1. Data and Interpretation What have you learnt?

2. The delver into nature’s aims Seeks freedom and perfection; Let calculation sift his claims With faith and circumspection -Goethe

3. Numerical approaches can never dispense … researchers from reflection on observations. Data analysis must be seen as an objective and non-exclusive approach to carry out in-depth analysis of the data. Legendre and Legendre

4. Organization of this presentation The scientific method – from the question to the answer and back again The scientific method – from the question to the answer and back again Data analysis – beyond statistical inference (some tools) Data analysis – beyond statistical inference (some tools) From analysis to conclusions – modeling From analysis to conclusions – modeling Causal loop diagrams – a useful tool for beginning to explore modeling Causal loop diagrams – a useful tool for beginning to explore modeling Some practical things about drawing conclusions from data and models – fitting your data into what is already known, extrapolation and speculation Some practical things about drawing conclusions from data and models – fitting your data into what is already known, extrapolation and speculation Updating theory and practice Updating theory and practice

6. General Research Area Specific problem Sampling and lab work Data analysis and interpretation Conclusions Unusable data New hypotheses

7. Analysis: Beyond statistical inference Relationships between natural conditions and outcome of observations Methods for analyzing and modeling the data Deterministic: only on possible result Deterministic models Random: many possible results (frequency) Numerical analysis Strategic: results depend on strategies of organisms Game theory Uncertain: many possible outcomes Chaos theory

8. Autocorrelation and spatial structure Spatial heterogeneity is a functional characteristic of many systems and is not the result of random or noise generating processes. Autocorrelation: The value of y j observed at site j is assumed to be the overall mean of the process ( y ) plus a weighted sum of the centered values (y i –  y ) at surrounding sites. Y j =  y +f(y i - y ) +  j i1i1 i2i2 i3i3 i4i4 j

9. Spatial dependence If there is no auto- correlation in the variable of interest, spatial variability may be the result of explanatory variables exhibiting spatial structure Y j =  y + f( explanatory variables) +  j

10. Many tools exist for spatial analysis Correlograms Correlograms Variograms Variograms Periodograms Periodograms The nature of the shapes of these graphical models are indicative of the nature of the processes that create spatial autocorrelation

11. Some applications Biogeochemical cycles Biogeochemical cycles Hydrology Hydrology Poverty dynamics Poverty dynamics Vegetation structure Vegetation structure

12. Mapping Trend surface analysis - a regression approach Trend surface analysis - a regression approach Interpolated maps – contour maps generated from a regular grid of measurements Interpolated maps – contour maps generated from a regular grid of measurements Kriging – a geostatistical approach based on semivariance analysis Kriging – a geostatistical approach based on semivariance analysis

13. Classification Many research goals involve classifying objects that are sufficiently similar into useful or recognizable categories.

14. Cluster analysis Multidimensional analysis Multidimensional analysis Partition a dataset into subsets Partition a dataset into subsets Subsets form a series of mutually exclusive cells Subsets form a series of mutually exclusive cells

15. Example of hierarchically nested partitions Partition 1 Partition 2 Sampling sites Observations in environment A Cluster 1 7,12 Cluster 2 3,5,11 Cluster 3 1,2,6 Observations in environment B Cluster 4 4,9 Cluster 5 8,10,13,14

16. Ordination in reduced space Many multivariate datasets have more dimensions than we can easily comprehend or manipulate in a meaningful way. There are a number of techniques to reduce the dimensionality of these datasets Meaningful relationships are deduced from the relative positions of observation units in this reduced space

17. Factor analysis Frequently used in the social sciences Frequently used in the social sciences Aims at representing the covariance structure of the dataset in terms of a predetermined causal model Aims at representing the covariance structure of the dataset in terms of a predetermined causal model

18. Principal components analysis Similar to factor analysis, but for quantitative data. Analysis generates new axes that capture the variance

19. General Research Area Specific problem Sampling and lab work Data analysis and interpretation Conclusions Unusable data

20. Modeling Conceptual models Conceptual models Numerical models Numerical models Application models – based on laws and theoriesApplication models – based on laws and theories Calculation tools – based on empirical relationships and correlationsCalculation tools – based on empirical relationships and correlations

21. Conceptual model

22. Modeling for a purpose Throwaway models – used to improve the understanding of how a system is functioning in a specific study Throwaway models – used to improve the understanding of how a system is functioning in a specific study Career models – Some scientists make a career out of one or a few models Career models – Some scientists make a career out of one or a few models

23. Causal loop diagrams: A tool to help understand your system and begin to model it

24. Causal loop diagrams Capturing your hypotheses about the causes of dynamics Capturing your hypotheses about the causes of dynamics Capturing mental models of individuals and teams Capturing mental models of individuals and teams Understanding important feedbacks that may be operating in a system Understanding important feedbacks that may be operating in a system

25. Birth ratePopulationDeath rate What would happen if a variable were to change + + + - B R Average Lifetime - Fractional Birth Rate +

26. Positive feedbacks of fire risk in Amazon basin

27. These an many other techniques can be useful in probing data beyond statistical inferences to gain deeper insight into your data

28. Beyond analysis of your data What is known about your subject from other studies? What is known about your subject from other studies? Don’t just compare your results to the results of others, synthesize what is known from other work and use the synthesis to put your new knowledge into context Don’t just compare your results to the results of others, synthesize what is known from other work and use the synthesis to put your new knowledge into context Dig to understand what is different about your system and what novel knowledge you have generated Dig to understand what is different about your system and what novel knowledge you have generated

29. Speculation Build your discussion on your data, not on speculation. Build your discussion on your data, not on speculation. Clearly label speculation in your discussion Clearly label speculation in your discussion Speculation is never the basis for a conclusion Speculation is never the basis for a conclusion

30. Extrapolation

31. Extrapolation

32. Extrapolation I have seen a number of papers that extrapolate to the globe based on one or two observations. They rarely get it right.

33. General Research Area Specific problem Sampling and lab work Data analysis and interpretation Conclusions Unusable data New hypotheses

34. Updating theory and practice Science works incrementally Science works incrementally One paper is rarely sufficient to update theory or practice One paper is rarely sufficient to update theory or practice Interpret your results appropriately, but do not over interpret them Interpret your results appropriately, but do not over interpret them