This document discusses combining different types of species occurrence data in species distribution models. It describes point process models that can incorporate presence-only data, abundance data, expert range maps, and citizen science observations. These different data sources are combined and fit using integrated nested Laplace approximations (INLA) to predict distributions for a case study of the solitary tinamou. The results show that expert range maps and citizen science data drive the predicted distribution, with net primary productivity being the most important environmental covariate over forest cover and altitude.

1. 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 Centre
Frankfurt am Main
Germany bobohara
2Department of Ecology and Evolutionary Biology
Yale University
New Haven, CT, USA

2. Combining Data in Species Distribution Models
Motivation
Map Of Life
www.mol.org/

3. Combining Data in Species Distribution Models
The Problem
Different data sources
GBIF
expert range maps
eBird and similar citizen science efforts
organised surveys (BBS, BMSs)

4. Combining Data in Species Distribution Models
Pointed Process Models
Point process representation of actual distribution
Continuous space models
Build different sampling models on top

5. Combining Data in Species Distribution Models
Point Processes: Model
Intensity ρ(ξ) at point s. Assume covariates (features?) X(ξ), and
a random field ν(ξ)
log(ρ(ξ)) = η(ξ) = βX(ξ) + ν(ξ)
then, for an area A,
P(N(A) = r) =
λ(A)r e−λ(A)
r!
where
λ(A) =
A
eη(s)
ds

6. 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

7. Combining Data in Species Distribution Models
Some Data Types
Abundance
e.g. Point counts
Presence/absence
surveys, areal lists
Point observations
museum archives, citizen science observations
Expert range maps

8. Combining Data in Species Distribution Models
Abundance
Assume a small area A, so that η(ξ) is constant, and observation
for 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 intercept
Can also add a sampling model to log(p)

9. 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 before
Again, can make log(|A|) + log(t) + log(p) an intercept

10. Combining Data in Species Distribution Models
Presence only: point process
log Gaussian Cox Process
Likelihood is a Poisson GLM (but with non-integer response)

11. 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

12. Combining Data in Species Distribution Models
Expert Range Maps
Not the same as areal presence.
Instead, use distance to range as
a covariate
within range, this is 0.
Have to estimate the slope
for outside the range
Use informative priors to force
the slope to be negative 0 20 40 60 80 100
0.00.20.40.60.81.0
Space (1d)
Intensity
Species'
Range

13. 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)

14. Combining Data in Species Distribution Models
The Solitary Tinamou
Photo credit: Francesco Veronesi on Flickr
(https://www.flickr.com/photos/francesco veronesi/12797666343)

15. Combining Data in Species Distribution Models
Data
Whole Region
Expert range
Park, absent
Park, present
eBird
GBIF
expert range
2 point
processes (49
points)
28 parks

16. Combining Data in Species Distribution Models
A Fitted Model
mean sd mode
Intercept -0.30 0.09 -0.30
b.PP 1.37 0.40 1.37
b.GBIF 1.43 0.26 1.43
Forest -0.03 0.04 -0.03
NPP 0.15 0.05 0.15
Altitude -0.02 0.04 -0.02
DistToRange -0.01 0.02 -0.01

17. 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 Region
Expert range
Park, absent
Park, present
eBird
GBIF

18. 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

19. Combining Data in Species Distribution Models
Summary
Parks and expert range seem to drive distribution
NPP is main covariate, not forest or altitude

20. Combining Data in Species Distribution Models
What Next
Multiple species
already being done elsewhere
estimate sampling biases
More Data
Point counts (have it working)
Can we estimate absolute probability of presence?
Distance sampling?
Mark-recapture?
scaling issues (in time and space)

21. Combining Data in Species Distribution Models
Not the final answer...
http://www.gocomics.com/nonsequitur/2014/06/24