Key lecture for the EURO-BASIN Training Workshop on Introduction to Statistical Modelling for Habitat Model Development, 26-28 Oct, AZTI-Tecnalia, Pasaia, Spain (www.euro-basin.eu)

1. EURO-­‐BASIN,
www.euro-­‐basin.eu
Introduc)on
to
Sta)s)cal
Modelling
Tools
for
Habitat
Models
Development,
26-­‐28th
Oct
2011

2. projec1ng
spa1al
distribu1ons
niche-­‐based
models
climate
predicted
forecast/scenario
spa1al
distribu1on
biological
response
+
environment
EuroBasin training workshop – 26-28 October 2011 - Modelling the spatial distribution of fish: some key concepts and an application.

3. Why
model
the
spa1al
distribu1on
of
fish?
Interpolate between observations
Project distributions under scenarios
Understand processes that control distributions
…multiple objectives
EuroBasin training workshop – 26-28 October 2011 - Modelling the spatial distribution of fish: some key concepts and an application.

4. A
general
view
of
the
modelling
method
adapted from Anderson, 2010
EuroBasin training workshop – 26-28 October 2011 - Modelling the spatial distribution of fish: some key concepts and an application.

5. uncertain1es
in
observa1ons
sampling
design:
sampling
intensity,
spa1al/temporal
scales,
aggregated
distribu1ons
sampling
gear
(trawl)
or
observa1on
(acous1cs):
accessibility
to
observa1on,
sensi1vity,
bias
and
precision
EuroBasin training workshop – 26-28 October 2011 - Modelling the spatial distribution of fish: some key concepts and an application.

6. uncertain1es
in
conceptual
models
environmental
conditions
density
geographical
dependent
attachment
habitat selection
a
spatial Proportional Constant Basin
distribution
Local density
spatial
Persistence dependency
spatial location
b
high
Habitat suitability
medium
species demographic
interactions structure
low
high
Local density
medium
low
EuroBasin training workshop – 26-28 October 2011 - Modelling the spatial distribution of fish: some key concepts and an application.
spatial location

7. uncertainty
in
numerical
formula1on
func1onal
rela1onships
linear,
polynomial,
piecewise,
etc...
model
complexity
number
of
parameters,
non-­‐linearity
interac1ons
addi1ve,
mul1plica1ve,
other
sta1s1cal
distribu1ons
Normal,
Poisson,
Log-­‐Normal,
Gamma,
Binomial,...
EuroBasin training workshop – 26-28 October 2011 - Modelling the spatial distribution of fish: some key concepts and an application.

8. uncertainty
in
parameter
es1mates
and
model
fiKng
sta1s1cal
distribu1on
of
parameters
confidence
intervals,
sta1s1cal
significance
correlated
parameters
are
parameters
independent,
and
how
is
this
handled
by
the
modeling
method?
overparametrisa1on
and
overfiKng
number
of
parameters
vs.
number
of
independent
observa1ons
autocorrelated
observa1ons
spa1al/temporal
autocorrela1on
reduces
the
true
number
of
independent
observa1ons
metric
for
model
fiKng
performance
variance,
deviance,
likelihood,
AIC,
AUC,
GCV,...
EuroBasin training workshop – 26-28 October 2011 - Modelling the spatial distribution of fish: some key concepts and an application.

9. uncertainty
in
model
evalua1on
metric
for
model
predic1ve
performance
variance,
deviance,
likelihood,
AIC,
AUC,...
true
independence
of
the
valida1on
data
are
the
valida1on
data
correlated
with
fiKng
data?
EuroBasin training workshop – 26-28 October 2011 - Modelling the spatial distribution of fish: some key concepts and an application.

10. Addi1onal
considera1ons
Spa1al
scale
is
spa1al
scale
considered?
are
the
scales
of
observa1on
and
modelling
consistent?
adaptability
of
living
systems
complex
adap1ve
systems,
these
may
modify
their
behaviour
in
the
future,
surprise
is
to
be
expected
EuroBasin training workshop – 26-28 October 2011 - Modelling the spatial distribution of fish: some key concepts and an application.

11. Evalua1ng
uncertain1es
future
world
adaptation
Scale(s)
EuroBasin training workshop – 26-28 October 2011 - Modelling the spatial distribution of fish: some key concepts and an application.

12. Conceptual
models
EuroBasin training workshop – 26-28 October 2011 - Modelling the spatial distribution of fish: some key concepts and an application.

13. Null hypothesis / Geography
H0: no control
• Random spatial distribution,
• Not really plausible, but often use (implicitly) to test other
hypotheses
H1: geography
• Spatial distribution is determined by fixed geographical
coordinates (site attachment)
• This is usually not used unless no other hypotheses are
available
• It can be used as a null hypothesis for habitat control by
other factors
EuroBasin training workshop – 26-28 October 2011 - Modelling the spatial distribution of fish: some key concepts and an application.

14. H2:environment
• The habitat can be defined as the geographic
manifestation of the realized niche
• It may or may not be occupied by the species
Species abundance
Environmental gradient
habitat
EuroBasin training workshop – 26-28 October 2011 - Modelling the spatial distribution of fish: some key concepts and an application.

15. H3: density-dependent habitat selection
EuroBasin training workshop – 26-28 October 2011 - Modelling the spatial distribution of fish: some key concepts and an application.

16. spatial location
H3: density-dependent habitat selection
b
high
Habitat suitability
medium
low
The basin model
high
Local density
medium
low
spatial location
EuroBasin training workshop – 26-28 October 2011 - Modelling the spatial distribution of fish: some key concepts and an application.

17. H3: density-dependent habitat selection
• Recent evidence from Lake Windermere (UK) show
that pike fish moves between two basins as predicted
by DDHS
EuroBasin training workshop – 26-28 October 2011 - Modelling the spatial distribution of fish: some key concepts and an application.
Haugen et al. 2006.

18. H4: Spatial dependency
"… everything is related to everything else, but near things are more related than distant things”
Tobler, 1970
Sea Surface Temperature Chlorophyll Plaice
EuroBasin training workshop – 26-28 October 2011 - Modelling the spatial distribution of fish: some key concepts and an application.

19. H4: Spatial dependency
• Patterns of spatial distribution are explained by
spatial interactions between (groups of) individuals
such as attraction or repulsion
• It can be driven by many processes: spawning or
feeding aggregations, swimming capabilities, gamete
dispersal/retention
• It is often referred to as patchiness
EuroBasin training workshop – 26-28 October 2011 - Modelling the spatial distribution of fish: some key concepts and an application.

20. H4: Spatial dependency
EuroBasin training workshop – 26-28 October 2011 - Modelling the spatial distribution of fish: some key concepts and an application.

21. H5: Demographic structure
• Spatial distributions of individuals vary depending on
their size, age, sex or other individual traits
Anchovy length Lesser spotted dogfish
distribution Circles
diameter show
mean body
size of
anchovy
Females
Males
Planque et al. (2005)
EuroBasin training workshop – 26-28 October 2011 - Modelling the spatial distribution of fish: some key concepts and an application.

22. H6: species interactions
Balanus alone
Balanus
growth fundamental
rate niche
Chthamalus alone
Chthamalus fundamental niche
low middle high
Location in intertidal zone
EuroBasin training workshop – 26-28 October 2011 - Modelling the spatial distribution of fish: some key concepts and an application.

23. H7: memory
• The spatial distribution does not solely results from
instantaneous conditions but also from the
population’s history
– Imprinting (e.g. natal homing)
– Social learning (tradition)
– Individual memory (habit formation)
EuroBasin training workshop – 26-28 October 2011 - Modelling the spatial distribution of fish: some key concepts and an application.

24. the
conceptual
models
summarised
environmental
conditions
density
geographical
dependent
attachment
habitat selection
spatial
distribution
spatial
Persistence dependency
species demographic
interactions structure
EuroBasin training workshop – 26-28 October 2011 - Modelling the spatial distribution of fish: some key concepts and an application.

25. Environmental
gradients,
niches
and
models
Gradients Niches
• Resource • Fundamental
• Direct • Realised
• Indirect
Models
• Mechanistic
• Statistical
• Mixed
EuroBasin training workshop – 26-28 October 2011 - Modelling the spatial distribution of fish: some key concepts and an application.

26. Observa1ons,
data,
distribu1ons?
Observation process, scale & support
• How is the data collected?
• Trawl samples
• Sub-sampling
• Hydroacoustics
• Sampling design
• Random, stratified, transects,…
• Observation scale
• Distance between observations
• Observation support
• Volume/area sampled
EuroBasin training workshop – 26-28 October 2011 - Modelling the spatial distribution of fish: some key concepts and an application.

27. Observa1ons,
data,
distribu1ons?
Observation process, scale & support
What statistical distribution to choose?
• Continuous:
• Normal
• Log-Normal
• Gamma
• Discrete:
• Binomial, multinomial
• Poisson
• Negative binomial
EuroBasin training workshop – 26-28 October 2011 - Modelling the spatial distribution of fish: some key concepts and an application.

28. Count
observa1ons
versus
latent
density
distribu1on
Survey area Sampling unit
Trawl haul
Number of fish in haul=
draw from a binomial distribution
with mu= underlying density at the scale of the sampling unit
and ‘size’= underlying dispersion at the scale of the sampling unit
EuroBasin training workshop – 26-28 October 2011 - Modelling the spatial distribution of fish: some key concepts and an application.

29. An
example:
TrawlCatchModels.R
Context and data
• 9y of trawl sampling. Stratified random sampling. Bottom
trawl. Same location each year. 30’ at 3 knots. 25 x 5m
opening. Number of individual fish.
• Additional data on temperature and chlorophyll (surface)
and bottom topography
Hypotheses
• Fish spatial distribution is controlled by 1) temperature, 2)
chla, 3) bathymetry, 4) past distribution, or any
combination of the above
EuroBasin training workshop – 26-28 October 2011 - Modelling the spatial distribution of fish: some key concepts and an application.

30. An
example:
TrawlCatchModels.R
Analysis
• Plot your data: spatial & statistical distributions,
scatterplots
• Explore your data: spatial structures, temporal structures,
appropriate statistical distributions, sampling effects
• Model the spatial distributions: write model equations for
various hypotheses, fit models on a subset of the data and
predict the other
Interpretation
• Which models fit best? predict best? Which predictor
should be retained? How complex should the model be?
Projections
• Projections of future spatial distribution of fish density
• Projections of future survey results
EuroBasin training workshop – 26-28 October 2011 - Modelling the spatial distribution of fish: some key concepts and an application.

31. What
you
need
to
run
the
exercise
• R (2.13.2) • Data files:
• Librairies: • TrawlCatches_9199.txt
• fields (6.6.1) • depth.Rdata
• mgcv (1.7-8) • R code
• spatial (7.3-3)
• gstat (1.0-6)
• gamlss (4.1-0)
• gamlss.dist (4.0-5)
• gamlss.mx (4.0-4)
• plotrix (3.2-6)
EuroBasin training workshop – 26-28 October 2011 - Modelling the spatial distribution of fish: some key concepts and an application.

32. EURO-­‐BASIN,
www.euro-­‐basin.eu
Introduc)on
to
Sta)s)cal
Modelling
Tools
for
Habitat
Models
Development,
26-­‐28th
Oct
2011