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Combining Data in Species Distribution Models
Combining Data in Species Distribution Models
Bob O’Hara1 Petr Keil 2 Walter Jetz2
1BiK-F, Biodiversity and Climate Change Research CentreFrankfurt am MainGermany bobohara
2Department of Ecology and Evolutionary BiologyYale University
New Haven, CT, USA
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Combining Data in Species Distribution Models
Motivation
Map Of Life
www.mol.org/
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Combining Data in Species Distribution Models
The Problem
Different data sources
I GBIF
I expert range maps
I eBird and similar citizen science efforts
I organised surveys (BBS, BMSs)
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Combining Data in Species Distribution Models
Pointed Process Models
Point process representation of actual distribution
I Continuous space models
Build different sampling models on top
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Combining Data in Species Distribution Models
Point Processes: Model
Intensity ρ(ξ) at point s. Assume covariates (features?) X (ξ), anda random field ν(ξ)
log(ρ(ξ)) = η(ξ) =∑
βX (ξ) + ν(ξ)
then, for an area A,
P(N(A) = r) =λ(A)re−λ(A)
r !
where
λ(A) =
∫Aeη(s)ds
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Combining Data in Species Distribution Models
In practice...
Constrained refined Delaunay triangulation
λ(A) ≈N∑
s=1
|A(s)|eη(s)
Approximate λ(ξ) numerically:select some integration points,and sum over those
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Combining Data in Species Distribution Models
Some Data Types
I AbundanceI e.g. Point counts
I Presence/absenceI surveys, areal lists
I Point observationsI museum archives, citizen science observations
I Expert range maps
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Combining Data in Species Distribution Models
Abundance
Assume a small area A, so that η(ξ) is constant, and observationfor a time t, then n(A, t) ∼ Po(eµ(A,t)) with
µA(A, t) = η(A) + log(|A|) + log(t) + log(p)
where p is the proability of observing each indidivual.Don’t know all of |A|, t and p, so estimate an interceptCan also add a sampling model to log(p)
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Combining Data in Species Distribution Models
Presence/Absence for ’points’
As n(A, t) ∼ Po(µ(A, t)),
cloglogPr(n(A, t)) = µI (A, t)
with µI (A, t) as beforeAgain, can make log(|A|) + log(t) + log(p) an intercept
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Combining Data in Species Distribution Models
Presence only: point process
log Gaussian Cox ProcessLikelihood is a Poisson GLM (but with non-integer response)
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Combining Data in Species Distribution Models
Areal Presence/absence
If an area is large enough, we can’t assume constant covariates, so
Pr(n(A) > 0) = 1− e∫A eρ(ξ)dξ
in pracice this is calculated as
1− e∑
s |A(s)|eρ(s)
which causes problems with the fitting
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Combining Data in Species Distribution Models
Expert Range Maps
Not the same as areal presence.Instead, use distance to range asa covariate
I within range, this is 0.
I Have to estimate the slopefor outside the range
Use informative priors to forcethe slope to be negative 0 20 40 60 80 100
0.0
0.2
0.4
0.6
0.8
1.0
Space (1d)
Inte
nsity
Species'Range
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Combining Data in Species Distribution Models
Put these together with INLA
Quicker than MCMC
SolTim.res <- inla(SolTim.formula,
family=c('poisson','binomial'),
data=inla.stack.data(stk.all),
control.family = list(list(link = "log"),
list(link = "cloglog")),
control.predictor=list(A=inla.stack.A(stk.all)),
Ntrials=1, E=inla.stack.data(stk.all)$e, verbose=FALSE)
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Combining Data in Species Distribution Models
The Solitary Tinamou
Photo credit: Francesco Veronesi on Flickr(https://www.flickr.com/photos/francesco veronesi/12797666343)
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Combining Data in Species Distribution Models
Data
Whole RegionExpert rangePark, absentPark, presenteBirdGBIF
I expert range
I 2 pointprocesses (49points)
I 28 parks
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Combining Data in Species Distribution Models
A Fitted Model
mean sd mode
Intercept -0.30 0.09 -0.30b.PP 1.37 0.40 1.37
b.GBIF 1.43 0.26 1.43Forest -0.03 0.04 -0.03
NPP 0.15 0.05 0.15Altitude -0.02 0.04 -0.02
DistToRange -0.01 0.02 -0.01
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Combining Data in Species Distribution Models
Predicted Distribution
−0.10
−0.05
0.00
0.05
0.10
0.15
0.20
0.25
Whole RegionExpert rangePark, absentPark, presenteBirdGBIF
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Combining Data in Species Distribution Models
Individual Data Types
Expert Range
−10
−8
−6
−4
−2
0
GBIF−0.060
−0.058
−0.056
−0.054
−0.052
−0.050
−0.048
eBird−0.060
−0.058
−0.056
−0.054
−0.052
−0.050
−0.048
Parks
−10
−8
−6
−4
−2
0
all data
−0.10
−0.05
0.00
0.05
0.10
0.15
0.20
0.25
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Combining Data in Species Distribution Models
Summary
Parks and expert range seem to drive distributionNPP is main covariate, not forest or altitude
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Combining Data in Species Distribution Models
What Next
Multiple species
I already being done elsewhere
I estimate sampling biases
More Data
I Point counts (have it working)
Can we estimate absolute probability of presence?
I Distance sampling?
I Mark-recapture?
I scaling issues (in time and space)
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Combining Data in Species Distribution Models
Not the final answer...
http://www.gocomics.com/nonsequitur/2014/06/24