Statistical tools for European biodiversity risk assessment

Statistical tools for European biodiversity Statistical tools for European biodiversity risk assessmentrisk assessment

Adam Butler, Stijn Bierman, Glenn Marion Biomathematics & Statistics Scotland

With: Alex Cook & Gavin Gibson (Heriot-Watt), Ruth Doherty (Edinburgh), Ingolf Kuehn (UFZ), Phil Hulme (CEH)

22ndnd annual NCSE workshop, UKC, June 2007 annual NCSE workshop, UKC, June 2007

The ALARM projectThe ALARM project

• Assessing Large-scale risks to biodiversity with tested methods

• Project of the 6th framework programme of the European Union

• Runs from 2004-2009, involves 200+ scientists and social scientists, working in 67 organisations in 35 countries

• Main website: www.alarmproject.net

• BioSS is a partner, with three staff currently working on the project

Key objectives

• Develop an integrated risk assessment for biodiversity in

terrestrial and freshwater ecosystems at the European scale

• Focus on four key pressures – climate change, invasive species,

chemical pollution, pollinator loss – and their interactions

• Contribute to the dissemination of scientific knowledge and to

the development of evidence-based policy

Scenarios

Assessments relate to six scenarios of climate & land use change

• GRAS: deregulation, free

trade, growth, globalization

• BAMBU: “Business as might

be usual”

• SEDG: Sustainable European

Development Goal

• CUT: collapse of the

thermohaline circulation

• SEL: energy price shock,

mass growth in biofuels

• DEATH: global pandemic

The role of BioSS

• Research-consultancy: develop & apply novel quantitative

methods to support scientific research within ALARM

• Training: Development of an online training course on statistical

methods for environmental risk assessment

• Dissemination: Contribute to the construction of a risk

assessment toolkit for European biodiversity

Research themes

1 Statistical analysis of species atlas data

2 Quantification of uncertainty in complex mechanistic models

3 Elicitation of expert opinion regarding environmental risk

Species atlas dataSpecies atlas data

mean annual temperature (1960-1990)(degrees centigrade)

>18

16-18

14-16

12-14

10-12

<10

Galium pumilum (slender bedstraw) Mean annual temperature 1960-1990 (oC)

Species atlas data record the presence/absence of species, for each cell

on a regular grid – e.g. Florkart database of German vascular plants

• Atlas data are often used to analyze relationships between

environmental variables & the spatial distribution of a

particular species

• Aim is often predictive:

e.g. climate envelope modeling

• Crude statistical analyses are based on multiple regression

• Analyses should be modified to account for spatial

autocorrelation & non-detection

Distribution of individual species

Spatial autocorrelation

Zi = I(species present in cell i)

xi = covariates for cell i

dij = distance between cells i and j

Autologistic model (Augustin et al., 1996)

iii nZ xP ),,|1(logit

Bierman, S.M., Wilson, I.J., Elston, D.A., Marion, G., Butler, A. & Kühn, I. (in preparation) Bayesian image restoration techniques to analyze species atlas data with spatially varying non-detection probabilities.

Zi is a latent random variable

ii Nj ijNj ij

ji dd

Zn

1

Mit = 1 if Oit =1

Mit = 0 or 1 if Oit = 0

set up Markov chain Monte Carlo sampler on Mit such that Oit = 0/1;

Non-recording

yi = I(species recorded present in cell i)

zi = I(species actually present in cell i); a

latent random variable

Prior

iii yzy

i

iii y

zzy

1,|P

ByzAyii

iiizyBA 1,,,|P

Bierman, S.M., Wilson, I.J., Elston, D.A., Marion, G., Butler, A. & Kühn, I. (in preparation) Bayesian image restoration techniques to analyze species atlas data with spatially varying non-detection probabilities.

BABA

BABA

1),|(

,Beta~,|

P

Likelihood

Posterior

<0.05

0.5

1

a Galium pumilum

<0.05

0.5

1

b Papaver argemone

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control group

a

1 2 3 4 5 6 7 8 9

05

00

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20

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control group

nu

mb

er

of g

rid

ce

lls

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Galium pumilum (slender bedstraw)Detection effort

insect

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N

xx x x x xx x x x xx xx x x x x x x x x

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x x x x xx

c

d e

low

medium

high

proportion of

poll. types/

wind speed

0 - <75

75 - <150

150 - <300

300 - <450

450 - <600

600 - <900

900 - <1200

1200 - <1500

1500 - <2100

>= 2100

topography:

altitudes

Distribution of functional traits

Pollination types in Germany

Kühn, I., Bierman, S.M., Durka, W. & Klotz, S. (2006) Relating geographical variation in pollination types to environmental and spatial factors using novel statistical methods. New Phytologist, 172(1), 127-139.

Spread of invasive species

• Species atlas data for invasive species may also contain information on time of arrival, establishment or naturalization

• We can, with care, use such data to draw inferences about the spatio-temporal spread of a species across a landscape, and thereby to assess the risks associated with future expansion

• Need to deal with environmental heterogeneity: land use & climate

By 1910

Spread of Giant Hogweed (Spread of Giant Hogweed (Heracleum MantegazzianumHeracleum Mantegazzianum))

Data : Data : National Biodiversity NetworkNational Biodiversity Network

By 1920



By 1930



By 1940



By 1950



By 1960



By 1970



By 1980



By 1990



By 2000



• Dispersal rate modelled using a symmetric power law kernel:

• Arrival rate is treated as additive

• Colonization rate

Dispersal modelled using symmetric power law kernel

Colonization suitability for each site a function of Land-cover & Climatic covariates

Key methodological challenge: estimate covariate effects

Cook, A., Marion, G., Butler, A. and Gibson, G. (2007). Bayesian

inference for the spatio-temporal invasion of alien species.

Bulletin of Mathematical Biology, in press.

dji = distance from cell i to cell j xi = covariates for cell i

Ni = neighborhood of cell I Ti = year of colonization

)()()( tSt iiii x

iji TTNjjii tt

,

)()(

22)( jii dt

• Extend previous work by inclusion of “suitability”, S(xi)

Colonization suitability

Colonization probability: 10 year prediction

Posterior meanPosterior mean

Cook, A., Marion, G., Butler, A. and Gibson, G. (2007)

Cumulative rate of colonization

Cook, A., Marion, G., Butler, A. and Gibson, G. (2007)

with covariates

without covariates

• Deal with inhomogeneities in the recording process:

e.g. could analyse as three atlas surveys

• Allow for decolonisation

• Allow for time-varying covariates: e.g. land use change

Further work

Complex modelsComplex models

• Complex mechanistic models provide a valuable tool for

generating projections of large-scale environmental change

• Models are typically deterministic, but with uncertain inputs

(parameter values, initial values & boundary conditions)

• Models are evaluated across a regular spatio-temporal lattice

• Model outputs tend to exhibit systematic bias, e.g. because

sub-gridscale processes are not represented

• Use the Lund-Potsdam-Jena dynamic vegetation model to generate projected trends in global vegetation for the 21st century

• Control run: use climate inputs provided by observational data

• Other runs: inputs provided by simulations from one of nine General Circulation Models

Scenario SRES A2

“A future world of very rapid economic growth, low population growth

and rapid introduction of new and more efficient technology. Major underlying themes are economic and cultural convergence and capacity building, with a

substantial reduction in regional differences in per capita income. In this world, people pursue personal wealth rather than environmental quality…”

Doherty, R., Butler, A. & Marion, G. (in prep.) title to be decided

Data: PCMDI (www-pcmdi.llnl.gov), CRU (www.cru.uea.ac.uk)

Global annual net primary productivity

“Net

primary production is the rate at which

new biomass

accrues in an

ecosystem”

(Wikipedia)


Statistical post-processing

• Regression (Allen et al., 2002):

x = mM mym + e

• Hierarchical Bayesian modeling (Tebaldi et al., 2005):

Model each of x and y1,…,y|M| as independent realisations of “reality”, which

is a latent variable,

• Bayesian model averaging (Raftery et al., 2005):

f(x) = mM wm g(ym)

g(ym) estimated from a simple statistical model

ym = output from model mM

x = corresponding data

1) Assign weights w1,…,w|M|

Butler, A., Marion, G. & Doherty, R. (in prep.) Statistical averaging of

long-term projections generated by a set of environmental models




2) Calculate zm = ym - x






2) Calculate zm = ym – x

3) Fit a set of possible statistical models, hn(zm), where nN








4) Apply a simple form Bayesian model averaging,

gm(zm) = mM vn hn(zm),

where vn exp(-BICn / 2)








4) Apply a simple form Bayesian model averaging,

gm(zm) = nN vn hn(zm),

where vn exp(-BICn / 2)

5) Apply a second level of model averaging,

f(x) = mM wm gm(ym – x)





Statistical methods: an overview

Single deterministic model

SACCO: Statistical Analysis of Computer Code Output

Single stochastic model

ABC: Approximate Bayesian Computation

Multiple deterministic models

Statistical post-processing

SACCO methodsR bundle: http://cran.r-project.org/src/contrib/Descriptions/BACCO.html

Generate a set of ensembles, y(1),…, y(M)

Emulation: construct a statistical model, (), which describes the relationship between inputs & outputs – a basis for interpolation

Calibration (Kennedy & O’Hagan, 2001): relate output to reality, via x = () + () + e, where and are Gaussian processes

y() = output from model given inputs


ABC methods

Assign informative prior distribution () to parameters

Simulate from the prior, m ~ (), and then model, y(m) ~Y(m)

Accept m if any only if

D(y(m), x) <

where D is a suitable distance metric and is small

Samples from an approximation to the posterior of |x,Y

Y() = output from model given inputs


Integrated risk assessmentIntegrated risk assessment

• One of the key tasks of ALARM is to produce a risk assessment

toolkit (RAT) for European biodiversity

• The RAT requires us to link detailed, often quantitative, scientific

assessments about risk with the requirements of policy-makers

• This involves the integration of observational data, output from

mechanistic models, and expert knowledge

A process of representing expert beliefs and opinions

about the properties of a system in the form of one or

more probability distributions

“The goal of elicitation, as we see it, is to make it as easy as possible for subject-matter experts to tell us what they believe, in probabilistic terms, while reducing how much they need to know about probability theory to do so…”

(Kadane & Wolfson, 1998)

Expert elicitation

The elicitation process

Kadane & Wolfson (1998), O’Hagan (1998)

Elicit basic quantities: means, quantiles

Produce a graphical representation

Fit a statistical model

Negative feedback Negative feedback

Potential dangers

Availability

Overconfidence

Anchoring

Inconsistency

Hindsight bias

Principles

Focus on observables

Quantiles rather than moments

Avoid tail probabilities

Focus on prediction

Interactive process

• Within ALARM, we are assisting Koos Biesmeijer (Leeds) in using expert opinion to identify the primary cause of decline in threatened European bee species

Habitat lossIntrinsic factors

Climate change

Native species dynamics

Low densitiesRestricted range

Resource changes:Host plantsHosts (cleptoparasitic bees)

Primary threat: species on UK red list

Threats to Bees

Potential threats

Statistical tools for European biodiversity risk assessment

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