Mapping and modeling species distributions
Department of Botany and Zoology, Masaryk University
Bi9661 Selected issues in Ecology, Autumn 2013
Borja Jiménez-Alfaro, PhD
Part 2:
MODELING
MODELING METHODS
MODELING METHODS
SDMs are correlative models
Johnston, 1993
Species distribution is infered from known environmental conditions
* Habitat suitability
* Realized niche?
Assessing the bio-physiological aspects of a species to generate the
conditions in which the species can ideally persist, based on observations
made in controlled field or laboratory studies
* The Real NICHE
* Fundamental niche?
But models can be also mechanistic (process-based)
MODELING METHODS
TYPES OF (CORRELATIVE) MODELS
We will use the classification of Hijmans and Elith (2013)
for “dismo” package in R
Similar classification is provided in Wikipedia
MODELING METHODS
Profile methods Bioclim
Domain
Mahalanobis distance
Regression models Generalized Linear Models (GLM)
Generalized Additive Models (GAM)
Machine learning Boosted Regression Trees (BRT)
Random Forests (RF)
MaxEnt
(Presence data)
(Presence/absence data)
(Presence data)
(+background data)
A brief overview of methods and algorithms
MODELING METHODS
Profile methods
Only consider presence data
Based on the environmental distance to known sites
Simple algorithms easy to understand
Bioclim, Domain, Mahalabobis
Others: Environmental Niche Factor Analyses (ENFA)
MODELING METHODS
BIOCLIM
The BIOCLIM algorithm – environmental envelope – computes the
similarity of a location by comparing the values of environmental
variables at any location to a percentile distribution of the values at
known locations of occurrence (’training sites’)
Nix, H.A. (1986) A biogeographic analysis of Australian elapid snakes. In: Atlas of
Elapid Snakes of Australia. (Ed.) R. Longmore, pp. 4-15. Australian Flora and Fauna
Series Number 7. Australian Government Publishing Service: Canberra
Implemented in:
R (dismo), Openmodeller, Diva-GIS
MODELING METHODS
Cutoff = 0.67 Cutoff = 0.99
Each variable has its own envelope represented by the interval
[m - c*s, m + c*s]
The result is a cubic space (box) of n dimensions
Example for one species using temperature x precipitation
MODELING METHODS
DOMAIN
The Domain algorithm is a distance-based method based on the
Gower distance between environmental variables at any location
and those at any of the known locations (’training sites’). Results
are not a probability of occurrence but a measure of similarity
Implemented in:
R (dismo), Openmodeller, Diva-GIS
Carpenter G., A.N. Gillison and J. Winter, 1993. Domain: a flexible modelling
procedure for mapping potential distributions of plants and animals. Biodiversity
Conservation 2: 667-680
MODELING METHODS
Ecological distance methods – Multivariate similarity
DISTANCIAS ECOLÓGICAS
MODELING METHODS
models in the environmental space (temperature x precipitation) generated with the
same input (Thalurania furcata boliviana localities) but with different parameters
(source: openmodeller)
Mahalanobis distance to
the centroid
Gower distance to the
centroid
Euclidean distance to
the centroid
MODELING METHODS
MAHALANOBIS Distance
Unlike Euclidean distance, Mahalanobis distance takes into account
the correlations of the variables in the data set, and it is not
dependent on the scale of measurements. It is based on a
descriptive statistic developed by P.C. Mahalanobis in 1936.
Implemented in:
R (dismo), Openmodeller, IDRISI, ArcView
Mahalanobis, P.C., 1936. On the generalised distance in statistics. Proceedings of
the National Institute of Sciences of India 2: 49-55.
MODELING METHODS
A comparison of
PROFILE ALGORITHMS
(Tsoar et al 2007)
MODELING METHODS
PROFILE ALGORITHMS
Pros
Models of easy interpretation and representation
Support low number of occurrences
Widely used for large-scale approaches
Cons
Lack of procedures for variable selection
Interactions between variables are not allowed
All the variables have the same weight
Very sensitive to bias data and marginal points
MODELING METHODS
Regression models
Combine presence and absence data
Models are calibrated by extracting the values of locations
Robust methods and classical statistics (probabilistic inference)
GLMs, GAMs (implemented in most stat software)
Other: Multiple Adaptive Regression Splines (MARS)
MODELING METHODS
GENERALIZED LINEAR MODELS (GLM)
.
MODELING METHODS
GENERALIZED LINEAR MODELS (GLM)
MODELING METHODS
GENERALIZED LINEAR MODELS (GLM)
MODELING METHODS
GENERALIZED ADDITIVE MODELS (GAM)
MODELING METHODS
GENERALIZED ADDITIVE MODELS (GAM)
MODELING METHODS
GENERALIZED ADDITIVE MODELS (GAM)
“Semi-parametric”
extension of GLM
Very flexible, it can fit
very complex models
Main limitation: GAM
cannot be used to
calculate species
response parameters
Good for exploratory
analysis of responses
MODELING METHODS
Example of applications in SDMs
Prediction surface for mullein, Lava Beds NM
(From Edwards 2009)
MODELING METHODS
Machine learning techniques
They consider presence data and absence or background data
Also called ´data mining´methods
Based on information theory and artificial inteligence
Probablistic distributions are infered from incomplete data
Boosted Regresion Trees (RT), Random Forests (RF), MaxEnt
Others: Artificial Neural Networks, Genetic algorithm (GARP)
MODELING METHODS
Why machine learning systems?
SDMs can be considered as a supervised learning problem
In statistical inference you must decide distributional form and parametres
ML methods learn the function inductively from training data
Inductive (supervised) machine learning
methods are commonly used in artificial
inteligence (computer vision, robotics,
medical diagnosis, etc)
MODELING METHODS
Boosted Regression Trees
(= ”Gradient Boost”, ”Stochastic Gradient Boosting”)
It uses a technique of boosting (a regression-like method based on
Machine learning) to combine large numbers of simple tree models
adaptively, to optimize predictive performance
Implemented in:
R (dismo, gbm)
Elith, J., J.R. Leathwick and T. Hastie, 2009. A working guide to boosted regression
trees. Journal of Animal Ecology 77: 802-81
MODELING METHODS
Boosted Regression Trees
Ensemble models based on a LARGE number of tree models
Computationally intensive methods
MODELING METHODS
Random Forests
Random Forest (Breiman, 2001) method is an extension of
Classification and regression trees (CART; Breiman et al., 1984)
It builds a multitude of decision trees at training time and outputting
the class that is the mode of the classes output by individual trees
Implemented in:
R (randomForest), openmodeller
.
Breiman, L., 2001. Random Forests. Machine Learning 45: 5-32
MODELING METHODS
Random Forests
Not a real models like in logistic regression
Higher prediction accuracy than ordinary decision trees
No graphical tree model like in classification trees
http://www.ualberta.ca/~drr3/random-forest.html
MODELING METHODS
MODELING METHODS
From Edwards (2009)
MODELING METHODS Step #4 – TheTest:
Independent Validation - Which isBest?
Logistic GAM CART RF
PCC 75.5 75.9 77.6 87.7
Specificity 74.5 74.4 76.8 89.4
Sensitivity 84.1 90.3 86.5 71.0
kappa 0.29 0.32 0.35 0.46
AUC 0.88 0.89 0.85 0.88
Edwards et al., ECOCHANGE, , Lausanne, Sep 2009
From Edwards (2009)
MODELING METHODS
MAXENT
MaxEnt (Maximum Entropy; Phillips et al., 2006) is the most widely
used SDM algorithm. Is a general-purpose machine learning method
with precise mathematical formulation. It uses presences and
absences (generating a background layer to fit the model)
Implemented in:
R (dismo, others), Stand-alone Java program
Phillips SJ et al. 2006. Maximum entropy modeling of species geographic
distributions. Ecological Modelling 190 231-259
MODELING METHODS
MAXENT
Main statement: a probability distribution with maximum entropy (the most spread
out, closest to uniform), subject to known constrains, is the best approximation of
an unknown distribution. It combines machine learning with statistical methods
Exponential output
(difficult to intepret)
Logistic
output (0 - 1)
MODELING METHODS
Model comparisons
MODELING METHODS
Elith et al. 2006. Novel methods improve prediction of species’ distributions
from occurrence data. Ecography 29: 129 -151
MODELING METHODS
NEXT WEEK… PRACTICE WITH MAXENT