Biometric Analysis in Systematics What is it, where did it come from, and what can it do for me

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Biometric Analysis in Systematics What is it,
where did it come from, and what can it do for me?
Norman MacLeodPalaeontology Department, The
Natural History Museum
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Analysis of Morphology
Central tendency (mean)? Modal Shape(s)? Distribut
ion of modes? Continuous or discontinuous
variation?
Covariance with environment? Covariance with
ecology? Covariance with geography? Covariance
with genotype?
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Some Definitions

• Data Analysis - the process of gathering,
  modeling, and transforming data with the goal of
  highlighting useful information, suggesting
  conclusions, and supporting decision making
• Statistics - the branch of mathematics devoted to
  the summarization and/or description of
  collections of data
• Descriptive Statistics - methods that describe
  the main features of a collection of data in
  quantitative terms
• Inferential Statistics - methods used to make
  inferences about some unknown aspect of a
  population from which a sample has been drawn

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Some Definitions

• Biometry - the application of statistical methods
  to biological problems (Sokal Rohlf 1980)
• Ordination - the graphical representation of
  relations among members of a sample or population
• Morphometrics - the mathematical study of changes
  in, and covariation with, the form of organisms
• Size - the spatial dimension of a form
• Shape - that aspect of a forms geometry that
  remains after scale ( size), position, and
  rotation have been normalized.

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Origins of Biometry
Nessuma humana investigazione si pio dimandara
vra scienzia sessa non pass per le matimatiche
dimenstrazione Leonardo da Vinci
Leonardo da Vinci (1452 - 1519)
Vitruvian Man (c. 1487)
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Origins of Biometry
Albrech Dürer (1471 - 1528)
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Origins of Biometry
John Graunt (1620 - 1674)
William Petty (1623 - 1687)
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Origins of Biometry
Blaise Pascal (1623 - 1662)
Jacob Bernoulli (1654 - 1705)
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Origins of Biometry
Pierre Simon Laplace (1749 - 1827)
Karl Friedrich Gauss (1777 - 1855)
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Origins of Biometry
Francis Galton (1822 - 1911)
Regression Analysis - The quantitative study of
the manner in which variation in one (or more)
variable(s) can be expressed in terms of
variation in one (or more) other variable(s).
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Origins of Biometry
DArcy W. Thompson (1860 - 1948)
If diverse and dissimilar organisms can be
referred as a whole to identical functions of
very different coordinate systems, this fact will
of itself constitute a proof that variation has
proceeded on definite and orderly lines, that a
comprehensive law of growth has pervaded the
whole structure in its integrity, and that some
more or less simple and recognisable system of
forces has been in control ... Thompson (1917)
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Origins of Biometry
Karl Pearson (1857 - 1936)
Created the modern field of statists, chairman of
the first university statistics department, made
fundamental contributions to regression analysis,
developed the correlation coefficient and
chi-square tests, and laid the foundation for
principal components analysis.
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Statistics Data Analysis
Basic Concepts

• Population - the totality of individual
  observations existing within a specified and/or
  time
• Sample - the subset of the population containing
  individual specimens from which data have been
  collected. Ideally the sample should be composed
  of independent individuals randomly selected from
  the population.
• Variable - the actual property measured or
  observed on the specimens

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Statistics Data Analysis
Types of Variables

• Measurement Variables - variables whose different
  states can be expressed in a numerically ordered
  manner.
• Continuous - variables that can assume an
  infinite number of states (e.g., 1.25, 1.57,
  1.73)
• Discontinuous - variables than can only assume
  certain, fixed states (e.g., 1, 2, 3)
• Ranked Variables - variables whose different
  states can be expressed in rank order (e.g.,
  small, medium, large)
• Attributes - variables whose differing states can
  only be expressed by qualitative labels (e.g.,
  smooth, striate, costate, papillose)

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Statistics Data Analysis
Describing a Collection
500 values drawn from a normal distribution
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Statistics Data Analysis
Describing a Collection

• Mean - the arithmetic centre of the distribution
• Median - position of the 50th percentile
• Mode - the most common observation or the peak of
  a continuous probability distribution
• Range - difference between highest and lowest
  observation
• Variance - mean square of deviations from the
  mean
• Standard Deviation - mean of deviations from the
  mean

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Statistics Data Analysis
Descriptive Statistics
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Statistics Data Analysis
Descriptive Statistics
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Statistics Data Analysis
Descriptive Statistics Comparing Collections
Two 500-value sets drawn from a normal
distribution
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Statistics Data Analysis
Descriptive Statistics Comparing Collections
Distance - arithmetic difference between a pair
of means
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Statistics Data Analysis
Descriptive Statistics Comparing Distributions
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Statistics Data Analysis
Comparing Distributions
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Analysis of Morphology
Central tendency (mean)? Modal Shape(s)? Distribut
ion of modes? Continuous or discontinuous
variation?
Covariance with environment? Covariance with
ecology? Covariance with geography? Covariance
with genotype?
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Biometry
Its the systematists job to

• Develop hypotheses concerning the nature of
  causal processes
• Determine how such processes would be expected to
  affect patterns of similarity and difference
• Devise observations or measurements that will
  distinguish between alternative process-level
  hypotheses (incl. the null hypothesis)
• Obtain a representative sample of the organisms
  under study
• Interpret the results by ascertaining which
  hypotheses model(s) best predict the ordination
  patterns found

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Biometry
Its the data analysts job to

• Select the appropriate ordination method(s) to
  best distinguish between alternative causal
  models
• Perform the necessary data collection procedures
  and analyses

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Where Does Biometry Fit?

• Systematics - the scientific study of the kinds
  and diversity of organisms and of any and all
  relationships among them
• Classification - the ordering of organisms into
  groups based on their relationships
• Identification - the allocation or assignment of
  unidentified organisms to established groups
• Taxonomy - the theoretical study of
  classification including its bases, principles,
  procedures, and rules

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Where Does Biometry Fit?

• Systematics - the scientific study of the kinds
  and diversity of organisms and of any and all
  relationships among them
• Classification - the ordering of organisms into
  groups based on their relationships
• Identification - the allocation or assignment of
  unidentified organisms to established groups
• Taxonomy - the theoretical study of
  classification including its bases, principles,
  procedures, and rules

Biometry Numerical Taxonomy
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Does n-Taxonomy Phenetics?

• Numerical Taxonomy - the theoretical study of
  mathematical approaches to classification
  including its bases, principles, procedures, and
  rules
• Phenetics - the principle and practice of
  inferring phylogenetic ancestry based on average
  similarity among operational taxonomic units
  (OTUs)
• Cladistics - the principle and practice of
  inferring phylogenetic ancestry based on the
  mutual possession of shared derived character
  states ( synapomorphies)

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Does n-Taxonomy Phenetics?

• Numerical Taxonomy - the theoretical study of
  mathematical approaches to classification
  including its bases, principles, procedures, and
  rules
• Phenetics - the principle and practice of
  inferring phylogenetic ancestry based on average
  similarity among operational taxonomic units
  (OTUs)
• Cladistics - the principle and practice of
  inferring phylogenetic ancestry based on the
  mutual possession of shared derived character
  states ( synapomorphies)

Numerical Taxonomy ? Phenetics
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Advantags of n-Taxonomy
Numerical taxonomy ...

• ... has the power to integrate data from a
  variety of sources
• ... leads to greater objectivity and
  reproducibility of taxonomic results
• ... promotes the statistically testing of
  characters and classifications derived from both
  traditional and n-taxonomic approaches
• ... can facilitate complete automation of the
  taxonomic identification process
• ... promotes collaboration between taxonomists
  and the formation of interdisciplinary approaches
  to taxonomy

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Disadvantags of n-Taxonomy
Numerical taxonomy ...

• ... is hard to master
• ... is all about mathematics, not organisms
• ... requires users to have advanced IT skills
• ... is a contentious and argument-prone field
• ... cant be used on real organisms in real-world
  situations
• ... will reduce demand for genuine taxonomic
  expertise
• ... is incompatible with phylogenetic systematics

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Biometric Analysis in Systematics What is it,
where did it come from, and what can it do for me?
Norman MacLeodPalaeontology Department, The
Natural History Museum