Dr Ole R. Vetaas, ole.vetaas@global.uib.no

1. BIODIVERSITY and ENVIRONMENTAL MANAGMENT Dr Ole R. Vetaas, ole.vetaas@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

2. Numbers, statistics, and Biology WHY statistical analyses?

3. 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

4. STRUCTURE OF A THESIS • INTRODUCTION • MATERIALS AND METHODS • RESULTS; text, tables, and figures • DISCUSSION • References • Appendices, raw data

5. 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

6. 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

7. 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?

8. THEORY

9. 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)

10. 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

11. 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

12. 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 !!

13. 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.

14. STRUCTURE OF A THESIS • INTRODUCTION • MATERIALS AND METHODS • RESULTS; text, tables, and figures • DISCUSSION • References • Appendices, raw data

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

16. Data that may indicate causation Isolate the potential causes Effect of Land use on Biodiversity Same slope inclination Same aspect Same type of soil

17. STRUCTURE OF A THESIS • INTRODUCTION • MATERIALS AND METHODS • RESULTS; text, tables, and figures illustrating statistical results • DISCUSSION • References • Appendices, raw data

18. 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

19. 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

20. STRUCTURE OF A THESIS • INTRODUCTION • MATERIALS AND METHODS • RESULTS; text, tables, figures and graphs that illustrate statistical results • DISCUSSION • References • Appendices, raw data

21. 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)

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

23. Universities, faculties and tradition Natural Sciences FIELD SCIENCES BIOLOGY, GEOLOGY, GEOGRAPHY Art & Humanities

24. 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

25. Good results depend on • Testable hypothesis, • Good sampling design • Reduced set of potential causal factors

26. 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

27. 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 EXPLANATORYVARIABLES  NORMAL DISTRIBUTION SKEWED DISTRIBUTION OF VARIABLES AND ERROR OF VARIABLES AND ERROR REPRESENTATIVESAMPLE GEOGRAPHICALLIMITATION INDEPENDENT SAMPLES SPATIAL OR TEMPORAL AUTOCORRELATED SAMPLES = DEPENDENT INDEPENDENT VARIABLES PHYLOGENNETICAL RELATION-SHIPS =DEPENDENT

28. Statistics orginally made for experimental situation Most species in north or south slope

29. 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.

30. Statistics orginally made for experimental situation Test tubes with green alaga: add a toxic element to test effect Add toxic element different doses control

31. Real world Many factores influnce species richness

32. 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.

33. 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

34. Dry weight wheat Gr. Pr. m2 Mean growing season temperature

35. 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

36. IN CLASSICAL ANOVA AND REGRESSION RESIDUALS HAVE TO BE NORMAL DISTRIBUTED GENERALIZED LINEAR MODELS OR GENERALIZE ADDITIVE MOEDLS CAN COPE WITH VARIOUS DISTRIBUTIONS

37. 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

38. 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

39. 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.

40. REPRESNTATIVE SAMPLE >Random sampling >State 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 

41. 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

42. 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.