Combining Data in Species Distribution Models Combining Data in Species Distribution Models Bob O’Hara 1 Petr Keil 2 Walter Jetz 2 1 BiK-F, Biodiversity and Climate Change Research Centre Frankfurt am Main Germany bobohara 2 Department of Ecology and Evolutionary Biology Yale University New Haven, CT, USA
Using point process models to combine different data types for species distribution models.
Slides for talk at ISEC 2014, presented on the 3rd July
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
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
Combining Data in Species Distribution Models
Motivation
Map Of Life
www.mol.org/
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)
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
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
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
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
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)
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
Combining Data in Species Distribution Models
Presence only: point process
log Gaussian Cox ProcessLikelihood is a Poisson GLM (but with non-integer response)
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
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