Measuring Biological Diversity
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• May overestimate Simpson diversity value
Lecture 5 – Choosing Between Diversity Indices
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
Abundance Model Fitting
Assumptions
Alpha diversity indices do not make many assumptions
No assumptions made about species abundance distributions
• Cause of distribution not needed
these aspects
determines whether can be used for your data
Lecture 5 – Choosing Between Diversity Indices
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
S Pielou’s t
Pielou’s t
H’ Shannon
Pielou’s t 1/D Simpson
Pielou’s t 1/d Berger-Parker
10
20
30
40
Sample Addition Sequence
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
Log Alpha Log-Normal Lambda Q-Statistic Simpson McIntosh Berger-Parker Shannon-Wiener Brillouin
How to choose between these?
Lecture 5 – Choosing Between Diversity Indices
– species abundance models have assumptions about these » Geometric – niche pre-emption, regular arrivals » Log – niche pre-emption, irregular arrival intervals » Log-Normal – successively apportioning available niche space of all resources in proportion to abundance » Broken Stick – simultaneously apportioning available niche space of one resource in proportion to abundance
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
Bases for Choice
Appropriateness of each index for your data Discriminant ability of the index Statistical Comparability Widespread utility of the index Your Question
Indices insensitive to sampling effort
Always: Log series a, 1/d (influenced by abd of most abd sp) If more than 50% of spp represented: Q
Lecture 5 – Choosing Between Diversity Indices
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
Appropriateness - Sampling Effort
How to determine when you have completely sampled the environment?
Lecture 5 – Choosing Between Diversity Indices
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
Appropriateness – Sample Effort
Some indices are tremendously sensitive to sample size
Choosing Between Diversity Indices
James A. Danoff-Burg Dept. Ecol., Evol., & Envir. Biol.
Columbia University
Alpha Diversity Indices
A diversity of diversities
• Shape of curve
“Non-parametric”
• Normality is not needed
Lecture 5 – Choosing Between Diversity Indices
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
Small data sets fit many models
• Few spp in each abundance class decreased discriminability
Lecture 5 – Choosing Between Diversity Indices
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
Leveling off point = adequate sample size
Lecture 5 – Choosing Between Diversity Indices
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
Appropriateness, Sample Size When is Enough Enough?
Abundance Model Fitting
Secondary problem: Log-Normal is a frequent consequence
Often because of the central limit tendency of large data sets
If a data set has many species often log-normal distribution results
• Most data have less than 11 • E.g., less than 256 individuals in a species
– Resulting in only 8 classes
Fewer classes, mean fewer opportunities for departures from fit
Lecture 5 – Choosing Between Diversity Indices
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
Bases for Choice
Appropriateness of each index for your data Discriminant ability of the index Statistical Comparability Widespread utility of the index Your Question
Index
Value
Leveling off of Pielou’s t 20
point
If interest is proportional
10
abundance
Any diversity index can be 0
used
Lecture 5 – Choosing Between Diversity Indices
Lecture 5 – Choosing Between Diversity Indices
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
Approp源自文库iateness
Index assumptions need to be met Abundance model of data Sensitivity to sample size Each index needs to be considered for all of
Leveling off of S with adding
more samples
50
If interest is largely richness S is more sensitive to sample40
size than diversity indices
Need more samples Diversity 30
Main problem: Often have multiple models that fit the data
Occasionally because of low number of abundance classes
Log2 has only 11 classes (octaves) even possible
Does not necessarily mean that the community has assembled by a successive breaking of the available nice space
• As is the assumption with the log-normal distribution
Assuming prior information
• Leveling off of S with adding more samples
– If interest is largely richness
• Leveling off of Pielou’s t point
– If interest is proportional abundance
Geometric
• Underestimate Simpson diversity value
Log
• Underestimate Simpson diversity value
Log-Normal
• Best for Simpson diversity analysis analysis
Broken Stick
Abundance Model
Some indices perform better under a specific abundance model
Example: Simpson – probability that two individuals are of the same species
Low replication skewed values
• Idiosyncratic results • Not truly representative of the environment
Indices sensitive to inadequate sampling
S = very sensitive to sampling effort Dominance indices (Simpson, Berger-Parker, McIntosh) Information statistics indices (Shannon) Evenness indices
Sampling Effort
Need consistency in sampling effort
Lecture 5 – Choosing Between Diversity Indices
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
Abundance Model Fitting
Assumptions
Alpha diversity indices do not make many assumptions
No assumptions made about species abundance distributions
• Cause of distribution not needed
these aspects
determines whether can be used for your data
Lecture 5 – Choosing Between Diversity Indices
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
S Pielou’s t
Pielou’s t
H’ Shannon
Pielou’s t 1/D Simpson
Pielou’s t 1/d Berger-Parker
10
20
30
40
Sample Addition Sequence
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
Log Alpha Log-Normal Lambda Q-Statistic Simpson McIntosh Berger-Parker Shannon-Wiener Brillouin
How to choose between these?
Lecture 5 – Choosing Between Diversity Indices
– species abundance models have assumptions about these » Geometric – niche pre-emption, regular arrivals » Log – niche pre-emption, irregular arrival intervals » Log-Normal – successively apportioning available niche space of all resources in proportion to abundance » Broken Stick – simultaneously apportioning available niche space of one resource in proportion to abundance
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
Bases for Choice
Appropriateness of each index for your data Discriminant ability of the index Statistical Comparability Widespread utility of the index Your Question
Indices insensitive to sampling effort
Always: Log series a, 1/d (influenced by abd of most abd sp) If more than 50% of spp represented: Q
Lecture 5 – Choosing Between Diversity Indices
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
Appropriateness - Sampling Effort
How to determine when you have completely sampled the environment?
Lecture 5 – Choosing Between Diversity Indices
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
Appropriateness – Sample Effort
Some indices are tremendously sensitive to sample size
Choosing Between Diversity Indices
James A. Danoff-Burg Dept. Ecol., Evol., & Envir. Biol.
Columbia University
Alpha Diversity Indices
A diversity of diversities
• Shape of curve
“Non-parametric”
• Normality is not needed
Lecture 5 – Choosing Between Diversity Indices
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
Small data sets fit many models
• Few spp in each abundance class decreased discriminability
Lecture 5 – Choosing Between Diversity Indices
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
Leveling off point = adequate sample size
Lecture 5 – Choosing Between Diversity Indices
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
Appropriateness, Sample Size When is Enough Enough?
Abundance Model Fitting
Secondary problem: Log-Normal is a frequent consequence
Often because of the central limit tendency of large data sets
If a data set has many species often log-normal distribution results
• Most data have less than 11 • E.g., less than 256 individuals in a species
– Resulting in only 8 classes
Fewer classes, mean fewer opportunities for departures from fit
Lecture 5 – Choosing Between Diversity Indices
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
Bases for Choice
Appropriateness of each index for your data Discriminant ability of the index Statistical Comparability Widespread utility of the index Your Question
Index
Value
Leveling off of Pielou’s t 20
point
If interest is proportional
10
abundance
Any diversity index can be 0
used
Lecture 5 – Choosing Between Diversity Indices
Lecture 5 – Choosing Between Diversity Indices
© 2003 Dr. James A. Danoff-Burg, jd363@columbia.edu
Approp源自文库iateness
Index assumptions need to be met Abundance model of data Sensitivity to sample size Each index needs to be considered for all of
Leveling off of S with adding
more samples
50
If interest is largely richness S is more sensitive to sample40
size than diversity indices
Need more samples Diversity 30
Main problem: Often have multiple models that fit the data
Occasionally because of low number of abundance classes
Log2 has only 11 classes (octaves) even possible
Does not necessarily mean that the community has assembled by a successive breaking of the available nice space
• As is the assumption with the log-normal distribution
Assuming prior information
• Leveling off of S with adding more samples
– If interest is largely richness
• Leveling off of Pielou’s t point
– If interest is proportional abundance
Geometric
• Underestimate Simpson diversity value
Log
• Underestimate Simpson diversity value
Log-Normal
• Best for Simpson diversity analysis analysis
Broken Stick
Abundance Model
Some indices perform better under a specific abundance model
Example: Simpson – probability that two individuals are of the same species
Low replication skewed values
• Idiosyncratic results • Not truly representative of the environment
Indices sensitive to inadequate sampling
S = very sensitive to sampling effort Dominance indices (Simpson, Berger-Parker, McIntosh) Information statistics indices (Shannon) Evenness indices
Sampling Effort
Need consistency in sampling effort