BES/SfE talk 2014

A unified framework to combine disperate data types in species distribution modelling

A unified framework to combine disperate datatypes in species distribution modelling

Slides on Slideshare:http://www.slideshare.net/oharar/bessfe-talk-2014

Bob O’Hara1 Petr Keil 2 Walter Jetz2

1BiK-F, Biodiversity and Climate Change Research CentreFrankfurt am Main

GermanyTwitter: @bobohara

2Department of Ecology and Evolutionary BiologyYale University

New Haven, CT, USA


A ”Real” Curve

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A Curve


Approximated with a Discretised Curve

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A CurveDiscrete


Better: linear interpolation

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A CurveDiscreteInterpolated


With more points, the approximations improve

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A CurveDiscreteInterpolated


What does this have to do with distribution models?


What does this have to do with distribution models?

This is how SDMs see the world:

source: http://bit.ly/1l8sG7M

Map produced by Peter Blancher, Science and Technology Branch, Environment Canada, based on data from the

North American Breeding Bird Survey


DiscretionProjected maps look like this:

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Can we be less discrete?This might be better:

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Point Processes: Model

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Model of where individuals are Ahigher intensity means moreindividuals


Pointless Processes?

How do we use this approach?


Need to use talk about sausage

Lincolnshire Sausage! by Caro Wallis, https://www.flickr.com/photos/carowallis1/806455819


Point processes

Represent density by a surface, with intensity λ(s)Number in area A follows Poisson distribution with mean µ(A):

µ(A) =

∫Aλ(s)ds

Raw Blood Sausage by Carlos Lorenzo, https://www.flickr.com/photos/carlos lorenzo/447670758


Intense Models

Model the expected density through the intensity:

log(λ(s)) =∑

βjXj(s) + ν(s)

Xj(s) are covariates (also continuous in space)ν(s) is a residual spatial term

Gastrocast #91 by Neal Foley, https://www.flickr.com/photos/86571141@N00/345595467


Point Processes: Model

In practice, approximate the surface with triangles


How about the data?

Pig faces by Karen,

https://www.flickr.com/photos/unsureshot/167930176

Presence only points: thinnedpoint processAbundance: PoissonPresence/Absence: binomial,cloglog(large) areas:

Pr(n(A) > 0) = 1− e∫A eρ(ξ)dξ


Abundance to Presence

N ∼ Poisson(λ)

so

Pr(N > 0) = 1− Pr(N = 0) = 1− λ0exp(−λ)0!

= 1− exp(−λ)

or

cloglog(Pr(N > 0)) = log(λ)

i.e. we just use a GLM with a cloglog link function


Fitting models in PracticeNeed a sausage grinder

Fat Grinder by Danielle Harms,

https://www.flickr.com/photos/daniellemharms/5597688960

R + INLA


An Example

Data from MoL

Picus tridactylus by Biodiversity Heritage Library,

https://www.flickr.com/photos/biodivlibrary/9514435393


Data

eBird GBIF (not eBird)

BBS Expert Range


We run the model

Sausage machine by clement127, https://www.flickr.com/photos/clement127/15004844674


Predicted Distribution

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Predicted Distribution from Each Data Set

All Data

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eBird

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GBIF

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We can make a better sausage

Combining data is betterDon’t lose positional informationBut still have to approximate a surface

Nakki by hugovk, https://www.flickr.com/photos/hugovk/27828598


We can make a better sausage

Great Marbling! by Gabriel Bucataru, https://www.flickr.com/photos/gabstero/4660842166

BES/SfE talk 2014

Science

disperate data types

ed framework

distribution models

disperate datatypes

follows poisson distribution

intensity snumber

ahigher intensity

expected density