00 1.00

13! 1! 13! 10!

= − = − = × ×

Rarefaction

Continue this same set of calculations for each species (to determine the expected number) and then sum the values (as per the Σ in the equation).

Zero values need not be included as they have no influence on the estimate.

6.58E(S)

0.571

0.571

0.571

0.571

0.571

0.822

0.984

0.933

1.009

ExpectedNi

Conclusion: If Trap-A contained 13 individuals, we would expect it to contain 6.58 species--about the same as Trap-B.

Diversity Indices

As already alluded to, the diversity of a community needs (in most instances) to account for both species richness and the evenness with which individuals are distributed among species.

One way to do this is through the use of a proportional abundance index. There are two major forms of these indices: dominance indices and information indices.

While more than 60 indices have been described, we will look at the three most widely used in the ecological literature: Simpson's, Shannon-Weiner, and Brillouin.

Simpson's Index

Simpson's Index is considered a dominance index because it weights towards the abundance of the most common species.

Simpson's Index gives the probability of any two individuals drawn at random from an infinitely large community belonging to different species.

For example, the probability of two trees, picked at random from a tropical rainforest being of the same species would be relatively low, whereas in boreal forest in Canada it would be relatively high.

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Simpson's Index

( )( )( )( )

i

S1

n 1D

N N 1

Si

i

n

=

−=

−∑

The bias corrected form of Simpson's Index is:

where ni is the number of individuals in the ith species.

Since Ds and diversity are negatively related, Simpson's index is usually expressed as the reciprocal (1-D) so that as the index goes up, so does diversity.

Simpson's Index

A worked example for 201 trees of 5 species assessed in several quadrats:

201Total

1E

20D

30C

50B

100A

No. Individuals

Tree spp.

S

100 99 50 49 1 0D ... 0.338

201 200 201 200 201 200

Then 1/D = 1/0.388 = 2.96

× × × = + + = × × ×

Shannon-Weiner Index

The Shannon-Weiner Index belongs to a subset of indices that maintain that diversity can be measured much like the information contained in a code or message (hence the name information index).

The rationale is that if we know a letter in a message, we can know the uncertainty of the next letter in a coded message (i.e., the next species to be found in a community).

The uncertainty is measured as H', the Shannon Index. A message coded bbbbbb has low uncertainty (H' = 0).

Shannon-Weiner Index

The Shannon Index assumes that all species are represented in a sample and that the sample was obtained randomly:

S

i ii = 1

H' = - p ln p∑where pi is the proportion of individuals found in the ith species and ln is the natural logarithm.

Shannon-Weiner Index

A worked example from a community containing 100 trees distributed among 5 species:

-1.2011.001005Total

-0.0460.011E

-0.2170.099D

-0.2300.110C

-0.3610.330B

-0.3470.550A

pi ln pipiAbundSpecies

H' = 1.201

Shannon-Weiner Index

The most important source of error in this index is failing to include all species from the community in the sample.

This makes a species-area curve assessment very important at the beginning of a study.

Values of the Shannon diversity index for real communities typically fall between 1.5 and 3.5.

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Shannon-Weiner Index

The Shannon index is affected by both the number of species and their equitability, or evenness.

A greater number of species and a more even distribution BOTH increase diversity as measured by H'.

The maximum diversity (Hmax) of a sample is found when all species are equally abundant. Hmax = ln S, where S is the total number of species.

Evenness

We can compare the actual diversity value to the maximum possible diversity by using a measure called evenness.

The evenness of the sample is obtained from the formula:

Evenness = H'/Hmax = H'/lnS

By definition, E is constrained between 0 and 1.0. As with H', evenness assumes that all species are represented within the sample.

Brillouin Index

When the randomness of a sample cannot be guaranteed, the Brillouin Index HB is preferable to the H':

iB

ln N! - ln n !H

N= ∑

where N is the total number of individuals and ni is the number of individuals in the ith species.

A worked example follows...

Brillouin Index

Σ = 23.95N = 25S = 5

4.7955

4.7954

4.7953

4.7952

4.7951

ln ni !No. IndividualsSpecies

iB

ln N! - ln n ! ln 25! - 23.95H 1.362

N 25= = =∑

Evenness

Evenness for the Brillouin Index is estimated as:

BHE =

Hwhere HBmax represents the maximum possible Brillouin diversity, that is, a completely equitable distribution of individuals between species.

In our example, we had complete equitability, therefore, HBmax = HB = 1.0.

Diversity Indices

As you have probably figured out, the choice of a particular index is chosen with respect to the goals of the study (emphasis on abundant vs rare species) and to what extent sampling can be assured to be random.

There are other factors that come in to play, but these are the 3 most widely used measures of diversity that incorporate both richness and evenness into the determination.

Note: There is generally NO relationship between one index and another.

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Species Abundance Models

One of the earliest observations made by plant ecologists was that species are not equally common in a given community. Some were very abundant, other were uncommon.

A graphical way was sought to describe this pattern, and so arose species abundance models.

These models are strongly advocated among some ecologists because they emphasize abundance while utilizing species richness information and therefore provide the most complete mathematical description of the data.

Species Abundance Models

A species abundance model is generated by graphing the abundance of each species against its rank order abundance from 1 = highest to N = lowest.

One of four distributions usually arise:

Log normal distributionGeometric seriesLogarithmic seriesMcArthur's broken stick model

Species Abundance Models Species Abundance Models(Changes through succession - Bazzaz 1975)