Measurement of Measurement of Biological Diversity:Biological Diversity:

Shannon Diversity Index Shannon Diversity Index and and

Shannon’s EquitabilityShannon’s Equitability

Comparing the diversity found in two Comparing the diversity found in two or more habitatsor more habitats

What is Biological Diversity?What is Biological Diversity?(from Whitaker, 1960)(from Whitaker, 1960)

alpha diversityalpha diversity: diversity within a sample : diversity within a sample beta diversitybeta diversity: diversity associated with : diversity associated with

changes in sample composition along an changes in sample composition along an environmental gradient (between samples)environmental gradient (between samples)

gamma diversitygamma diversity: diversity due to differences : diversity due to differences among samples when they are combined into a among samples when they are combined into a single sample (this tells us something about single sample (this tells us something about how samples are collected – not about how samples are collected – not about communities in nature)communities in nature)

Biological Diversity Includes:Biological Diversity Includes: Number of different species (species diversity)Number of different species (species diversity) Relative abundance of different species Relative abundance of different species

(species evenness)(species evenness) Ecological distinctiveness of different species, Ecological distinctiveness of different species,

e.g., functional differentiation – often done in e.g., functional differentiation – often done in microbiology (Functional Diversity). microbiology (Functional Diversity).

Evolutionary distinctiveness of different Evolutionary distinctiveness of different species species

(The last two of these are rarely addressed)(The last two of these are rarely addressed)

Why is Biological Diversity Why is Biological Diversity Important?Important?

It is commonly believed that the more diverse It is commonly believed that the more diverse a system is, the more stable it will be.a system is, the more stable it will be.

Studies with plants suggest that productivity Studies with plants suggest that productivity in more diverse plant communities is more in more diverse plant communities is more resistant to, and recovers more fully from, a resistant to, and recovers more fully from, a major drought.major drought.

Diverse communities are more resistant to Diverse communities are more resistant to invasion by exotic species than are less diverse invasion by exotic species than are less diverse communities.communities.

The Shannon Diversity Index The Shannon Diversity Index (SDI) – what is it?(SDI) – what is it?

Claude Shannon was not a biologist – he was a Claude Shannon was not a biologist – he was a mathematician and communications engineer mathematician and communications engineer who worked for Bell Laboratories.who worked for Bell Laboratories.

Shannon originated a field called Information Shannon originated a field called Information Theory.Theory.

The Shannon Diversity Index is a The Shannon Diversity Index is a mathematical measure of species diversity in a mathematical measure of species diversity in a community.community.

What does the Shannon Diversity What does the Shannon Diversity Index tell us about biological Index tell us about biological

diversity?diversity? It provides information about community It provides information about community

composition beyond just species richness (how composition beyond just species richness (how many different species are present). many different species are present).

It also takes the relative abundance of each It also takes the relative abundance of each species into account. species into account.

It provides important information about rarity It provides important information about rarity and commonness of species in a community. and commonness of species in a community.

The Variables examined when The Variables examined when calculating the SDIcalculating the SDI

H = the SDIH = the SDI

S = the total number of species in the S = the total number of species in the community (richness)community (richness)

ppii = the proportion of S made up of the “ith” = the proportion of S made up of the “ith” species (the number of individuals of a species (the number of individuals of a particular species divided by the total particular species divided by the total number of all species) number of all species)

EEHH = Shannon’s Equitability (species = Shannon’s Equitability (species evenness).evenness).

The The SDISDI accounts for both accounts for both abundanceabundance and and evennessevenness of the species present. of the species present.

The proportion of species i relative to the total The proportion of species i relative to the total number of species (we call it pnumber of species (we call it p ii) is calculated, ) is calculated,

and then multiplied by the natural logarithm of and then multiplied by the natural logarithm of this proportion (ln pi). this proportion (ln pi).

The resulting product is summed across The resulting product is summed across species and multiplied by -1.species and multiplied by -1.

Let’s assume the following data set:Let’s assume the following data set:

Species foundSpecies found NumberNumber

foundfound

Proportion (pProportion (pii))

(number (number ÷ total)÷ total)

BeetleBeetle 66 6/13 = 0.4626/13 = 0.462

EarwigEarwig 33 3/13 = 0.2313/13 = 0.231

SpiderSpider 22 2/13 = 0.1542/13 = 0.154

CentipedeCentipede 22 1/13 = 0.1541/13 = 0.154

Total (Sum)Total (Sum) 1313

The formula for SDI is:The formula for SDI is:

S

i

ii ppH1

ln

H = -1 times the sum of all pH = -1 times the sum of all pii ln p ln pii

= -1 x -1.271 = = -1 x -1.271 = 1.2711.271

Species Species foundfound

NumberNumber

foundfound

Proportion (pProportion (pii))

(number (number ÷ total)÷ total)

ppii ln p ln pii

BeetleBeetle 66 6/13 = 0.4626/13 = 0.462 - 0.357- 0.357

EarwigEarwig 33 3/13 = 0.2313/13 = 0.231 - 0.338- 0.338

SpiderSpider 22 2/13 = 0.1542/13 = 0.154 - 0.288- 0.288

CentipedeCentipede 22 1/13 = 0.1541/13 = 0.154 - 0.288- 0.288

TotalTotal 1313 - 1.271- 1.271

Now that we have calculated the SDI Now that we have calculated the SDI for our sample, we can calculate for our sample, we can calculate

Shannon’s EquitabilityShannon’s Equitability

Shannon’s Equitability (EShannon’s Equitability (EHH) is a measure of ) is a measure of

species species evenness evenness or or relative abundancerelative abundance..

Equitability assumes a value between 0 and 1, Equitability assumes a value between 0 and 1, with 1 being complete evenness (equal with 1 being complete evenness (equal numbers of every species in the sample). numbers of every species in the sample).

Shannon’s Equitability for Shannon’s Equitability for our example would be:our example would be:

Shannon’s Equitability (EShannon’s Equitability (EHH) = SDI (H) divided ) = SDI (H) divided by the natural log of Hby the natural log of HMAX MAX or…or…

H/ln S (where S = 4)H/ln S (where S = 4)

In this case, EIn this case, EHH = 1.27/1.39 = .91 = 1.27/1.39 = .91 Knowing that EKnowing that EHH is always between zero and is always between zero and

one, our sample has pretty high equitability.one, our sample has pretty high equitability.

Now, let’s see how SDI and Equitability Now, let’s see how SDI and Equitability change under different circumstances.change under different circumstances.

Let’s look at how species richness and species Let’s look at how species richness and species evenness affect SDI and Equitability. evenness affect SDI and Equitability.

In the first situation, let’s look at four In the first situation, let’s look at four imaginary samples where the number of imaginary samples where the number of species differs, and where there are always an species differs, and where there are always an equalequal number of each species in the sample. number of each species in the sample.

We’ll call these our “even” communities.We’ll call these our “even” communities.

SDI and Equitability for “Even” SDI and Equitability for “Even” Communities (equal number of each Communities (equal number of each

species in the sample)species in the sample)

Number of Number of Species in the Species in the

SampleSampleSDISDI EquitabilityEquitability

55 1.611.61 1.01.0

1010 2.312.31 1.01.0

2020 3.003.00 1.01.0

5050 3.913.91 1.01.0

But what if the number of species in each But what if the number of species in each sample are NOT equal (Equitability is low)?sample are NOT equal (Equitability is low)? In this second situation, let’s look at four imaginary In this second situation, let’s look at four imaginary

samples where the number of species again differs, samples where the number of species again differs, and where there are always an and where there are always an unequal unequal number of number of each species in the sample.each species in the sample.

In this case, one species makes up 90% of the total In this case, one species makes up 90% of the total number of individuals in the sample and the number of individuals in the sample and the remaining species each make up an equal proportion remaining species each make up an equal proportion of the remaining 10%.of the remaining 10%.

We’ll call these our “uneven” communities.We’ll call these our “uneven” communities.

SDI and Equitability for “Uneven” SDI and Equitability for “Uneven” Communities (one species makes up 90% Communities (one species makes up 90% of the total sample and the rest each make of the total sample and the rest each make

up an equal portion of the last 10%)up an equal portion of the last 10%)

Number of Number of Species in the Species in the

SampleSampleSDISDI EquitabilityEquitability

55 0.460.46 0.290.29

1010 0.540.54 0.230.23

2020 0.620.62 0.210.21

5050 0.710.71 0.180.18

There are two methods to calculate There are two methods to calculate SDI – one uses natural log, the other SDI – one uses natural log, the other

uses log base 10uses log base 10 As it turns out, Microbiologists often use one method As it turns out, Microbiologists often use one method

(the natural log version) in their publications, while (the natural log version) in their publications, while botanists and biologists often use the log 10 version. botanists and biologists often use the log 10 version.

Either way, you always use the same method when Either way, you always use the same method when you compare the SDI of one sample to that of another you compare the SDI of one sample to that of another to determine which has more diversity.to determine which has more diversity.

Calculating eCalculating eHH or the or the exponent of SDIexponent of SDI

Finally, if we calculate the exponent of Finally, if we calculate the exponent of our SDI or eour SDI or eHH, we get a number , we get a number between 1 and S for that sample. You between 1 and S for that sample. You can use your calculator to do this (use can use your calculator to do this (use the ethe exx) function and put your H (SDI) in ) function and put your H (SDI) in for the x. You can also do this in excel for the x. You can also do this in excel (see the Word file that explains this). (see the Word file that explains this). If, for example, you haveIf, for example, you have

Calculating eCalculating eHH or the or the exponent of SDIexponent of SDI

What does this tell us? If, for example, you What does this tell us? If, for example, you have a sample with species richness of 12 have a sample with species richness of 12 and your eand your eHH is approximately 8.5, this means is approximately 8.5, this means that your sample has the same evenness as that your sample has the same evenness as a perfectly even sample with 8.5 species. In a perfectly even sample with 8.5 species. In other words, your sample of 12 species is other words, your sample of 12 species is dominated by about 8.5 species. If you had a dominated by about 8.5 species. If you had a sample with S = 12 and your eH is 12, it is sample with S = 12 and your eH is 12, it is perfectly even and not dominated by any perfectly even and not dominated by any species – they are equally distributed.species – they are equally distributed.

Now you do itNow you do it

Using the numbers of ants from the Using the numbers of ants from the pitfall data, calculate the SDI, pitfall data, calculate the SDI, Evenness, Species Richness, and Evenness, Species Richness, and exponent of SDI for three forest types exponent of SDI for three forest types

Melina forest – sylvaculture forestMelina forest – sylvaculture forest Primary forest – rainforest, never cutPrimary forest – rainforest, never cut Secondary forest – rainforest, Secondary forest – rainforest,

selectively logged 30 years agoselectively logged 30 years ago