Species Distribution Models: a tool for studying the ecology, evolution,

and conservation of biodiversity

Margaret E. K. EvansDepartment of Ecology & Evolutionary Biology, Yale Institute for Biospheric Studies, Yale University, U. S. A.

Ecole Normale Superieure and Museum National d’Histoire Naturelle, Paris, France

Collaborators:Stephen Smith, Michael Donoghue, Kent Holsinger,Eric Menges, Sean McMahon, Jeff Diez, Andrew Latimer

Outline

1. What are species distribution models?

2. How are they made?

3. What are they used for?

4. How can they be improved?

Ecological niche models

Environmental niche models

Climatic niche models

Habitat modeling

Climate envelope models

Bioclimatic envelope models

Bioclimatic modeling

Predictive distribution models

Predictive habitat models

Etc…

many names…

Species Distribution Models

Georeferenced locality data

+

Environmental layers

source of locality datae.g. museum specimen

climate data (temperature, precipitation), soil type, land use, fire history, etc.

Predicted species distribution

algorithm

Where the species is

What the environment is like there

Where you should find the species on the landscape

Species Distribution Models

Many Algorithmsrecipes for associating locality data & environmental data

Climate envelope models

Genetic Algorithm

GLM, GAM models (generalized linear models, generalized additive models)

(BIOCLIM in DIVA-GIS)

(GARP)

Maximum entropy (Maxent)

Disciminant analysis, classification tree analysis

Artificial neural networks

Hierarchical Bayesian models

Many Algorithmsrecipes for associating locality data & environmental data

Climate envelope models

Genetic Algorithm

GLM, GAM models (generalized linear models, generalized additive models)

(BIOCLIM in DIVA-GIS)

(GARP)

Maximum entropy (Maxent)

Disciminant analysis, classification tree analysis

Artificial neural networks

Hierarchical Bayesian models

Climate envelope modelse.g. BIOCLIM in DIVA-GIS

mean annual temperature

the range of values where the species is found= climate envelope

19 climate envelopes…the 19 Bioclim variables:

Bioclim 1 = annual mean temperatureBioclim 2 = mean monthly T rangeBioclim 3 = isothermality...

Climate envelope models (BIOCLIM in DIVA-GIS)

annual mean temperature

climate envelope

Those pixels that fall within the “climate envelope” are assigned a high probability of having the species

Many Algorithmsrecipes for associating locality data & environmental data

Climate envelope models

Genetic Algorithm

GLM, GAM models (generalized linear models, generalized additive models)

(BIOCLIM in DIVA-GIS)

(GARP)

Maximum entropy (Maxent)

Disciminant analysis, classification tree analysis

Artificial neural networks

·Performed well in the NCEAS “bake-off”

Hierarchical Bayesian models

the NCEAS “bake-off”

Compared: Bioclim, BRT, BRUTO, dk-GARP, DOMAIN, GAM, GDM, GDM-SS, GLM, LIVES, MARS, MARS-COMM, MARS-INT, Maxent, Maxent-T, om-GARP

Maxent was a top performer

NCEAS = National Center for Ecological Analysis and Synthesisin Santa Barbara, California, sponsored by the National Science Foundation

log(response) = β1*feature1 + β2*feature2 + … + β19*feature19

“features” are the environmental layers:

Bioclim 1 = annual mean temperatureBioclim 2 = mean monthly T rangeBioclim 3 = isothermality...Bioclim 19

for each pixel:

Maxent generates a probability distribution…

•with maximum entropy•subject to the constraint that the predicted mean climate matches the empirical average

for each pixel:

Maxent generates a probability distribution…

•with maximum entropy•subject to the constraint that the predicted mean climate matches the empirical average

log(response) = β1*bioclim1 + β2*bioclim2 +…+ β19*bioclim19 + β20*(bioclim1)2 + β21*(bioclim2)2 + … + β39*bioclim1*bioclim2 + …

The response is a probability…a number between 0 and 1The sum of these probabilities across the prediction landscape is 1.0

that is, the prediction takes the form of a probability distribution…

Probability Distribution -predicted suitability of the landscape

Maxent output

cumulative probability of occurrence

sum of the probabilities ≤ a threshold…≤ 0.01, ≤ 0.02, ≤ 0.03, etc.…rescales probabilities from zero to one

Outline

1. What are species distribution models?

2. How are they made?

3. What are they used for?

How will biodiversity be affected by climate change?

15-37% of species “committed to extinction”by climate change

Species Distribution Models

Species Distribution ModelsDo parks and reserves retain their species in the face of climate change?

Species Distribution ModelsWhat are they used for?

How is current species diversity shaped by paleoclimate?

Species Distribution ModelsWhat are they used for?

To study niche conservatism…

Species Distribution ModelsWhat are they used for?

How much niche evolution accompanies speciation?

To study niche evolution…

phylogeography, speciation, evolution of traits

Tomorrow: Climate, niche evolution, and diversification ofevening primroses

with Michael Donoghue, Stephen Smith

Outline

1. What are species distribution models?

2. How are they made?

3. What are they used for?

4. How can they be improved?

Species Distribution Models

Statistical associations between occurrences and climate suffice to predict response to climate change

assumption

Species Distribution Models

the next generation of models predicting responses to climate change…process-based modeling

with Kent Holsinger and Eric Menges

Sean McMahon, Jeff Diez, Andrew Latimer

…Process-based modeling

processes that we know give rise to patterns of abundance and spatial distribution

demography

migration

metapopulation dynamicsphenology

biotic interactions

…missing from niche models, necessary for non-equilibrium forecasting

evolution

…Process-based modeling

a variety of approaches (plant-oriented)

Plant population modeling

Vegetation modelingClimate-vegetation modelsDynamic global vegetation models (DGVMs)

Population viability analysis

Spatially-explicit simulations modelsindividual-based models, cellular automata models, gap models

Metapopulation models

Plant functional type models

Phenological models

Diffusion/migration/invasion models

Population Viability of the rare plant Dicerandra frutescens,

a hierarchical Bayesian analysisMargaret Evans, Kent Holsinger , Eric Menges

Fire Ecology Dicerandra frutescens is specialized to gaps created by fire

those gaps close with time-since-fire

Population Viability Analysis is…a quantitative analysis of population dynamics

with the goal of assessing extinction risk

DemographicData

MathematicalAnalysis

Prediction ofextinction risk

•survival and fertility of marked individuals•population size over time•birth and death rates

•matrix model•time series analysis•branching process•stochastic birth-death process•reaction-diffusion equation

•population growth rate (λ)•extinction probability•time to extinction•future population size or structure

Step 1: Estimate parameters from data

MathematicalAnalysis

•estimate vital rates from data•including the effect of time-since-fire on vital rates

DemographicData

Prediction ofextinction risk

•20 years of data from marked individuals in 5 populations

Evans, Holsinger and Menges. 2008. Population Ecology.

Step 1: Estimate parameters from data

MathematicalAnalysis

•estimate vital rates from data•construct a model that reflects factors affecting demography•simulation of population growth

DemographicData

Prediction ofextinction risk

Step 2: Simulate population growth

•probability of extinction

Life cycle of Dicerandra frutescens

n(t+1) = A(t) · n(t)

vector vectormatrix

seedbank vegetative

mediumfloweringseedling

smallflowering

largeflowering

sb

veg

mf

sdlg

sf

lf

sb veg mfsdlg sf lf

0

0

0.636

0.182

3.809

651.9

0

0

0.667

30.55

0.167

0.178

0.2

0.067

0.113

0.333

0.333

19.280

0

0.2

0.4

0.12

0.04

0

0

0

0.2

0.2

0.2

0.1

0.001

0

0

0

0 25

15

11

6

5

200

16

9

13

12

45

7,663

time ttime t+1

= x

n(t+1) = A(t) · n(t)

vector vectormatrix

Bayesian hierarchical model

estimates vital rates as a function of time-since-fire

directed acyclic graph (DAG)

boxes = data

circles = parameters

Use samples from posterior distributions of parameters for simulations

flowering branches regression

ln(fl

ower

ing

bran

ches

) symbols = data

lines = model estimates of slope, intercept

joint posterior distribution of slope, intercept

Use samples from joint posterior distribution for simulations of population dynamics

Probability of quasi-extinction, as a function of fire return interval

fire return interval (yrs)

Suggests a fire regime of once per 22-28 years

2 8 14 20 26 32 38 2 8 14 20 26 32 38

Evans, Holsinger and Menges. In prep. Ecological Monographs.

infer seed bank parameters, including effect of tsf on germination

partition sampling uncertainty vs. process variability

estimate many parameters (complex models)

interpret model output in terms of probability

use model output in decision analysis

combine data sets, impute missing data

The Bayesian model allows us to…

Forecasting species’ responses to climate change will require “numerical simulation”, “data assimilation”, “reanalysis”…as practiced by climatologists, oceanographers