Mark McGinley

Honors College and Department of Biological Sciences

Texas Tech University

Biodiversity

Diversity Before we tackle “biodiversity” let’s think about the concept

of diversity In the simplest terms, diversity is influenced by variation

within and among groups As will hopefully make sense in just a little while, diversity is

influenced by The type and amount of variation How that variation is distributed

Below is a group of letters.What “variation” do you see here?

AAaa

Bbbbbbbb

cc

DDddd

Eeee

f

Variation Within a Group Different letters (variation in type of letter) Variation within a type of letter

Capital vs. lower case Different sizes Different colors

Different letters are represented different number of times

Variation Within a Group Thus, within a group

Different types (letters) Variation of characteristics within a particular type.

What about variation between groups?

Which Group Contains More Variation? Group 1

A B C D E

Group 2 A A A A A

Group 1 is more variableNo variation in Group 2

-all of the letters are exactly the same

More different types of letters in Group 1.

Variation Between Groups Groups can differ in the number of types they contain Therefore we think of a group containing more types

of things as being more variable than a group that contains fewer types. In this case we would consider groups with more

variation to be more diverse.

Which Group Contains More Variation? Group 1

B B B B B

Group 2 B B B B B

Variation Between Groups The two groups share the same number of types and number

of representatives within a type However, Group 2 has more variation among representatives

within a type

In this case we would consider the group with more variation with a type to be more diverse.

Which group has more variation? Group 1

A A A A A A

Group 2 A A

Variation Between Groups There is variation between groups in the number of letters.

Group 1 has more letters in it than Group 2 However,

they are all the same letter all are the same format within a letter.

Thus, variation in numbers of things doesn’t appear to affect diversity.

Which group has more variation? Group 1

AAA BBB CCC

Group 2 AAAAAAA B C

Group 1 is more variableGroup 1 and Group 2 have

- the same total number of letters- the same number of different types of letter

Therefore the variation among the two groups might be considered to be the same.

But almost all of the letters in Group 2 are A.- therefore we might consider that Group 1 is more diverse than group 2.

Variation Between Groups So differences in the number of individuals within a type can

influence diversity in some cases. New Term

Diversity can be influenced by the “evenness” of the distribution of individuals among different types

Which Group is Most Even? Group 1

AAA BBB CCC DDD

Group 2 AAAA BB CCC D

Factors That Influence Diversity Number of different types of things Variation of characteristics within a type Evenness of number of individuals across different types of

things

Which Group is More Diverse? Group 1

AA BB CC DD EE

Group 2 A BB CCC D EE F

This is a Tricky Question!!!!! Group 2 has more types of letters so we might consider it to

be more diverse Group 1 contains a more even distribution of letters within a

type so we might consider it to be more diverse

Which group we consider to be the most diverse depends on how we rate the relative influence of number of types vs. evenness. The World is Complicated!!!!! (but luckily we can use math to

help us solve this problem)

What is “Biodiversity”? Biodiversity is a contraction of the two words “biological

diversity”.

Because biodiversity is such a broad, all encompassing concept there is not one well agreed on definition.

However, most definitions are similar.

Biodiversity A measure of the variety of organisms within a local area or

region, often including genetic variation, taxonomic uniqueness, and endemism.

- Ricklefs, The Economy of Nature

Biodiversity The variety of organisms considered at all levels from genetic

variants belonging to the same species through arrays of species to arrays of genera, families, and still higher taxonomic levels; includes the variety of ecosystems, which comprise both the communities of organisms within a particular habitat and the physical conditions under which they live. E.O Wilson- The Diversity of Life

Biodiversity The variability among living organisms from all sources

including, inter alia, terrestrial, marine and other aquatic ecosystems and the ecological complexes of which they are a part; this includes diversity within species, between species, and of ecosystems."

Convention on Biological Diversity

Genetic Diversity Members of the same population or species can vary in which

particular alleles they possess at a particular gene locus. Population geneticists have a variety of techniques and

metrics they use to measure the amount of genetic variation within and among populations. To learn more about this take an Evolution, Population

Genetics, or Conservation Biology course.

Species Species are usually the focus of diversity studies in ecology

Species- actually many definitions/species concepts

Biological Species Concept - group of potentially interbreeding individuals that are

reproductively isolated from other such groups

Biological Species Concept Two individuals are considered to be members of the same

biological species if they can potentially exchange genes.

Often difficult to apply this concept Asexual species Species that are geographically isolated

How do we know whether a bird found in Europe can interbreed with a bird in North America

Ring species

But this is a conceptually pleasing definition of a species

Biological Species Species are basic unit of biodiversity

Species may be subdivided into sub-species

Phenotypic Variation Within Species Variation at the genetic, molecular, physiological,

morphological, or behavioral levels. Conservation biologists can be especially concerned about

genetic variation Genetic variation influences the potential for natural selection

Species Diversity Species diversity is a characteristic of a community Two components of species diversity

The number of species in a community Species richness

evenness

Diversity Indices Ecologists have developed several metrics to quantify species

diversity These indices differ in how they weight the two critical

components of species diversity Species richness Evenness

Species Richness Species richness simply counts the number of species found

in a community

Diversity Example Species number of individuals 1 10 2 20 3 15

Species Richness Because there are three species found in this community

Species Richness = 3

Species Richness Strengths

We are often interested in knowing about the numbers of species in a community

Easy number to calculate All we have to do is count the number of species

This is an easily understandable metric Weakness

Ignores the evenness component of diversity

Shannon Diversity Index s H = - ∑ (pi * ln pi) i=1

where:H = the Shannon diversity indexPi = proportion of the population made up of species iS = numbers of species in sample

Let’s Try an Example Species # individuals

1 102 203 30

Shannon Index ExampleFirst calculate the pi for each of the S species in the sample

(S = 3 species)

1. determine the total number of individuals sampled in the community

# sp.1 = 10 # sp.2 = 20

# sp.3 = 30

Total # = 60 ind

Shannon Index Example2. For each of the S species

pi = # ind species i/total # ind

p isp 1- 10/60 = 0.17

sp 2- 20/60 = 0.33sp 3- 30/60 = 0.50

Shannon Index Example Next calculate H

s H = - ∑ (pi * ln pi)

i=1

Shannon Index Example

H =- ((0.17*ln0.17 + 0.33*ln0.33 + 0.50*ln0.50))

H = - (0.17*-1.77 + 0.33*-1.11 + 0.50*-0.69)

H = - (-0.30 – 0.37 – 0.35)

H = - (-1.01)

H = 1.01

Shannon Index The Shannon Index was designed such that

H gets larger when there are more species Not surprising because H should get larger when there are more species

in the sample (larger S)

Shannon Index The Shannon Index was designed such that

H gets larger when evenness is greater

Shannon IndexPi

0.1ln pi

-2.30259Pi * ln pi

-0.23026

0.2 -1.60944 -0.32189

0.3 -1.20397 -0.36119

0.4 -0.91629 -0.36652

0.5 -0.69315 -0.34657

0.6 -0.51083 -0.3065

0.7 -0.35667 -0.24967

0.8 -0.22314 -0.17851

0.9 -0.10536 -0.09482

1 0 0

Shannon Index The value of H gets larger whe

There are more species There is greater evenness

Thus, diversity of a community increases as the value of H increases

Shannon Index Advantages

The value of H changes in a way that is consistent with our view of how changing species richness and evenness should affect species diversity

It is relatively easy to calculate Disadvantage

The value of H doesn’t have a direct biological meaning What do you know if someone tells you that H = 2.3? Useful only for comparison

Pielou’s Evenness Index - based on Shannon Index

E = H/Hmax

H is the value of the Shannon Diversity Index for a particular population

Hmax is the maximum value for the Shannon Diversity Index in a population with the same number of species and total number of individuals sampled

Hmax

For a particular community the maximum value of H would occur if all species were equally abundant.

After doing the algebra, Hmax can be calculated as follow-

Hmax = lnS

Evenness Index ExampleE = H/Hmax

E = 1.01/ln3

E = 1.01/1.098

E = 0.919

Simpson’s Index

D = ∑ pi2

D measures the probabil ity that two randomly selected individuals in a populat ion belong to the same species

D ranges from 0 – 1D will be largest when all individuals in a populat ion are members of the same populat ion

Thus, as D gets larger diversity decreases

Simpson’s IndexSpecies # individuals

1 102 203 30

Example D = ∑ pi

2

D = (0.172 + 0.332 + 0.502)

D = (0.0289 + 0.109 + 0.25)

D = 0.388

Simpson’s Index of DiversitySimpson's index of diversi ty = 1 - D

The probabil i ty that two randomly selected individuals in a community belong to di f ferent species.

Thus, as the Simpson’s Index of Divers i ty increases the species divers i ty of the populat ion increases.

Simpson’s Index of DiversitySimpson's index of diversi ty = 1 - D

The probabil i ty that two randomly selected individuals in a community belong to di f ferent species.

Thus, as the Simpson’s Index of Divers i ty increases the species divers i ty of the populat ion increases.

Diversity Indices Shannon Index is more sensitive to changes in species

richness

Simpson’s Index is more sensitive to changes in evenness

Diversity Indices Which diversity index should you choose to use?

It might depend on whether you were more concerned about rare species E.g., changes in the number of rare species has a much greater effect on

Shannon’s Index than it does on the Simpson Index Many researchers choose to use a number of different diversity

indices because they provide different information.