Data and InterpretationData and Interpretation

What have you learnt?What have you learnt?

The delver into nature’s aimsThe delver into nature’s aims

Seeks freedom and perfection;Seeks freedom and perfection;

Let calculation sift his claimsLet calculation sift his claims

With faith and circumspectionWith faith and circumspection

-Goethe-Goethe

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

Legendre and LegendreLegendre and Legendre

Organization of this presentationOrganization of this presentation

The scientific method – from the question to the The scientific method – from the question to the answer and back againanswer and back again

Data analysis – beyond statistical inference (some Data analysis – beyond statistical inference (some tools)tools)

From analysis to conclusions – modelingFrom analysis to conclusions – modeling Causal loop diagrams – a useful tool for beginning Causal loop diagrams – a useful tool for beginning

to explore modelingto explore modeling Some practical things about drawing conclusions Some practical things about drawing conclusions

from data and models – fitting your data into from data and models – fitting your data into what is already known, extrapolation and what is already known, extrapolation and speculationspeculation

Updating theory and practiceUpdating theory and practice

General Research Area

Specific problem

Sampling and lab work

Data analysis and interpretation

ConclusionsUnusable

data

New hypotheses

Analysis:Analysis:Beyond statistical inferenceBeyond statistical inference

Relationships between natural conditions Relationships between natural conditions and outcome of observationsand outcome of observations

Methods for Methods for analyzing and analyzing and modeling the datamodeling the data

Deterministic: only on Deterministic: only on possible resultpossible result

Deterministic Deterministic modelsmodels

Random: many possible Random: many possible results (frequency)results (frequency)

Numerical Numerical analysis analysis

Strategic: results depend on Strategic: results depend on strategies of organismsstrategies of organisms

Game theoryGame theory

Uncertain: many possible Uncertain: many possible outcomesoutcomes

Chaos theoryChaos theory

Autocorrelation and spatial Autocorrelation and spatial structurestructure

Spatial heterogeneity is a functional characteristic of many systems and is not the result of random or noise generating processes.

Autocorrelation: The value of yj observed at site j is assumed to be the overall mean of the process (y) plus a weighted sum of the centered values (yi – y) at surrounding sites.

Yj = y +f(yi-y) + j

i1

i2

i3

i4

j

Spatial dependenceSpatial dependence

If there is no auto-If there is no auto-correlation in the variable correlation in the variable of interest, spatial of interest, spatial variability may be the variability may be the result of explanatory result of explanatory variables exhibiting variables exhibiting spatial structurespatial structure

YYjj = = yy + + ff( explanatory variables) + ( explanatory variables) + jj

Many tools exist for spatial analysisMany tools exist for spatial analysis

00.5

11.5

22.5

33.5

44.5

5

0 5 10 15 20 25 30 35 40

Lag distance (m)

Sem

ivari

an

ce

CorrelogramsCorrelograms VariogramsVariograms PeriodogramsPeriodograms

The nature of the shapes of these graphical models are indicative of the nature of the processes that create spatial autocorrelation

Some applicationsSome applications

Biogeochemical cyclesBiogeochemical cycles

HydrologyHydrology

Poverty dynamicsPoverty dynamics

Vegetation structureVegetation structure

MappingMapping

Trend surface analysis - a regression Trend surface analysis - a regression approachapproach

Interpolated maps – contour maps Interpolated maps – contour maps generated from a regular grid of generated from a regular grid of measurementsmeasurements

Kriging – a geostatistical approach Kriging – a geostatistical approach based on semivariance analysisbased on semivariance analysis

ClassificationClassification

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

0.4 0.5 0.6 0.7 0.8 0.9 1

LCMLCM

LCM

LTFLTFLTF

TCM

TCMTCM

TTFTTFTTF

OWMOWMOWM

OWLOWLOWL

OCMOCMOCM

OTFOTFOTF

KCMKCMKCMKT

KTKTKWM

KWMKWM

KWLKWLKWL

Figure 5

Cluster analysisCluster analysis

Multidimensional analysisMultidimensional analysis Partition a dataset into subsets Partition a dataset into subsets Subsets form a series of mutually Subsets form a series of mutually

exclusive cellsexclusive cells

Example of hierarchically nested Example of hierarchically nested partitionspartitions

Partition 1Partition 1 Partition 2Partition 2 Sampling sitesSampling sites

Observations in Observations in environment Aenvironment A

Cluster 1Cluster 1 7,127,12

Cluster 2Cluster 2 3,5,113,5,11

Cluster 3Cluster 3 1,2,61,2,6

Observations in Observations in environment Benvironment B

Cluster 4Cluster 4 4,94,9

Cluster 5Cluster 5 8,10,13,148,10,13,14

Ordination in reduced spaceOrdination in reduced space

Many multivariate datasets have more Many multivariate datasets have more dimensions than we can easily dimensions than we can easily comprehend or manipulate in a comprehend or manipulate in a meaningful way. There are a number of meaningful way. There are a number of techniques to reduce the dimensionality of techniques to reduce the dimensionality of these datasets these datasets

Meaningful relationships are deduced from Meaningful relationships are deduced from the relative positions of observation units the relative positions of observation units in this reduced spacein this reduced space

Factor analysisFactor analysis

Frequently used in the social Frequently used in the social sciencessciences

Aims at representing the covariance Aims at representing the covariance structure of the dataset in terms of a structure of the dataset in terms of a predetermined causal modelpredetermined causal model

Principal components analysisPrincipal components analysis

Similar to factor Similar to factor analysis, but for analysis, but for quantitative data.quantitative data.

Analysis generates Analysis generates new axes that new axes that capture the capture the variancevariance

Principal component analysis of PLFA profiles

-15 -10 -5 0 5 10 15

-6

-4

-2

0

2

4

6

8

ACOW

AMIX

ANONE

AWILD DCOW

DMIX

DNONE

DWILD ECOW

EMIX

ENONE

EWILD

HYCOW

HYNONE

HYWILD

General Research Area

Specific problem

Sampling and lab work

Data analysis and interpretation

ConclusionsUnusable

data

ModelingModeling

Conceptual modelsConceptual models Numerical modelsNumerical models

• Application models – based on laws and Application models – based on laws and theoriestheories

• Calculation tools – based on empirical Calculation tools – based on empirical relationships and correlationsrelationships and correlations

Conceptual modelConceptual model

O 2

O rg a nic -C C O 2

C H4

Atm o sp he re

So il

ro o t a nd m ic ro b ia l re sp ira tio n

M e tha no -g e ne sis

M e tha no -tro p hy

C H4

litte rfa lla nd

ro o t m o rta lity

Litte r 1

2

2

Modeling for a purposeModeling for a purpose

Throwaway models – used to Throwaway models – used to improve the understanding of how a improve the understanding of how a system is functioning in a specific system is functioning in a specific studystudy

Career models – Some scientists Career models – Some scientists make a career out of one or a few make a career out of one or a few models models

Causal loop diagrams:Causal loop diagrams:A tool to help understand A tool to help understand your system and begin to your system and begin to

model itmodel it

Causal loop diagramsCausal loop diagrams

Capturing your hypotheses about the Capturing your hypotheses about the causes of dynamicscauses of dynamics

Capturing mental models of Capturing mental models of individuals and teamsindividuals and teams

Understanding important feedbacks Understanding important feedbacks that may be operating in a systemthat may be operating in a system

Birth rate Population Death rate

What would happen if a variable What would happen if a variable were to changewere to change

+

+ +

-

BR

Average Lifetime

-

Fractional Birth Rate

+

Positive feedbacks of fire risk in Positive feedbacks of fire risk in Amazon basinAmazon basin

Evapotranspiration

Leaf Area indexPrecipitation

Smoke

Fire

+

+

-

-

+

Human health-

Investments-

-

Logging

-

El Niño

-

+

These an many other These an many other techniques can be useful in techniques can be useful in

probing data beyond probing data beyond statistical inferences to gain statistical inferences to gain

deeper insight into your deeper insight into your datadata

Beyond analysis of your dataBeyond analysis of your data What is known about your subject from What is known about your subject from

other studies? other studies?

Don’t just compare your results to the Don’t just compare your results to the results of others, synthesize what is known results of others, synthesize what is known from other work and use the synthesis to from other work and use the synthesis to put your new knowledge into context put your new knowledge into context

Dig to understand what is different about Dig to understand what is different about your system and what novel knowledge your system and what novel knowledge you have generatedyou have generated

SpeculationSpeculation

Build your discussion on your data, Build your discussion on your data, not on speculation. not on speculation.

Clearly label speculation in your Clearly label speculation in your discussiondiscussion

Speculation is never the basis for a Speculation is never the basis for a conclusionconclusion

ExtrapolationExtrapolation

Nitrification Potential1 (g-N g-soil-1 d-1)

0 2 4 6 8 10

N2O

+ N

O (

ng-N

cm

-2 h

-1)

0

1

2

3

4

5

r2 = 0.85

y = 0.39 + 0.39x

ExtrapolationExtrapolation

Nitrification Potential1 (g-N g-soil-1 d-1)

0 5 10 15 20 25 30

N2O

+ N

O (

ng-N

cm

-2 h

-1)

0

3

6

9

12

15

ExtrapolationExtrapolation

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

General Research Area

Specific problem

Sampling and lab work

Data analysis and interpretation

ConclusionsUnusable

data

New hypotheses

Updating theory and practiceUpdating theory and practice

Science works incrementallyScience works incrementally

One paper is rarely sufficient to One paper is rarely sufficient to update theory or practiceupdate theory or practice

Interpret your results appropriately, Interpret your results appropriately, but do not over interpret thembut do not over interpret them