Numbers, statistics, and Biology

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BIODIVERSITY and ENVIRONMENTAL
MANAGMENT
Dr Ole R. Vetaas, ole.vetaas_at_global.uib.
no UNIFOB - Global, University of Bergen,
www.global.uib.no  Ecology and Environmental
Change Research Group, Dept. of Biology, UiB
www.eecrg.uib.no
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Numbers, statistics, and Biology

• WHY statistical analyses?

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SCIENCE BASED MANAGMENT

• The value of this degree you may obtain depend on
  
• GOOD THESIS
• Good research question
• Good research question relay on theory and
  observations
• Facts or factual observation
• Theory Facts linked in causal logical frame
  work

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STRUCTURE OF A THESIS

• INTRODUCTION
• MATERIALS AND METHODS
• RESULTS text, tables, and figures
• DISCUSSION
• References
• Appendices, raw data

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STRUCTURE OF A THESIS as a basic introduction
to philosophy of science

• INTRODUCTION
• Other researchers observation
• Theory
• Models
• Deduction
• Hypotheses
• Aims to test or evaluate hypothesis about nature

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Hypothesis formulation

• Everything is connected to everything
• YES, But the strength is different
• From strong causal link to indifferent
• Science is to find the strongest connections, and
  evaluate the plausible causations
• If we know causal links we understand the system
  better

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HYPOTHESIS

• Hypotheses are potential statements that answers
  Research questions
• Example
• Are there more birds in the mid-hills than in
  tropical lowland?
• Hypothesis there are more birds in the mid-hills
  than in the tropical lowland .
• Where is the theory?

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THEORY
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THEORY

• Habitat diversity or heterogeneity theory
• Heterogeneity in topography increase surface
• microclimate south-north-exposed slopes
• Create many habitats
• Mixture of forest and open meadows suitable for
  birds
• Model topography ?micro climate ? many habitats?
  DEDUCE an HYPOTHESIS
• Hypothesis MORE BIRDS in mid hills than FLAT
  AREA
• (H0 (Null hypothesis) no difference in bird
  richness in due to habitat diversity)

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TESTING the HYPOTHESIS

• Hypothesis there are more birds in the mid-hills
  than in the tropical lowland
• Predication more birds in the mid-hills than in
  the tropical lowland
• Collection of data with a scientific method
  (repeatable for others)
• FIGURE B represents BIRDS richness along the
  elevation gradient
• Our hypothesis is falsified or rejected
• THIS GOOD!!?

Low High
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Hypothetic Deductive method.

• hypothesis should be deduced from a model
• model based on rational theory that describes a
  certain phenomenon
• possible to falsify these hypotheses
• That is they can be wrong
• If always correct no good hypothesis

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What is science
Carl Popper

• Science and non-science
• real science should be able to formulate testable
  hypothesis
• be possible to falsify these hypotheses
• falsification criteria !!

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History philosophy of science

• 1900 century
• hypothesis testing program
• Numerical methods aimed to test hypothesis
  were developed by
• Pearson (correlation )
• R. A. Fisher ( t-test)
• Carl Popper made the theoretical basis for
  hypothesis testing which utilised the
  development in the statistical science.

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STRUCTURE OF A THESIS

• INTRODUCTION
• MATERIALS AND METHODS
• RESULTS text, tables, and figures
• DISCUSSION
• References
• Appendices, raw data

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Filed study

• Several different causes
• Several interactions
• Feedback loops cause and effect reinforcing the
  original cause
• True Interdisciplinary work is a new paradigm

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Data that may indicate causation

• Isolate the potential causes
• Effect of Land use on Biodiversity
• Same slope inclination
• Same aspect
• Same type of soil

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STRUCTURE OF A THESIS

• INTRODUCTION
• MATERIALS AND METHODS
• RESULTS text, tables, and figures illustrating
  statistical results
• DISCUSSION
• References
• Appendices, raw data

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NUMERICALMEETHODS What is statistical analyses

• Statistics is a branch of mathematics, which is a
  special language
• This special language is international
• Statistical methods should be viewed as a tool
  for analyses and presentations of data in a
  standardised way

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Statistical expressions elucidate the results
for an international audience

• repeatable for other researchers
• the procedure is arguable
• the progressive scientific process.
• enhance the degree of objectivity in the analysis
  

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STRUCTURE OF A THESIS

• INTRODUCTION
• MATERIALS AND METHODS
• RESULTS text, tables, figures and graphs that
  illustrate statistical results
• DISCUSSION
• References
• Appendices, raw data

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Discussion

• What did I find
• This agrees with other finding
• Other researchers found contrasting results
• What is the reason for agreement and disagreement
• What is the main causal factor
• INTERPRETATION
• Ecological sound reasoning
• Statistical significant may be different from
  biological significant (specie richness example)

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INTERPRETATION

• QUNTITATIVE METHOD DO NOT NECCESARILY GIVE CLEAR
  CUT RESULTS
• INTERPRETATION
• QULITATIVE EVALUATION OF PLAUSIBLE EXPLANTION
• YOU WILL ALSO LEARN QULITATIVE METHODS IN BERGEN

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Universities, faculties and tradition
Natural Sciences
FIELD SCIENCES BIOLOGY, GEOLOGY, GEOGRAPHY
Art Humanities
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The Scientific Field-method

• RESEARCH PROCEDURE IN MOST FIELD STUDIES
• 1. THEORHY state of art what do we know,
• 2. Research question
• 3. Hypothesis or hypotheses
• 4. Collect data in the field
• 5. Qualitative and quantitative analyses
  confronting the hypothesis with the field-data
• 5. Interpret the result and explain it for the
  scientific community public

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Good results depend on

• Testable hypothesis,
• Good sampling design
• Reduced set of potential causal factors

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Numerical methods. aimed to test hypothesis

• accomplish certain assumptions in order to be a
  valid test
• difficult to fulfil when the hypothesis relates
  to the processes in the real world,
• field situation

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THE DIFFERENCE BETWEEN
IDEAL AND REAL WORLD   IDEAL WORLD
(LAB.) REAL WORLD ASSUMPTIONS IN NATURE
LANDSCAPE ----------------------------------------
------------------------------------------------  
ONE RESPONSE VARIABLE MANY INTERACTIVE
RESPONSE VARIABLES   ONE OR A SET OF FEW
INDEPENDENT MANY INTERACTIVE EXPLANATORY
VARIABLES EXPLANATORY VARIABLES  
    NORMAL DISTRIBUTION SKEWED DISTRIBUTION OF
VARIABLES AND ERROR OF VARIABLES AND
ERROR REPRESENTATIVE SAMPLE GEOGRAPHICAL
LIMITATION   INDEPENDENT SAMPLES SPATIAL OR
TEMPORAL AUTOCORRELATED SAMPLES
DEPENDENT INDEPENDENT VARIABLES PHYLOGENNETICAL
RELATION-SHIPS DEPENDENT  
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Statistics orginally made for experimental
situation
Most species in north or south slope
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A test of the null hypothesis by inferential
statistics is in a strict sense only valid if

• Ø There is only one causal factor that causes the
  investigated changes in the response variable, or
  there is a set of few independent causal factors
  that cause the response.

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Statistics orginally made for experimental
situation
Test tubes with green alaga add a toxic element
to test effect
Add toxic element different doses
control
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Real world
Many factores influnce species richness
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Normal or gaussian dsitribution

• Ø The variables of interest have a normal
  distribution, or the residual error after a
  regression should have a normal distribution.
• Biological variables may take many forms of
  distribution, e.g. skewed or bimodal.

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NORMAL DISRTRIBUTION   MISCONCEPTION REGARDING
THE EXPLANATORY VARIABLE   EXPERIMENTAL DESIGNE
UNIFORM DISTRIBUTION   RESPONSE VARIBELS HAVE TO
BE NORMAL IF WE ARE COMAPRING MEANS OF TWO OR
MORE POPULATIONS BY t-TEST OR ANOVA     IN
CLASSICAL ANOVA AND REGRESSION RESIDUALS HAVE TO
BE NORMAL DISTRIBUTED     GENERALIZED LINEAR
MODELS OR GENERALIZE ADDITIVE MOEDLS CAN COPE
WITH VARIOUS DISTRIBUTIONS  
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Dry weight wheat Gr. Pr. m2
Mean growing season temperature
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ALWAYS CHECK RESIDUALS AFTER REGRESSION!!
Residuals after regression
Residuals after regression
Missing factor or wrong factor
ok
-2 -1 0 1 2
-2 -1 0 1 2
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IN CLASSICAL ANOVA AND REGRESSION RESIDUALS HAVE
TO BE NORMAL DISTRIBUTED     GENERALIZED LINEAR
MODELS OR GENERALIZE ADDITIVE MOEDLS CAN COPE
WITH VARIOUS DISTRIBUTIONS
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NORAMLITY t-TEST DIFFERENC OF MEAN
FREQUNCY of plots with x number of species
MEAN NUMBER OF SPECIES
Equal variance
south
north
X NUMBER OF SPECIES
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NORAMLITY t-TEST DIFFERENC OF MEAN
FREQUNCY of plots with x number of species
MEAN NUMBER OF SPECIES
Non-Equal variance
south
north
X NUMBER OF SPECIES
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Representative sample
Ø The objects sampled are a representative sample
of the total population. Normally, a very small
fraction of the total population of the target
organism is sampled in biological field studies.
Thus in a strict sense the analyses will be site
conditional, and the result may not be inferred
to be valid for the total population.
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REPRESNTATIVE SAMPLE

• gtRandom sampling
• gtState How big is the total polulation one aims
  to infer about  
• ESTIMATE THE NICHE OF AN ORGANISME, WITH DATA
  FROM A LIMITED REGION
• CAN WE INFER THAT THE RESULT IS VALID FOR THE
  SPECIES
•  
• HYPOTHEIS ABOUT THE TOTAL POPULATION, I.E. THE
  SPECIES 

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Popperian falsification
The classical popperian falsification can not be
done without some ad-hoc adjustment of the
degrees of freedom  MAJOR PROBLEM IN CAUSAL
ANALYESE NOT IN DESCRIPTIVE ANALYSES BY MEANS OF
NUMERICAL METHODS  SOFTWARE AND NUMERICAL OPTIONS
EXSIT TO COPE WITH THIS PROBLEM  SAMPLING MOST
IMPORTANT MAKE A GRID ! Comparative biology
phylogenetic relationships among the objects
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SPATIAL AUTOCORRELATION DISTANCE DECAY 
All objects have a geographical distribution,
objects located close to each other are on
average more similar than those with a more
distant location,    Hence the similarity among
objects are a function of their distance to each
other spatial dependency.   Hence the
objects are not independet of each other   The
degrees of freedom is not equal to the number of
samples minus one (df n 1 is not
true)   Thus the statistical p-value can not
be used to evaluate if the hypotehsis is
falsified or not.