data analysis talk_jan2015

The Analysis of Ecological Data

Juan Antonio BalbuenaMarine Zoology Unit (ICBiBE, UV)[email protected]

Jan. 2015 Curso de Pós-graduação em Ecologia de Ambientes Aquáticos ContinentaisCurso de Pós-graduação em Biologia Comparada

Institut Cavanilles de Biodiversitat i Biologia Evolutiva

Contents

1.Multivariate data in ecology

2.Functional vs. structural methods

3.Inference and modelling

4.Further readingJan. 2015 Curso de Pós-graduação em Ecologia de Ambientes Aquáticos ContinentaisCurso de Pós-graduação em Biologia Comparada

Multivariate data in ecology


The usual starting point is a data matrix

Multivariate data in ecologycode FishSp Sex SL W POLYCH COPEP MOLLU AMPHIP DECAPB1B3D107 barba 0 16.1 104.0 10 5 5 5 1

B1B3D108 barba 1 13.1 50.0 6 0 0 3 3

B1B3D109 barba 0 16.0 86.0 0 0 0 1 1

B1O1D103 barba 1 11.5 33.0 0 0 0 3 3

B3O1D302 barba 0 15.8 95.0 0 1 0 1 1B3O1D303 barba 0 17.8 133.0 0 0 0 2 4B3O1D304 barba 0 15.9 90.0 2 0 0 4 4

B3O1D305 barba 0 17.1 170.0 17 0 0 14 14

B3O1D306 barba 1 18.9 164.0 14 0 0 2 2

B3O1D307 barba 1 16.1 86.0 0 0 0 2 2

B3O1D308 barba 1 19.3 168.0 0 0 0 11 0B3O1D309 barba 1 19.4 159.0 5 0 0 9 9

B3O1D310 barba 1 16.6 108.0 0 0 0 7 7

SB013 surm 0 12.0 41.0 3 0 0 1 1

SBJ10 surm 0 12.5 49.1 0 0 0 2 2

SBJ11 surm 0 15.8 101.0 0 6 0 6 6

SBJ13 surm 1 15.5 97.0 0 0 0 5 0

SBJ14 surm 1 16.0 111.5 0 1 0 1 1SBJ17 surm 0 14.5 71.1 5 0 0 2 2

SBJ19 surm 1 14.7 83.1 0 0 0 2 2

SBJ20 surm 1 14.8 85.8 2 4 0 4 4

SSJ11 surm 0 17.8 139.5 0 0 0 2 0

SSJ12 surm 0 16.5 108.9 10 0 0 4 4

Stomach contents

Mullus spp.


There are different types of variables

Multivariate data in ecologycode FishSp Sex SL W POLYCH COPEP MOLLU AMPHIP DECAPB1B3D107 barba M 16.1 104.0 10 5 5 5 1

B1B3D108 barba F 13.1 50.0 6 0 0 3 3

B1B3D109 barba M 16.0 86.0 0 0 0 1 1

B1O1D103 barba F 11.5 33.0 0 0 0 3 3

B3O1D302 barba F 15.8 95.0 0 1 0 1 1B3O1D303 barba F 17.8 133.0 0 0 0 2 4B3O1D304 barba F 15.9 90.0 2 0 0 4 4

B3O1D305 barba F 17.1 170.0 17 0 0 14 14

B3O1D306 barba M 18.9 164.0 14 0 0 2 2

B3O1D307 barba M 16.1 86.0 0 0 0 2 2

B3O1D308 barba M 19.3 168.0 0 0 0 11 0B3O1D309 barba M 19.4 159.0 5 0 0 9 9

B3O1D310 barba M 16.6 108.0 0 0 0 7 7

SB013 surm F 12.0 41.0 3 0 0 1 1

SBJ10 surm F 12.5 49.1 0 0 0 2 2

SBJ11 surm F 15.8 101.0 0 6 0 6 6

SBJ13 surm M 15.5 97.0 0 0 0 5 0

SBJ14 surm M 16.0 111.5 0 1 0 1 1SBJ17 surm F 14.5 71.1 5 0 0 2 2

SBJ19 surm M 14.7 83.1 0 0 0 2 2

SBJ20 surm M 14.8 85.8 2 4 0 4 4

SSJ11 surm F 17.8 139.5 0 0 0 2 0

SSJ12 surm F 16.5 108.9 10 0 0 4 4

Categorical


…and there are different types of categorical variables …

Multivariate data in ecology

Categorical

Nominal

Ordinal

FishSp Sexbarba Msurm F

Seasonspringsummerfallwinter


Other variables are continuous


B1B3D108 barba F 13.1 50.0 6 0 0 3 3

B1B3D109 barba M 16.0 86.0 0 0 0 1 1

B1O1D103 barba F 11.5 33.0 0 0 0 3 3


B3O1D305 barba F 17.1 170.0 17 0 0 14 14

B3O1D306 barba M 18.9 164.0 14 0 0 2 2

B3O1D307 barba M 16.1 86.0 0 0 0 2 2


B3O1D310 barba M 16.6 108.0 0 0 0 7 7

SB013 surm F 12.0 41.0 3 0 0 1 1

SBJ10 surm F 12.5 49.1 0 0 0 2 2

SBJ11 surm F 15.8 101.0 0 6 0 6 6

SBJ13 surm M 15.5 97.0 0 0 0 5 0


SBJ19 surm M 14.7 83.1 0 0 0 2 2

SBJ20 surm M 14.8 85.8 2 4 0 4 4

SSJ11 surm F 17.8 139.5 0 0 0 2 0

SSJ12 surm F 16.5 108.9 10 0 0 4 4

Continuous


Where would you classify count data?


B1B3D108 barba F 13.1 50.0 6 0 0 3 3

B1B3D109 barba M 16.0 86.0 0 0 0 1 1

B1O1D103 barba F 11.5 33.0 0 0 0 3 3


B3O1D305 barba F 17.1 170.0 17 0 0 14 14

B3O1D306 barba M 18.9 164.0 14 0 0 2 2

B3O1D307 barba M 16.1 86.0 0 0 0 2 2


B3O1D310 barba M 16.6 108.0 0 0 0 7 7

SB013 surm F 12.0 41.0 3 0 0 1 1

SBJ10 surm F 12.5 49.1 0 0 0 2 2

SBJ11 surm F 15.8 101.0 0 6 0 6 6

SBJ13 surm M 15.5 97.0 0 0 0 5 0


SBJ19 surm M 14.7 83.1 0 0 0 2 2

SBJ20 surm M 14.8 85.8 2 4 0 4 4

SSJ11 surm F 17.8 139.5 0 0 0 2 0

SSJ12 surm F 16.5 108.9 10 0 0 4 4

Counts


Categorical or continuous?


B1B3D108 barba F 13.1 50.0 6 0 0 3 3

B1B3D109 barba M 16.0 86.0 0 0 0 1 1

B1O1D103 barba F 11.5 33.0 0 0 0 3 3


B3O1D305 barba F 17.1 170.0 17 0 0 14 14

B3O1D306 barba M 18.9 164.0 14 0 0 2 2

B3O1D307 barba M 16.1 86.0 0 0 0 2 2


B3O1D310 barba M 16.6 108.0 0 0 0 7 7

SB013 surm F 12.0 41.0 3 0 0 1 1

SBJ10 surm F 12.5 49.1 0 0 0 2 2

SBJ11 surm F 15.8 101.0 0 6 0 6 6

SBJ13 surm M 15.5 97.0 0 0 0 5 0


SBJ19 surm M 14.7 83.1 0 0 0 2 2

SBJ20 surm M 14.8 85.8 2 4 0 4 4

SSJ11 surm F 17.8 139.5 0 0 0 2 0

SSJ12 surm F 16.5 108.9 10 0 0 4 4

Counts


Functional vs. structural methods


Functional approaches: X -> Y

Functional vs. structural methodscode FishSp Sex SL W POLYCH COPEP MOLLU AMPHIP DECAPB1B3D107 barba 0 16.1 104.0 10 5 5 5 1

B1B3D108 barba 1 13.1 50.0 6 0 0 3 3

B1B3D109 barba 0 16.0 86.0 0 0 0 1 1

B1O1D103 barba 1 11.5 33.0 0 0 0 3 3


B3O1D305 barba 0 17.1 170.0 17 0 0 14 14

B3O1D306 barba 1 18.9 164.0 14 0 0 2 2

B3O1D307 barba 1 16.1 86.0 0 0 0 2 2


B3O1D310 barba 1 16.6 108.0 0 0 0 7 7

SB013 surm 0 12.0 41.0 3 0 0 1 1

SBJ10 surm 0 12.5 49.1 0 0 0 2 2

SBJ11 surm 0 15.8 101.0 0 6 0 6 6

SBJ13 surm 1 15.5 97.0 0 0 0 5 0

SBJ14 surm 1 16.0 111.5 0 1 0 1 1SBJ17 surm 0 14.5 71.1 5 0 0 2 2

SBJ19 surm 1 14.7 83.1 0 0 0 2 2

SBJ20 surm 1 14.8 85.8 2 4 0 4 4

SSJ11 surm 0 17.8 139.5 0 0 0 2 0

SSJ12 surm 0 16.5 108.9 10 0 0 4 4

YResponse variable(s)

XPredictor /

Explanatory variable(s)


Functional approaches

Functional vs. structural methodscode FishSp Sex SL W POLYCH COPEP MOLLU AMPHIP DECAPB1B3D107 barba 0 16.1 104.0 10 5 5 5 1

B1B3D108 barba 1 13.1 50.0 6 0 0 3 3

B1B3D109 barba 0 16.0 86.0 0 0 0 1 1

B1O1D103 barba 1 11.5 33.0 0 0 0 3 3


B3O1D305 barba 0 17.1 170.0 17 0 0 14 14

B3O1D306 barba 1 18.9 164.0 14 0 0 2 2

B3O1D307 barba 1 16.1 86.0 0 0 0 2 2


B3O1D310 barba 1 16.6 108.0 0 0 0 7 7

SB013 surm 0 12.0 41.0 3 0 0 1 1

SBJ10 surm 0 12.5 49.1 0 0 0 2 2

SBJ11 surm 0 15.8 101.0 0 6 0 6 6

SBJ13 surm 1 15.5 97.0 0 0 0 5 0

SBJ14 surm 1 16.0 111.5 0 1 0 1 1SBJ17 surm 0 14.5 71.1 5 0 0 2 2

SBJ19 surm 1 14.7 83.1 0 0 0 2 2

SBJ20 surm 1 14.8 85.8 2 4 0 4 4

SSJ11 surm 0 17.8 139.5 0 0 0 2 0

SSJ12 surm 0 16.5 108.9 10 0 0 4 4

Find a model / formula relating X with Y


XPredictor /

Explanatory variable(s)


A simple example

X => Dolphin age

Y => Presence/absence of cranial lesions

Related by a semiparametric regression model

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

Net

rate

of c

hang

e of

lesi

on p

reva

lenc

e (%

)

Dolphin age (yr)Balbuena & Simpkin 2014. Dis Aquat Org 108: 83-89

Parasite induced mortality



Structural methods



F Latent variable(s)

No explicit link between F and Y (F does not affect the analysis of Y)


For example


-0.18 -0.12 -0.06 0.00 0.06 0.12Coordinate 1

-0.20

-0.16

-0.12

-0.08

-0.04

0.00

0.04

0.08

Co

ordi

nate

2

NMDS ordination of 2 red mullet spp. based on 5 prey items

F -> fish species &

weight


A taxonomy of methods in ecology


* or a mixture of continuous and categorical variables

Functional methods

Structural methods

Y consists of

categorical variables

Y consists of

continuous variables*

Ordination

Regression Classification

ClusteringA B C


Inference and modelling


The inertia of classical statistics


A classical problem:A lab claims that an additive added to fish feed increases immune competence (measured as ACH50) of fish

Control Treatment


The inertia of classical statistics


The differences

between treatment and

control were evaluated

by GLM

Control Treatment

250

300

350

400

450

500

550

[AC

H50

] Estimate Std.Error t_value Pr(>|t|)(Intercept) 428.92313 103.74581 4.134 0.000471Weight -0.03788 0.12493 -0.303 0.764725Treatment -75.3188 39.86725 -1.889 0.072747

P > 0.05 –> insufficient evidence to conclude that there is an effect of feed on immune response


Ecological problems are somewhat different


For instance,Factors affecting hatching success of leatherback turtles in the Dominican RepublicRevuelta et al. 2014 Biodivers Conserv 23: 1529–39

Tartaruga-de-couro Dermochelys coriacea



Hatching

success

Distance to tide

Beach zone

(sand/veg.)

Beach (2 sections)

Year(2007-9)

Julian

Clutch size

N yolkless eggs

Incubation duration

Location

Reproductive

Temporal



Hatching

success

Distance to tide

Beach zone

(sand/veg.)

Beach (2)

Year(2007-9)

Date

Clutch size

N yolkless eggs

Incubation duration

Location

Reproductive

TemporalWhich of these factors are

significant?

Classical statistics:



Hatching

success

Distance to tide

Beach zone

(sand/veg.)

Beach (2)

Year(2007-9)

Date

Clutch size

N yolkless eggs

Incubation duration

Location

Reproductive

TemporalHow these factors

contribute to explain hatching success?

Modern approaches:



Hatching

success

Distance to tide

Beach zone

(sand/veg.)

Beach (2)

Year(2007-9)

Date

Clutch size

N yolkless eggs

Incubation duration

Location

Reproductive

TemporalHow these factors

contribute to predict hatching success?

Modern approaches:


P values can be misleading because


• They do not convey variable importance

• P is not a measure of effect size

• Collinear variables can lead to high P values

• Multiple comparisons require adjustments of significance levels Jan. 2015

Curso de Pós-graduação em Ecologia de Ambientes Aquáticos ContinentaisCurso de Pós-graduação em Biologia Comparada

Akaike’s Information Criterion (AIC)


• Measures de relative quality of a statistical model

• Allows considering a set of alternative models to explain de data

• Provides ways to evaluate variable importance and effect size

Goodness of fit

No. paramete

rs

AIC = 2k – 2ln(L)


Application to the hatching success study


Models AIC ΔAIC w

HS ~ SECT + ID + JULIAN + ClutchSZ + YEAR 211.3 0 0.28

HS ~ SECT + ID + JULIAN + ClutchSZ + DIST + YEAR 211.6 0.28 0.24

HS ~ SECT + ID + JULIAN + ClutchSZ + ZONE + YEAR 211.8 0.46 0.23

HS ~ SECT + ID + JULIAN +YEAR 212.9 1.66 0.12

HS ~ SECT + ID + JULIAN + ZONE + YEAR 213.1 1.79 0.12



Hatching

success

Distance to tide

Beach zone

(sand/veg.)

Beach (2 sectors)

Year(2007-9)

Date

Clutch size

N yolkless eggs

Incubation duration

Variable importance 1

1

1

1

0.75

0.35

0.24


Inference and modellingWhat about prediction?

• Model selection serves to explain your data.

• Predictive models require some kind of cross validation

X Y

Training set

Test set


data analysis talk_jan2015

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