Community Ecology

BDC321

Mark J Gibbons, Room 4.102, BCB Department, UWC

Tel: 021 959 2475. Email: mgibbons@uwc.ac.za

Image acknowledgements – http://www.google.com

Measures of Community Diversity

Species Richness - S

Description of Communities

A B

6565TOTAL

12LIGHT BLUE

23APPLE GREEN

79BLACK

24DARK BLUE

45LIGHT GREEN

36ORANGE

24YELLOW

314LILAC

4118RED

BACOLOUR

Same Number Species – 9

Same Number individuals - 65

Different Distribution of individuals amongst species

GuildTaxocene

Determining Species Richness

Species DensityNumber of Species Observed

Total Number of Individuals Counted

Botanists

Numerical Species Richness

Sample-based

Samples taken: all individuals within identified & counted

Individual-based

Individuals sampled sequentially

Focus of Community Studies

PROBLEM: Number of species reflects number of samples

or individuals

COMMUNITIES

vs

SAMPLES

Issues of Sample Area or Number

Species-Area or Accumulation Curves

0

2

4

6

8

10

12

0 2 4 6 8 10

Area (m2)

No

Sp

ec

ies

Asymptote considered to

represent the number of species occurring

in the community

Quadrat No Quadrat Area Number Spp Number Unique Spp Cumulative No Spp0 0 0 0 01 1 6 6 62 2 8 2 83 4 9 1 94 8 10 1 10

Quadrat No Quadrat Area Number Spp Number Unique Spp Cumulative No Spp0 0 0 0 01 1 6 6 62 2 8 2 83 4 9 1 94 8 10 1 10

Quadrat No Quadrat Area Number Spp Number Unique Spp Cumulative No Spp0 0 0 0 01 1 6 6 62 2 8 2 83 4 9 1 94 8 10 1 10

Quadrat No Quadrat Area Number Spp Number Unique Spp Cumulative No Spp0 0 0 0 01 1 6 6 62 2 8 2 83 4 9 1 94 8 10 1 10

1 2 3 4 5 6 7 8 9 10 11Black 1 3 2 2 1 1Red 1 3 3 3 1 1 1 1 1 3

Yellow 1 3 1 1 1 1 1Green 1 1Green 2 1Blue 1 1 1Blue 2 2 1 1 1 1 1 1

Purple 1 2 1 1 1Purple 2 1 1Orange 1 2 1 1 1 1

Total No spp 3 4 2 3 3 4 5 7 6 5 4Total No Individuals 4 8 4 7 6 5 5 7 6 5 6

No Unique Spp 3 2 0 1 0 0 0 1 1 1 0Cumulative No Spp 3 5 5 6 6 6 6 7 8 9 9

Cumulative Area 1 2 3 4 5 6 7 8 9 10 11

Quadrat NoSpecies

0123456789

10

1 2 3 4 5 6 7 8 9 10 11

Area

No

Sp

ec

ies

Species Quadrat No7 8 9 10 11 1 2 3 4 5 6

Black 1 1 1 3 2 2Red 1 1 1 1 3 1 3 3 3 1

Yellow 1 1 1 1 1 3 1Green 1 1Green 2 1Blue 1 1 1Blue 2 1 1 1 1 2 1 1

Purple 1 1 1 1 2Purple 2 1 1Orange 1 1 1 1 2 1

Total No spp 5 7 6 5 4 3 4 2 3 3 4Total No Individuals 5 7 6 5 6 4 8 4 7 6 5

No Unique Spp 5 3 1 0 0 0 0 0 0 0 0Cumulative No Spp 5 8 9 9 9 9 9 9 9 9 9

Cumulative Area 1 2 3 4 5 6 7 8 9 10 11

0

2

4

6

8

10

1 2 3 4 5 6 7 8 9 10 11

Area

No

Sp

ecie

s

Randomised 999 times

Rarefaction Curves

The absolute number of species likely to be found in the pool is obtained when the curve flattens out

WHEN IDENTIFYING or COMPARING COMMUNITIES, ARE YOU INTERESTED IN

ESTIMATING ABSOLUTE RICHNESS?

DEPENDS ON THE QUESTION BEING ASKED

There are a number of ways of determining this:

Effort (area or number of samples or individuals) is important

STANDARDIZE

a priori

HOW?

Species Diversity Indices

Heterogeneity Measures

Shannon Index (H’ )

A B C D E F G HI 0 0 0 0 0 2 5 8II 9 8 1 6 8 2 7 5III 1 3 0 3 9 7 0 0IV 2 2 1 5 7 8 3 8V 2 4 3 2 3 7 6 3VI 3 8 9 10 1 3 4 1VII 2 0 0 10 0 2 9 5VIII 7 0 3 6 0 1 2 7IX 4 2 10 7 0 8 3 6X 0 7 6 4 2 3 2 1XI 2 4 3 8 6 5 1 5XII 9 2 1 1 1 6 8 8XIII 4 9 8 2 4 10 0 4XIV 5 1 10 5 3 9 7 8

50 50 55 69 44 73 57 69TOTAL

SAMPLE

SP

EC

IES

A B C D E F G HI 0.00 0.00 0.00 0.00 0.00 0.03 0.09 0.12II 0.18 0.16 0.02 0.09 0.18 0.03 0.12 0.07III 0.02 0.06 0.00 0.04 0.20 0.10 0.00 0.00IV 0.04 0.04 0.02 0.07 0.16 0.11 0.05 0.12V 0.04 0.08 0.05 0.03 0.07 0.10 0.11 0.04VI 0.06 0.16 0.16 0.14 0.02 0.04 0.07 0.01VII 0.04 0.00 0.00 0.14 0.00 0.03 0.16 0.07VIII 0.14 0.00 0.05 0.09 0.00 0.01 0.04 0.10IX 0.08 0.04 0.18 0.10 0.00 0.11 0.05 0.09X 0.00 0.14 0.11 0.06 0.05 0.04 0.04 0.01XI 0.04 0.08 0.05 0.12 0.14 0.07 0.02 0.07XII 0.18 0.04 0.02 0.01 0.02 0.08 0.14 0.12XIII 0.08 0.18 0.15 0.03 0.09 0.14 0.00 0.06XIV 0.10 0.02 0.18 0.07 0.07 0.12 0.12 0.12

1 1 1 1 1 1 1 1

SAMPLE

SP

EC

IES

TOTAL

H’ = - pi ln(pi)∑pi = Proportion of the ith species

Varies between 1.5 and 4.

Should ONLY really be used for datasets where absolute richness known – otherwise Brillouin Index

Sensitive to the abundance of rare species

Brillouin Index

H1

Nln N!( )

n1! n2! n3! n4! ......=

n1 = Number of individuals of species 1n2 = Number of individuals of species 2

N = total number of individuals in the entire collection

^H can only use count data

Best used where data not random

Sensitive to the abundance of rare species

Simpson’s Index D = pi2∑

pi = Proportion of the ith species

This Index actually determines the probability of two organisms at random that are the same species

[ ]D = ^ ∑ ni (ni – 1)

N (N – 1)

ni = Number of individuals of species i in the sample

N = Total number of individuals in the sample

s = Number of species in the sample

i = 1

s

D can use biomass, cover, productivity & count data.

^D can only use count data.

Sensitive to the abundance of common species

Species Evenness Measures

1 - DSimpson’s Index of Diversity

The probability that two organisms drawn at random are different species

1D

Strictly speaking, D can only be used for an infinite population - Estimator

Evenness Diversity

Maximum Diversity

H’

Hmax

Shannon (J)

Hmax = ln(S) S = Number of Species

Simpson’s 1 / D

SE1/D =

Putting Confidence Intervals around Estimates

Jackknifing – the generation of pseudo-means

Species 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 0 0 0 0 0 0 0 0 0 0 12 0 32 2 0 0

2 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0

3 1 0 0 0 0 2 0 0 0 2 0 1 0 2 0 0

4 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0

5 2 0 0 0 0 1 0 0 0 2 0 0 0 0 1 2

6 0 0 0 2 0 0 0 0 0 0 0 0 0 1 0 1

7 6 0 4 3 4 3 2 1 0 1 5 11 0 3 9 2

8 1 1 0 3 0 2 0 0 0 1 0 5 0 0 3 0

9 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0

10 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0

11 0 1 0 0 0 4 1 0 0 0 0 2 0 1 0 0

12 1 0 0 0 4 0 0 0 0 1 0 9 0 0 1 0

13 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

14 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0

15 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0

16 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

17 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0

18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0

19 0 0 0 0 0 0 0 0 0 2 0 1 1 0 1 1

20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

TOTAL 13 3 4 10 9 17 3 2 1 9 17 32 35 9 16 8

SAMPLE

[ ]D = ^ ∑ ni (ni – 1)

N (N – 1)i = 1

s

Simpson’s Index of Diversity

1D

Example using:

Numbers of beetles in 16 hedgerow samples

Species 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 0 0 0 0 0 0 0 0 0 0 12 0 32 2 0 0 46

2 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1

3 1 0 0 0 0 2 0 0 0 2 0 1 0 2 0 0 8

4 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 3

5 2 0 0 0 0 1 0 0 0 2 0 0 0 0 1 2 8

6 0 0 0 2 0 0 0 0 0 0 0 0 0 1 0 1 4

7 6 0 4 3 4 3 2 1 0 1 5 11 0 3 9 2 54

8 1 1 0 3 0 2 0 0 0 1 0 5 0 0 3 0 16

9 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 2

10 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 2

11 0 1 0 0 0 4 1 0 0 0 0 2 0 1 0 0 9

12 1 0 0 0 4 0 0 0 0 1 0 9 0 0 1 0 16

13 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2

14 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 2

15 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4

16 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

17 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 2

18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1

19 0 0 0 0 0 0 0 0 0 2 0 1 1 0 1 1 6

20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1

TOTAL 13 3 4 10 9 17 3 2 1 9 17 32 35 9 16 8 188

SAMPLEn

Species 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 0 0 0 0 0 0 0 0 0 0 12 0 32 2 0 0 46 45 2070 0.0589

2 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0.0000

3 1 0 0 0 0 2 0 0 0 2 0 1 0 2 0 0 8 7 56 0.0016

4 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 3 2 6 0.0002

5 2 0 0 0 0 1 0 0 0 2 0 0 0 0 1 2 8 7 56 0.0016

6 0 0 0 2 0 0 0 0 0 0 0 0 0 1 0 1 4 3 12 0.0003

7 6 0 4 3 4 3 2 1 0 1 5 11 0 3 9 2 54 53 2862 0.0814

8 1 1 0 3 0 2 0 0 0 1 0 5 0 0 3 0 16 15 240 0.0068

9 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 2 1 2 0.0001

10 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 2 1 2 0.0001

11 0 1 0 0 0 4 1 0 0 0 0 2 0 1 0 0 9 8 72 0.0020

12 1 0 0 0 4 0 0 0 0 1 0 9 0 0 1 0 16 15 240 0.0068

13 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 2 0.0001

14 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 2 1 2 0.0001

15 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 3 12 0.0003

16 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0.0000

17 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 2 1 2 0.0001

18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0.0000

19 0 0 0 0 0 0 0 0 0 2 0 1 1 0 1 1 6 5 30 0.0009

20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0.0000

TOTAL 13 3 4 10 9 17 3 2 1 9 17 32 35 9 16 8 188 0.1612

SAMPLEn n-1 n.(n-1) n.(n-1)/N.(N-1)

DSt = 0.1612 1 / DSt = 6.20473

Repeat calculations n times, where n = number of samples, missing out each sample i in turn

Species 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 0 0 0 0 0 0 0 0 0 12 0 32 2 0 0 46 45 2070 0.0680

2 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0.0000

3 0 0 0 0 2 0 0 0 2 0 1 0 2 0 0 7 6 42 0.0014

4 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 3 2 6 0.0002

5 0 0 0 0 1 0 0 0 2 0 0 0 0 1 2 6 5 30 0.0010

6 0 0 2 0 0 0 0 0 0 0 0 0 1 0 1 4 3 12 0.0004

7 0 4 3 4 3 2 1 0 1 5 11 0 3 9 2 48 47 2256 0.0741

8 1 0 3 0 2 0 0 0 1 0 5 0 0 3 0 15 14 210 0.0069

9 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 2 1 2 0.0001

10 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 2 1 2 0.0001

11 1 0 0 0 4 1 0 0 0 0 2 0 1 0 0 9 8 72 0.0024

12 0 0 0 4 0 0 0 0 1 0 9 0 0 1 0 15 14 210 0.0069

13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0.0000

14 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 2 1 2 0.0001

15 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 4 3 12 0.0004

16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0.0000

17 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 2 1 2 0.0001

18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0.0000

19 0 0 0 0 0 0 0 0 2 0 1 1 0 1 1 6 5 30 0.0010

20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0.0000

TOTAL 0 3 4 10 9 17 3 2 1 9 17 32 35 9 16 8 175 0.1628

SAMPLEn n-1 n.(n-1) n.(n-1)/N.(N-1)

Record D(St-1) value – calculate reciprocal

D(St-1) 1 / D(st-1)

1 0.1628 6.14252 0.165 6.06063 0.156 6.41034 0.1666 6.00245 0.1613 6.19966 0.1785 5.60227 0.1598 6.25788 0.1615 6.19209 0.1628 6.1425

10 0.1704 5.868511 0.1448 6.906112 0.1746 5.727413 0.1618 6.180514 0.1609 6.215015 0.158 6.329116 0.168 5.9524

SA

MP

LE

Ф = n . 1 / D(St) – [(n-1) . 1 / D(St-1)]

Calculate pseudo-values (Ф)

Calculate mean pseudo-value (Ф)

D(St-1) 1 / D(st-1) n.1/D(St) - [(n-1).1/D(St-1)]1 0.1628 6.1425 7.13812 0.165 6.0606 8.36663 0.156 6.4103 3.12184 0.1666 6.0024 9.23975 0.1613 6.1996 6.28136 0.1785 5.6022 15.24217 0.1598 6.2578 5.40838 0.1615 6.1920 6.39649 0.1628 6.1425 7.1381

10 0.1704 5.8685 11.247511 0.1448 6.9061 -4.315512 0.1746 5.7274 13.365013 0.1618 6.1805 6.568614 0.1609 6.2150 6.050115 0.158 6.3291 4.339016 0.168 5.9524 9.9900

7.2236

SA

MP

LE

Mean

Calculate variance, standard error and 95% CI

D(St-1) 1 / D(st-1) n.1/D(St) - [(n-1).1/D(St-1)] (X - Mean)2

1 0.1628 6.1425 7.1381 0.00732 0.165 6.0606 8.3666 1.30653 0.156 6.4103 3.1218 16.82424 0.1666 6.0024 9.2397 4.06475 0.1613 6.1996 6.2813 0.88796 0.1785 5.6022 15.2421 64.29637 0.1598 6.2578 5.4083 3.29508 0.1615 6.1920 6.3964 0.68429 0.1628 6.1425 7.1381 0.0073

10 0.1704 5.8685 11.2475 16.192111 0.1448 6.9061 -4.3155 133.149612 0.1746 5.7274 13.3650 37.717513 0.1618 6.1805 6.5686 0.428914 0.1609 6.2150 6.0501 1.377115 0.158 6.3291 4.3390 8.320916 0.168 5.9524 9.9900 7.6530

7.223619.74754.44381.11102.13109.59104.8561

Critical tUpper 95% CILower 95% CI

VarianceSTDEV

SE

SA

MP

LE

Mean

A B C79 193 1

232 219 1930 0 120

198 1 10597 98 23653 238 2250 56 169 109 62

206 59 079 232 590 75 1982 80 55

118 110 2080 1 6080 0 21 0 186 196 1031 0 00 100 21 0 20073 0 106

232 227 10582 238 7080 75 94

118 114 0

Example Data sets to calculate all measures

THE END

Image acknowledgements – http://www.google.com