Species distribution models:where do we head for?

Munemitsu AKASAKANIES postdoctoral fellowNational Institute for Environmental Studies

First ASIAHORCs Joint Symposium: Topics in current trends

Predicted occurrence

What are species distribution models?-Empirical models that relate field observationof a species to environmental predictorsbased on statistically or theoretically derivedresponse surface. (Guisan & Zimmermann 2000)

http://ja.wikipedia.org/

Observation

+Environmental data

Distribution model

•To identify the core area for conservation

•Prediction of the response of species to environmental change

Why modeling species distribution ?

Prediction Y = f(aX1 + bX2 + cX3 …+ d)Inference

•To understand the environmental factor responsible for the distribution

An example of species distribution modeling

Syartinilia & Tsuyuki (2008)Biological conservation 141: 756-769

flickr.com

logit(Pr) = 0.23*slope – 0.01*elevation + 0.02*NDVI

+ 19.80AUTOCOV – 6.86

Pro

b.

Target: Spizaetus bartelsiJavan Hawk-Eagle (Threatened)

Overview the recently developed methods on distribution modeling from end users' perspective

Provide an idea abouthow does the distribution modeling contribute to evaluation and conservation of biodiversity

Purpose of this talk:

This talk will…

Recent developments have overcome several limitations of the conventional methods!

•Complex non-linear response of species

•Presence-only (occurrence) data

Types of data that would bother ecologists/biodiversity managerswhen bulding generalized linear models.

•Data with spatial autocorrelation

•Non-equilibrium distribution of species

•Interaction among predictor variables

•Observer bias

•Count data with lots of zero …

Why complex non-linear response is troublesome ?

Y = -0.8x + 13.5Y = -0.1x2 + 0.6x +11.2Y = 0.001x3 -0.2x2 +

0.7x +11.2・・・

Unable to represent the relationship properly by OLS or GLM !!

GAM, CART (, BRT, BCT)

Y = 1.9x + 3.4

Soil moisture

Sp

ec

ies

ab

un

da

nc

e

Coping with complex non-linear response: GAM

GAM : Generalized Additive Model

Y =Σ f(x) + c

Strength:•Capable of fitting to complex response

Limitation:•Sensitive to outlier

•Smoothing by non-linear function(e.g. spline, lowess)

Water temperature

Ab

un

da

nc

eo

f fi

sh

Example on implementation of GAM Fukushima et al. 2007Freshwater Biology 52:1511-1524

Years since dam construction

Logi

t(Pro

b. O

ccur

.)

Masu salmonWhitespotted char

•Using compiled database: apporx. 8000 fish surveys•Examined the influence of dam construction on occurrence of 41 fish taxa•Non-linear relationship between fish occurrence

and years after dam construction

Example on implementation of GAM Fukushima et al. 2007Freshwater Biology 52:1511-1524

Predicted impact of dam construction

Coping with complex non-linear response: CART

CART: Classification And Regression Tree

•Creates split-nodes to maximize the reduction in impurityStrength:

•Visually understandable output•robust to outlier•Inherent incorporation of interactions within the predictors

Limitation:Requires sufficient number of data

Name Tape of response variable

Classification Tree  Categorical

Regression Tree Numerical

x

y

Boosted Regression Tree : BRTBoosted Classification Tree: BCT( )

Coping with complex non-linear response: CART

CART: Classification And Regression Tree

•Creates split-nodes to maximize the reduction in impurityStrength:

•Visually understandable output•robust to outlier•Inherent incorporation of interactions within the predictors

Limitation:Requires sufficient number of data

x

y

Boosted Regression Tree : BRTBoosted Classification Tree: BCT( )

•complex non-linear response of species

•presence-only (occurrence) data

Data to be modeled:

•data with spatial autocorrelation

•non-equilibrium distribution of species

Presence only data: A type of data that lacks the informationwhere the species is absent.

Presence-only data are often found …

•Occurrence of highly mobile animals/insects •Opportunistically collected data•Museum or herbarium –records…

Absences cannot be inferred with certainty!

-Recursively sample the absence from backgroundMAXENT, GARP

- use presence data only BIOCLIM, DOMAIN, LIVES

For methods requiring absence

Occurrence record

Pseudo-absence(selected randomly)

No data

Evaluation of predictive performance on presence-only data

Wisz et al. 2008 Diversity and distributions 14: 763-773 Fig.3 (modified)

•Data: Non-systematically sample presence-only data41 species from 5 regions (birds, small vertebrates, and plants)

10010 30Sample size

Pre

dic

tive

pe

rfo

rma

nc

e(M

ed

ian

AU

C)

0.5

0.7

Low

HighGBM

MaxEnt

GLM

GAM

GARP

DOMAIN

BIOCLIM

LIVE

-p

-p

-p

-b

-b

-o

-o

-o

Method Principle*

*-p: pseudo absence-b: background sample-o: only presence

MaxEnt : Maximum Entropy modeling

•Recursively sample absence data from background

Strength:

• Capable of handling presence-only data• Can model complex non-linear responses• Capable of good prediction from small sample size

Limitation:

•Requires high computational power

Coping with presence-only data: MaxEnt

Example on implementation of MaxEnt

Study area: Hakone (National Park)Target: Rudbeckia laciniata (invasive)

*Invaded to Hakone ca. 2000.

Akasaka & Osawa (unpubl.)

To exterminate R. laciniataWhat landscape factor is related to their distribution?ProblemBecause this species have recently invaded to our study area, we only had32 observational records….

Known occurrence:32 sites

Road density Urban areadensity

Solar radiation TWI

Example on implementation of MaxEnt

Study area: Hakone (National Park)Target: Rudbeckia laciniata (invasive)

*Invaded to Hakone ca. 2000.

Akasaka & Osawa (unpubl.)

Prob

. Occ

ur.Known occurrence:

32 sites

Road density Urban areadensity

Solar radiation TWI

AUC=0.88

A

Example on implementation of MaxEnt

Kadoya et al. 2009Biological Conservation 142: 1011-1017

Target: Buff-tailed bumblebee(invasive)Bombus terrestris

•Proportion of woodland

PresentNo data

0 50 100 150 20025

km

.

0.0-

0.5-

Prob

. Occ

ur.Species occurrence:

volunteer gathered data

Potential distribution

•Water channel length•Tomato production

Proportion of woodlandWater channel lengthTomato production

+

AUC=0.813

•complex non-linear response of species

•presence-only (occurrence) data

Data to be modeled:

•data with spatial autocorrelation

•non-equilibrium distribution of species

Spatial autocorrelation?-nearby sites are similar

Present

Absent

Spatially autocorrelated

Spatially random

Spatial autocorrelation?

Models correcting for spatial autocorrelation (CAR, SAR…)

-nearby sites are similar

•Distance-related biological process (e.g. dispersal, facilitation)•Unmeasured important environmental factor•etc..

Caused by…

Data points can not be regarded as mutually independent!

Present

Absent

Spatially autocorrelated

Conditional autoregressive models (CAR)

Y = f(Xβ + ε)Explanatory variablesCorrelation coefficientsError

Spatial random effect: composed of the information on the response variable in the neighboring cells.

•Relatively well used in in the field of Ecology

Dormann et al. 2007 Ecography

+ ρW(Y - Xβ)

Example on implementation of CAR

Ishihama , Takeda, Oguma, & Takenaka (unpubl.)

Target: adder’s tongue fern (endangered) Ophioglossum namegatae

Max. grass heightRelative elevationPixel value of air photos

Predictor variables

Logistic (DIC= 799) CAR (DIC = 51)

Distribution data:

+presentabsent

Prob

. occ

urre

nce

High

Low

•complex non-linear response of species

•presence-only (occurrence) data

Data to be modeled:

•data with spatial autocorrelation

•non-equilibrium distribution of species

Static modeling to dynamic

Most of the species distribution models:included only abiotic environments as the predictor

Such models implicitly assume…•Abiotic factors are the primary determinants•The species have (nearly) reached equilibrium

If violated…

•Low predictive power•Poor characterization of the environmental response

×e.g. invasive species, species responding to changing environments

Include variable related to dispersal as a predictor

More detailed process-based model

Example of detailed process-based distribution model

Fukasawa et al. (in press)Ecological Research Target: Bishop wood (invasive)

Bischofia javanica

1977 2003Dispersal source Current distribution

Distribution Abiotic environments

•Elevation•Summit plane

elevation•Slope•Curvature•Watershed area•Skyline

Simultaneousmodel

( )

( )( ) ( )ZXX

qpy

nn

γββα

−×+++−+

=

×==

expexp1

11Pr

11 L

Logistic regression model: evaluate habitat suitabilityColonization kernel: evaluate seed dispersal

Simultaneous model

Example of detailed process-based distribution model

Fukasawa et al. (in press)Ecological Research Target: Bishop wood (invasive)

Bischofia javanica

Logisticmodel

Colonizationkernel

Simultaneousmodel

Example of detailed process-based distribution model

Fukasawa et al. (in press)Ecological Research Target: Bishop wood (invasive)

Bischofia javanica

•Recently developed methods and approach can deal with the limitations of OLS and GLM

Character of data Modeling method & approach

Complex non‐linear response of species

GAM, CART, (BRT, BCT )

Presence‐only data MaxEnt …

Non‐equilibrium distribution•Detailed process‐basedmodeling

Spatially autocorrelated data•Models to correcting for spatial autocorrelation (e.g. CAR)

Summary

Application of the introduced models

Modeling method R library Other free application

GLM: generalized linear models

base

GAM: generalized additive models

gam, mgcv

CART: classification and regression trees

tree, rpart

GBM: generalized boostedmodels

gbm

MaxEnt: Maximum entropy model

‐ MaxEnt software

CAR: conditional autoregressive 

modelsspdep WinBUGS

Freely available language and environment for statistical computing and graphics

http://cran.r-project.org/

Toward evaluation and conservation of biodiversity

2. To develop a sensible model …

Characteristics of the distribution data, sample size, and ecology of the target organism should be considered

3. Distribution model has increased its role in biodiversity conservation

1. Abundance and species richness can also be modeled by similar modeling methods

Process-based model

Let’s build distribution models together!!

Acknowledgements

Dr.Taku KADOYADr. Fumiko ISHIHAMAMr. Keita FUKASAWAMr. Takeshi OSAWADr. Akio TAKENAKAMr. Ehab salah

JSPSOrganizing committee

of ASIAHORCs Joint Symposium

Thank you for listening!