STATISTICS NETWORKING DAY
Species Distribution Models (SDM) for Presence Only
(PO) data.
Maria Angelica Lopez-Aldana
Principal Supervisor: Assoc. Prof. Bernd Gruber
Associate Supervisor: Dr. Carlos Gonzalez-Orozco
Prof. Arthur Georges
August 2015
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1
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Outline
• An overview about Species
Distribution Models (SDM)
• SDM methods
• SDM for presence only (PO) data.
• Learning resources.
• Complexities and recommendations.
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An overview about Species Distribution
Models (SDM)
Ecological question: What is the species occurrence
probability on a determined area?
Uses:
- Reserve design and conservation planning.
- Target areas for protected status.
- Assess threats to protected areas
- Design reserves
-
Ecological restoration
Risk and Impacts of Invasive Species.
Effects of global warming on biodiversity.
Describing or estimating macroecological patterns such as species
richness.
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Predictive modelling of species geographic distribution based on the
environmental conditions (Phillips et al 2006).
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Main Assumption. Species distribution are predictable from environmental
variables.
Ocurrence probability = 𝑓 𝑒𝑛𝑣𝑖𝑟𝑜𝑛𝑚𝑒𝑛𝑡𝑎𝑙 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑠
Species Occurrences
(geographic
coordinates X,Y)
Prediction
Covariates: Environmental data
Response variable:
Probability of presence
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SDM: Methods
GLM, Logistic
regression
Presence/absence
data
Systematic Biological
Survey
GAM, Generalized
additive models
MARS Multivariate
adaptive regression
splines
Type of data
Presence only data
Herbarium or
museum data
ManEnt, Maximum
Entropy
Maxlike Maximum
likelihood
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MAXENT
MAXLIKE
Machine Learning Method
Maximum likelihood Method
Automatic and flexible set of arrangements
(Linear, Quadratic, Product, Splines)
Subject to overfitting
Not as flexible, arrangements need to be
specified.
Not possible to apply the standard
statistical inference techniques.
Possible to apply the standard statistical
inference techniques (e.g. hypothesis test,
confidence intervals or model selection)
Explores the relative suitability of one place Logit-linear model which first ensures that
over another using the maximum entropy
the predicted value is a real probability
principle.
value
# run & predict (in parallel) maxlike models for k
randomizations
acalikeMods <- foreach(k=1:sets, .verbose=T,
.packages="maxlike") %dopar%
maxlike(~annual_mean_rad + I(annual_mean_rad^2)
+ annual_mean_temp + I(annual_mean_temp^2)
+annual_precipitation + I(annual_precipitation^2)
,rstrans, acaTrain[[k]],
control=list(maxit=10000), removeDuplicates=TRUE)
Learning Resources:
Coursera:
Programming in R by Roger D. Peng, PhD
Johns Hopkins University
DataCamp
R - bloggers
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R list
User Group
There are mailing lists for R users. For more information and to subscribe, see The R Project
for Statistical Computing (Mailing Lists). The primary mailing list is called "R-help"; it offers
swift and competent answers to problems with R.
Newsletter
Since January 2001, R has had an
online newsletter, which in 2009 became the R
Journal.
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Other learning Resources.
SDM Books.
A. Townsend Peterson, Jorge Soberón, Richard
G. Pearson, Robert P. Anderson, Enrique
Martínez-Meyer, Miguel Nakamura & Miguel B.
Araújo
SDM and R, available Online
https://cran.rproject.org/web/packages/d
ismo/vignettes/sdm.pdf
Species distribution
modeling with R
Robert J. Hijmans and
Jane Elith March 14,
2015
Janet Franklin, San Diego State University
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Complexities and Recommendations
- Modeling formulation, modeling fitting an modeling evaluation require specific
statistical methods.
Conceptual modeling formulation
• Variable selection
Statistical Modeling
• Different methods
• Model selection
Evaluation
• Model evaluation
- It is necessary to learn a set of software (e.g. Arcgis and R) and skills;
computational and theoretical.
- Processing time can be very extended.
- As a novel methods, Information might be limited and dispersed.
Recommendations
-
Learn R first. It is a valuable tool to apply over a set of problems.
-
As some inconvenient are very specific (e.g. code or software conditions) is
always a good idea google questions and read forums.
-
Do not hesitate to write paper’s authors.
-
Include all PhD student in the network?.
THANKS!!
1) How they use the method in their work;
2) How they learned about the method –
textbooks, websites, mentors;
3) Complexities they have experienced in
applying the method.
Conditions: No absence data.
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How to choose the covariates?
Purpose of the Study
Data availability
Biology of the Species
Scale
Extent Range
Environmental
Covariate
Climate
Topography
Land use
Soil type
Biotic Interaction
Global
Continental Regional
Landscape
Local
Site
Micro
>10000 km
2000-10000
km
10-200 km
1-10km
101000
m
< 10m
200-2000km
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Species Biology and SDM performance.
How the biology of the species affects the model performance?
(Franklin, 2009):
Higher accuracy:
- Rare species , better discrimination of suitability
- In plants, obligate seeders - site fidelity.
- Longevity.
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Statistical Modeling : Methods
How to choose the method?
Time and space
defined
Systematic Biological
Survey
Presence/absence
data
Standarized sampling
methods
Random Sampling
Origin of data
Opportunistic
method
Herbarium or
museum data
Presence only data
No random sampling
Difference in
sampling intensity
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Species Distribution Models and Presence Only data (PO).
Presence–absence survey data is generally not available
- Huge sampling efforts behind Museum data collection.
- Urgent decisions for conservation
- Only option when the landscapes extend to be
modeled are significantly large.
Yet,
- how can we contrast the environmental conditions of Presence WITHOUT
ABSENCES?
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MaxEnt
- Follows Maximum Entropy Principle
- Developed by Phillips et al. 2006.
- What is Maximum Entropy Principle? What does it mean in the SDM context?
Premise: the best approximation of a distribution is determined by maximum
entropy, subject to constraints on it’s moments.
Entropy component: Maximum Entropy model aims to find the distribution that is
most spread out (i.e. closest to the uniform).
Constraint component: restraint on the average of the covariates
- Uses background data. locations where presence/absences are unmeasured.
- Explores the relative suitability of one place over another using the maximum
entropy principle
F1(z) / F(z)
- F1(z) pdf of covariates where the sp is present
F(z) pdf of covariates across L
MaxEnt
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Exponential output (raw Maxent).
- MaxEnt distribution = Gibbs distribution (exponential function)
- As every distributions sums to 1.
- Cells with environmental variables close to the mean of presence locations have high
values.
Scale Dependent, not intuitite, projections no easy to interpreted
Cummulative output
- The value assigned to a pixel is the sum of the probabilities at that pixel and all other
pixels with equal or lower probability
Scale independent, easier to use in projections but is not proportional to
probability of presence!!
Logistic output
This approximation is derived from a logistic function over the maximum entropy function
Using this approximation, it is assumed that the probability of presence in a “typical
site” is 0.5!!.
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MaxEnt
Feature selection. Complexity
Allows different arrangements. Depends on the number of presences:
Too many arrangements, subject to over fitting.
-
Linear (always possible)
Quadratic (at least 10 points)
Product (at least 80)
Splines(at least 15 points)
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MaxEnt
- Most Popular Method! (Even for presence/absence data)
- (over 108 (2008-2012) used MaxEnt, 36% discarded absence.
- Yackulic, 2013)
- Limited customization:
Number of background points
Default prevalence
Output format.
- Variable importance.
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MaxLike
- Statistical Method.
Landscape divided by x number
of pixels
- Developed by Royle 2012.
- Random Sampling Principle.
Explore random sampling and Bayes Rule to derive the likehood for the presence-only
sample.
Using a hypotetical ¨first stage¨ random sample to create a ¨sample inclusion variable
w(x)¨
Describe: P(x / w(x)=1, y(x)=1 )
w(x)=1 if x appears in the first stage sample
y(x)=1 if the pixel is occupied
- Assumptions. Species detection probability is constant.
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MaxLike
- Possible to apply the standard statistical inference techniques
(e.g. hypothesis test, confidence intervals or model selection)
- Logit-linear model which first ensures that the predicted value is a real probability value
- It has a R package (Maxlike) to fit the model. (MaxEnt too!!!)
# run & predict (in parallel) maxlike models for k randomizations
acalikeMods <- foreach(k=1:sets, .verbose=T, .packages="maxlike") %dopar%
maxlike(~annual_mean_rad + I(annual_mean_rad^2) + annual_mean_temp + I(annual_mean_temp^2)
+annual_precipitation + I(annual_precipitation^2) ,rstrans, acaTrain[[k]],
control=list(maxit=10000), removeDuplicates=TRUE)
- Not as flexible as MaxEnt…
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PROGRAM AND DESIGN OF THE RESEARCH INVESTIGATION
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Objectives:
SDM -PO
Methods
i. Knowledge of the comparative accuracy of the
most recent methods (i.e. MaxEnt and Maxlike) to
describe the prevalence of species from Acacia
gender using presence only data in a continental
level.
ii. Knowledge of the performance of MaxEnt and
Maxlike models to accurately predict the distribution
of species over the time.
Applications
iii. Understanding of the ability of these two presence only (PO)
methods to accurately predict the prevalence of species over a
multitaxonomic groups set of data (plants, fishes, amphibian, reptile
and mammals) in the Murray Darling Basin.
iv. Integrate the distributions of these important
groups in a conservation map for MDB area.
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SDM -PO
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METHODS
Continental Level –
Australia
Objective 1
APPLICATIONS
FORECASTING OVER TIME
MAPPING FOR CONSERVATION
Continental Level –
Australia
Regional Level –MDB
Objective 2
Objective 3 & 4
MAXENT/MAXLIKE
Conceptual
modelling
formulation
•Acacia (30 sp)
FORECASTING OVER
TIME
Conceptual
modelling
formulation
•Turtles (4 sp)
MAPPING FOR
CONSERVATION
Conceptual
modelling
formulation
Statistical
Modelling,
Calibration,
Evaluation
Statistical
Modelling
Calibration,
Evaluation
Statistical
Modelling,
Calibration,
Evaluation
Mapping
Integration
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PROGRAM AND DESIGN OF THE RESEARCH INVESTIGATION
Methodogy.
i. Empical comparison between Maxlike and MaxEnt.
Conceptual
modeling
formulation
Statistical
Modeling
Calibration
Evaluation
• Covariates: mean annual radiation ,annual temperature, annual rainfall.
Presences :30 sp Acacia
• MaxEnt vs Maxlike
• Linear and Quadratic Features.
• Using cross validation (25/75)
• Akaike Information Criteria (AIC)
• Area Under Operator Curve (AUC)
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i. Empical comparison between Maxlike and MaxEnt
Conceptual
modeling
formulation
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• Covariates: mean annual radiation, annual temperature and annual
rainfall
• Presences :30 sp Acacia
High Abundance
A > 556 registers
Low Abundance
205 < A < 361
High Coverage
C >69 grids
Group 1. (AC)
A. ligulata
A. salicina
A. deanei
A. ramulosa
A. sibirica
A. monticola
A. stenophilla
A. Hologericea
Group 2. (aC)
A. paraneura
A. rhodophloia
A. strowardii
A. Ayersiana
A. pruinocarpa
A. gonoclada
A. adoxa
Low Coverage
30 < C < 43 grids
Group 3. (Ac)
A. crassa
A. floribunda
A. terminalis
A. rubida
A. mucronata
A. euthicarpa
A. pulchella
Group 4. (ac)
A. latipes
A. alleniana
A. triptera
A. hemiteles
A. lanigera
A. microcarpa
A. halliana
A. dimidiata
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Statistical
Modeling
• MaxEnt vs Maxlike
Response Variable
MaxEnt.
Suitability Index (Logistic Output)
Maxlike.
Probability of occurrence.
Covariates
Linear and Quadratic terms
-
mean annual radiation
annual temperature
annual rainfall
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• Using cross validation (25/75)
Calibration
& Evaluation
• Akaike Information Criteria (AIC)
• Area Under Operator Curve (AUC)
- Cross Validation (25/75)
(30 times)
- AIC. Akaike Information Criteria :
- < AIC, lower unexplained deviance. Better Model!!
- AUC. Area Under the Receiver Operating Curve
- AUC > 0.9
- 0.7 – 0.9
- 0.5-0.7
Very good model!!
Good model!
Bad model.
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Premilinary Results.
i.
Empical comparison between Maxlike and MaxEnt.
Selecting 2 species per group, as follows:
Group 1 (AC).
A.
ligulata
A.
sibirica
Group 2 (aC).
Group 3 (Ac).
Group 4 (ac).
A.
A.
floribunda
Euthicarpa
A.
A.
A.
A.
stowardii
gonoclada
lanigera
alleniana
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Models Performance
AIC values
Train/test
MaxLike
MaxEnt
MaxEnt – MaxLike
A. alleniana
69 / 206
4127.1
6674.815
2547.699553
A. euthicarpa
245 / 734
13633
26347.6
12714.49252
A. floribunda
152 / 456
8892.3
15595.12
6702.818403
A. gonoclada
A. lanigera
85 / 255
82 / 247
6397.3
4781.7
9805.981
8650.121
3408.703674
3868.431935
A. ligulata
713 / 2140
52648
86249.69
33601.81599
A. sibirica
150 / 450
9624.8
18449.53
8824.750298
A. stowardii
64 / 193
5206
7829.549
2623.598923
AIC. Akaike Information Criteria :
- < AIC, lower unexplained deviance. Better Model!!
- Maxlike Lower unexplained deviance than MaxEnt.
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- AUC. Area Under the Receiver Operating Curve (AUC > 0.9 :Very good model!!, 0.7
– 0.9 Good model, 0.5-0.7 Bad model).
AUC is consistent with AIC result
AUC-Maxlike values are always bigger
than AUC-MaxEnt values, however
the difference is almost insignificant
for species with low coverage
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- Mean Probability of presence.
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Because of the default value of 0.5 in
MaxEnt model, mean probability of
presence is close to this value.
The probability of presence for Maxlike
is, in most of the cases, bigger but
exhibit a wide variation.
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MaxLike vs MaxEnt: Mean Predicted Probability
Maxlike.
A. sibirica
AC
aC
A. gonoclada
MaxEnt
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MaxLike vs MaxEnt: Mean Predicted Probability
Maxlike.
A. floribunda
Ac
ac
A. alleniana
MaxEnt
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Which one is the best model?:
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MaxLike has better AUC and AIC values, but exhibits a huge
variability.
MaxEnt is more consistent between models (low variability), but
maintains a “probability of presence” of around 0.5.
We will choose the model that has the best fit, taking into
account the research questions, the biology of the species and
the influence of omission and comission error.
Taking into account SDM purpose…
Case 1. Reserve design.
Comission (False positive): False presences, inversion for conservation
over unappropiate areas.
MaxEnt Better option?
Case 2. Impact of invasive Species
Omission (False negative): False absences, areas uncontrolled!!
Maxlike Better option?
ii. predict the distribution of species over the time.
Conceptual
modeling
formulation
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• Covariates: 19 bioclim variables, soil and water temperature?, Soil
Moisture?
• Presences : Turtle species
Chelonia longicollis,
Emydura macquarti
Chelonia expansa (AUC=0.978)
Myuchelys bellii
Annual mean radiation
Precipitation driest quarter
Lowest period moisture
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Resources and Funding Required
Data requirement:
The PO data set to be used in this project and the collaborators are:
Aim 1. Acacia species, Carlos Gonzalez-Orozco
Aim 2. Turtle species, Arthur Georges.
Aim 3 and 4 . Plants, fishes, amphibian, reptile and mammal data sets. Carlos
Gonzalez-Orozco and Margarita Medina.
Software requirement: R for programming. The program is free and has been
obtained already.
Funding source:
The project is supported by Murray Darling Basin Futures project.
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Timetable
PhD duration
Literature review
Code R. maxEnt /Maxlike
Running Code Australia (Acacia)
Turtle model
Running Code MDB (Multitaxon)
Mapping for conservation
Writing
Conference to determine
2014
2013
2015
Confirmation seminar
Jun2014
Work in progress
seminar
8 Jul 15
Introductory seminar
Dec 13
PhD Starts
April 13
2016
2016
PhD Finishes
April 16
Final seminar
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Acknowledgment:
1. Funding!
MDB Futures Collaborative
Research Network.
2. Research Group :
- Bernd Gruber
- Carlos Gonzalez-Orozco
- Arthur Georges
- Peter Unmack
- Aaron Adamack
- Margarita Medina
Thanks for listening!!!!
AUC. Area under the ROC curve. A statistic generated from a receiver
operating characteristic plot (ROC).
AUC represents an overall performance measure of model performance
across all thresholds and strengths of a prediction.
AUC is a non-parametric measure that range between 0 and 1.
Summarize the model’s ability to rank presence records higher
than absence records (or background records in PO methods)
AIC. Akaike Information Criterion. It is a measure of the
relative goodness of fit of a statistical model. It offers a relative
measure of the information lost when a given model is used to
describe reality. It can be said to describe the tradeoff
between bias and variance in model construction, or loosely
speaking between accuracy and complexity of the model.
In the general case, the AIC is:
AIC = 2K - 2ln(L)
Where k is the number of parameters in the statistical model,
and L is the maximized value of the likelihood function for the
estimated model.
Given a set of candidate models for the data, the preferred
model is the one with the minimum AIC value.
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Factors impacting the geographic range of species
• The abiotic environment (fundamental niche)
temperature
precipitation
soil type
• The biotic community
food webs and ecological networks
• Movement: history and geography
dispersal
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Conceptual modeling formulation: niche theory
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Model Selection
Few Parameters
Simple
Parsimony
Generality
Descriptive accuracy
Overfitting
More flexibility
Sacrifice Predictive Performance
Modelling occurrence probability in with Maxlike.
Using yi = 1 to denote a presence at grid cell xi, and P(yi=1/Xi,β0,β) to denote
occurrence probability. The likelihood for Maxlike is given by (Royle et al. 2012).
L(β) =
𝑁
𝐼=1
P(y =1/ ,β ,β)
𝑋i 0
𝑖
P(
=1/
,β ,β)
𝑥 ∈𝐵
y
𝑖
𝑋i
0
Where N is the total number of presences, B is the background data, β0 is an
intercept parameter, and β is the vector of slope coefficients associated with
environmental covariates. The numerator describe the likelihood at presence
cells while the denominator describe the likelihood at background cells. Often
background cells are taken as random sample of cells over the landscape (Lele &
Keim 2006; Lele 2009; Royle et al 2012.
How to build the model?
STATISTICAL MODELING USING SDM (Guisan and Zimmermann 2000)
Conceptual modeling formulation
• Rely on ecological concepts
Statistical Modeling
• Choosing the best tool according with the
availability of the data
Calibration
• Estimation or fitting
Evaluation
Ability to discrimninate areas with presences.
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MaxLike vs MaxEnt_LF: Standar Deviation of Predicted Probability Maxlike
MaxEnt DF_BC
A. Denaei
A.flexifolia
A.semilunata
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MaxLike vs MaxEnt_LF_BC: Standar Deviation of Predicted Probability
Maxlike
MaxEnt LF_BC
A. Denaei
A.flexifolia
A.semilunata
Objetives and Research Questions:
1. Make an empirical comparison between MaxEnt (maximun entropy) and
MaxLike (maximun likelihood) in the predictions of Acacia in Australia
RQ. Which of these methodologies has a better performance in the Acacia
distribution?
2. Compare the performance of this methods over other species. (Eucalyptus,
Fish and Frogs) in the Murray Darling Basin.
RQ. Is this performance different between species and scales?
3. Integrate the distributions of this important groups in a conservation map for
MDB area.
RQ. Are the important areas consistent with the already defined conservation areas?
Summary Preliminary Results
Maxlike Lower unexplained deviance than MaxEnt (LF, LF_BC)
MaxEnt DF show better performance than MaxEnt LF
A. Fexifolia (“Site fidelity sp) show a good adjustment in all the different methods.
.
Area Proportion
Threshold
Statistical Modeling : Methods
Presence/absence data
Discriminant Analysis
Linear
Generalized Linear
Models (GLM)
Linear, polinomial,
interaction terms
Generalized additive
models (GAM)
Smoothing function
Decision tree (DT)
Divisive, monothetic
decision rules
Maximun entropy
(MaxEnt)
Linear, polinomial,
splines
Likelihood Analysis
(Maxlike)
Parameters estimated
by maximizing the
likelihood.
Methods
Presence only data
Statistical Modeling : MaxEnt
p(y=1/z)=
p(z/y=1) ∗ p(y=1)
Unknown
𝑝(𝑧)
p(y=1/z): the probability of presence species, conditioned on environment.
p(z/y=1): pdf of covariates across locations within the L (landscape of interest)
where the specie is present. F1(z)
p(y=1): prevalence of the specie
p(z): pdf of covariates across L. F(z)
Make estimation about the radio F1(z)/F(z) MaxEnt Raw output
In logistic Output: n(z)
Why make SDM?:
Predictions of
Specie
Prevalence
Current
distribution
Potential
Distribution
Conservation
Invasive Species
Estimate
richness or
diversity
Expanding
distribution
Land
transformation
scenarios
Listado de usos de SDM, los mas importantes
Retrospecive
studies
Climate change
scenarios
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Theme 2 : Environmental watering and allocation
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Project 3:Biodiversity Conservation
Example. Acacia aneura
Response variable:
A. aneura presence
“Prevalence”
Covariates:
Average Annual Rainfall
Max temperature
Probability of presence = 𝑓 𝑒𝑛𝑣𝑖𝑟𝑜𝑛𝑚𝑒𝑛𝑡𝑎𝑙 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑠
MDBfutures
Theme 2 : Environmental watering and allocation
Project 3:Biodiversity Conservation
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MDBfutures
Theme 2 : Environmental watering and allocation
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Project 3:Biodiversity Conservation
From SDM to conservation mapping: continental and regional approaches
Step 3. Mapping and integrating SDM results
to identify priority areas for conservation.
Step 2. Testing consistency of this performance across taxon
groups.
Taxon groups so far: Plants(Acacia and eucalypts),genera of
plants, frogs and fish.
Step 1. Testing Modelling Performance for P/Only data.
Models: MaxEnt vs Maxlike
Species: 50 Acacia Species
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Theme 2 : Environmental watering and allocation
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Project 3:Biodiversity Conservation
Testing methods, Part I: Comparing MaxEnt versus Maxlike
Acacia species:
A. deanei (n = 809)
A. flexifolia (n=203)
MaxEnt:
MaxEnt-Linear Features
MaxEnt-All Features
MaxEnt-Linear Features Bias-Corrected
MaxEnt-All Features Bias-Corrected
Maxlike
A semilunata (n=99)
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Theme 2 : Environmental watering and allocation
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Project 3:Biodiversity Conservation
A. semilunata
A. flexifolia
A. deanei
Maxlike
Maxent_allF
Maxent_allF_BC
Maxent_LF
Maxent_LF_BC
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Theme 2 : Environmental watering and allocation
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Project 3:Biodiversity Conservation : preliminary results SDM
A. semilunata
A. flexifolia
A. deanei
Maxlike
Maxent_allF
Maxent_allF_BC
Maxent_LF
Maxent_LF_BC