Which sample is more diverse? RNA Sequencing Study 700 600 Number - - PowerPoint PPT Presentation

Diversity Indices

• Usually used as biodiversity (as in species), but can apply to
• ther data where you count the number of times a

particular category occurs (e.g. nest shape).

• Comprises two components
• Species Richness: the number of species in an ecosystem.
• Species Evenness: a measure of how abundances are

distributed among the species.

• These are commonly combined into a single diversity index,

making interpretation really, really difficult.

Which sample is more diverse?

RNA Sequencing Study

• Pyrosequencing reads thousands of genetic sequences from a sample
• How many unique sequences are there? It depends on how many

total sequences you count.

• Number of species encountered in some way depends on the

number of individuals counted.

100 200 300 400 500 600 700 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Total number of reads Number of Unique Sequences

Species Richness

R2 = S n

Menhinick (1964)

R1= S −1 ln n

( )

Margalef (1958)

n=number of individuals S= number of species

These are based on some presumed relationship between S and n which may or may not hold for your case.

Rarefaction

Species Richness

A better way...

• Based on your actual data
• Computes probabilities of encountering a

species at n individuals.

Habitat N S 9 50 14 20 122 38 36 62 8

Rarefaction Curve

10 20 30 40 50 60 70 80 3 4 5 6 7 8 9 10

Number of Species Sample Size

10 20 30 40 50 60 70 80 1.6 1.65 1.7 1.75 1.8 1.85 1.9 1.95 2 2.05 2.1

Margalef

10 20 30 40 50 60 70 80 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

Menhinick

“Diversity” Indices

Evenness and Richness Combined Simpson’s index

λ = ni ni −1

( )

n n −1

( )

i=1 S

∑

Shannon’s Index

ʹ″ H = − ni n ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ln ni n ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⎡ ⎣ ⎢ ⎤ ⎦ ⎥

i=1 S

∑

ni=number of individuals of species i n = total number of individuals counted S = total number of species

Evenness Indices

E2 = e

ʹ″ H

S

Sheldon (1969) Heip (1974)

E3 = e

ʹ″ H −1

S −1

Pielou (1975)

E1= ʹ″ H ln(S)

a.k.a. J’

Hill (1973)

E4 = 1/λ e

ʹ″ H

dominance → 1

Alatalo (1981)

E5 = 1/λ

( ) −1

e

ʹ″ H −1

dominance → 0

But how different is different?

Actual Shannon Diversity

1) download the Biodiversity File from the web site 2) for each sample (TET38, S3 and ARIES 46) calculate the following: a) Margalef and Menhinick species richness b) Shannon and Simpson diversity indices c) Hill’s evenness index