Modelling Spatial Distribution of fish, by Benjamin Planque

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

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

projec1ng spa1al distribu1ons

niche-‐based models

+

predicted spa1al

distribu1on

environment

biolog

ical re

spon

se

climate forecast/scenario


Why model the spa1al distribu1on of fish?

Interpolate between observations Project distributions under scenarios Understand processes that control distributions …multiple objectives


A general view of the modelling method

adapted from Anderson, 2010


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


uncertain1es in conceptual models

spatial distribution

geographical attachment

environmental conditions

density dependent

habitat selection

spatial dependency

demographic structure

Persistence

species interactions

Local density

spatial location

low

medium

high

Proportional Constant Basin

Local density

Habitat suitabili

ty

low

medium

high

low

medium

high

a

b

spatial location


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,...


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,...


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?


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


Evalua1ng uncertain1es

Scale(s)

adaptation

future world


Conceptual models


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


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

Environmental gradient

Spec

ies

abun

danc

e

habitat


H3: density-dependent habitat selection



Local density

spatial location

low

medium

high

Proportional Constant Basin

Local density

Habitat suitabili

ty

low

medium

high

low

medium

high

a

b

spatial location

The basin model



•  Recent evidence from Lake Windermere (UK) show that pike fish moves between two basins as predicted by DDHS

Haugen et al. 2006.


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



•  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




H5: Demographic structure

•  Spatial distributions of individuals vary depending on their size, age, sex or other individual traits

Planque et al. (2005)

Circles

diameter show

mean body

size of

anchovy

Females Males

Lesser spotted dogfish Anchovy length distribution


H6: species interactions

growth rate

Location in intertidal zone

low high middle

Chthamalus alone

Balanus alone

Balanus fundamental

niche

Chthamalus fundamental niche


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)


the conceptual models summarised

spatial distribution

geographical attachment

environmental conditions

density dependent

habitat selection

spatial dependency

demographic structure

Persistence

species interactions


Environmental gradients, niches and models

Gradients •  Resource •  Direct •  Indirect

Niches •  Fundamental •  Realised

Models •  Mechanistic •  Statistical •  Mixed


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


Observa1ons, data, distribu1ons?

Observation process, scale & support What statistical distribution to choose? •  Continuous:

•  Normal •  Log-Normal •  Gamma

•  Discrete: •  Binomial, multinomial •  Poisson •  Negative binomial


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


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


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


What you need to run the exercise

•  R (2.13.2) •  Librairies:

•  fields (6.6.1) •  mgcv (1.7-8) •  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)

•  Data files: •  TrawlCatches_9199.txt •  depth.Rdata

•  R code

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

Technology

Modelling Spatial Distribution of fish, by Benjamin Planque