Approaches to niche-based modelling – theory and practice

1. Approaches to niche-based modelling – theory and practice Dr Barend Erasmus Wits University

2. Lecture Structure • Why model species ranges? • What is a niche? – fundamental and realised • Correlative range modelling – background and assumptions • Distribution datasets • Variables and their selection • Models and their selection • Model calibration and evaluation

3. Why model species ranges? We need to know where species occur and why they occur where they do: • We want to predict where a particular species occurs. • We want to know more about organism-environment relationships

4. Used in response to • increasing rates of habitat, and species loss, • incomplete (spatial and temporal) distribution info for a large number of taxa, • existing distribution data collected in an ad hoc fashion. Given the rate of species loss, it is unlikely that we will get the distribution data that we need in time if we rely on conventional survey techniques. Atlases are an invaluable data source and cover very few taxa but they are very important for model development and calibration.

5. Distribution models have been used to predict • species richness (Jetz & Rahbeck 2002) • centres of endemism (Johnson, Hay & Rogers 1998), • the occurrence of particular species assemblages (Neave, Norton & Nix 1996), • the occurrence of individual species (Gibson et al. 2004), • the location of unknown populations (Raxworthy et al. 2004) • the location of suitable breeding habitat (Osborne, Alonso & Bryant 2001), • breeding success (Paradis et al. 2000), • abundance (Jarvis & Robertson 1999), • genetic variability of species (Scribner et al. 2001)

6. They have also been used to • help target field surveys (Engler, Guisan & Rechsteiner 2004), • aid in the design of reserves (Li et al.1999), • inform wildlife management outside protected areas (Milsom et al. 2000) • guide mediatory actions in human–wildlife conflicts (Sitati et al. 2003). • monitor declining species (Osborne, Alonso & Bryant 2001), • predict range expansions of recovering species (Corsi, Dupre & Boitani 1999), • estimate the likelihood of species’ long-term persistence in areas considered for protection (Cabeza et al. 2004) • identify locations suitable for introduction (Debeljak et al., 2001) • identify locations suitable for reintroductions (Glenz et al., 2001). • identify sites vulnerable to local extinction (Gates & Donald 2000) • identify sites vulnerable to species invasion (Kriticos et al. 2003), • explore the potential consequences of climate change (Erasmus et al. 2002).

7. Principles: Fundamental niche Definition: n-dimensional hypervolume described by n environmental and resource constraints within which a species can maintain a viable population. The combination of conditions and resources required by an individual species defines the area in which it is able to live.  (from Begon, Harper & Townsend 1990)

8. Principles: Realised niche • Fundamental niche never completely occupied due to competitive interactions • Actual occupied niche space that maintains viable population is a subset of the fundamental niche = realised niche

9. Principles: Range edges What determines the edge of geographic ranges? • There are changes in local population dynamics at the edge of a distribution, and more net losses than net gains These population level changes are brought about by: • Changes in abiotic factors (physical barriers, climate factors, absence of essential resources) and biotic factors (impact of competitors, predators or parasites) • Genetic mechanisms that prevent species from becoming more widespread. Abiotic/biotic factors are only limiting because a species has not evolved the morphological / physiological / ecological means to overcome them.

10. Principles: Response curves • Plot of species presence with variation in some environmental variable. • Most models assume a Gaussian response, but in fact it is seldom Gaussian, and may take on a variety of shapes. Especially in complex communities, response curves may exhibit truncated forms due to biotic interactions. • The ability of the chosen model to represent this response curve is critical to model performance.

11. Response curves estimation of different models Click to enlarge. Source: Guisan and Zimmerman, 2000

12. Specifics: Niche-based modelling Species Distribution Environmental Variables Model Calibration Yes Independent evaluation dataset No 70/30% Random Calibration/Evaluation Sample Independent evaluation dataset Model Evaluation Final Model used to project current and future distributions

13. Niche-based modelling –assumptions • Assumptions: • Environmental factors drive species distribution • Species are in equilibrium with their environment • Limiting variables – are they really limiting? • Coincidence with climate or climate shift • Evidence for species dying/not reproducing due to climate • Collinearity of variables • Assumption of assembly rules: niche assembly vs dispersal assembly • Static vs dynamic approaches: data snapshot or time series response?

14. Cautionary note on modelling in general • Risk of all models: GIGO- Garbage in, garbage out • Need to understand assumptions, explicit and implicit • Models are an abstraction of reality, meant to improve our understanding of core processes.

15. Variables with biological relationship with study species Variables that correlate with study species because of correlation with series of intermediate direct factors rather than direct relationship Definition Climate, nesting sites, soil nutrients (plants), interacting species, site isolation Elevation, soil, topography, geology, soil nutrients (animals) Example Model structure easily interpreted in biological meaningful terms. Direct biological relationship should generalize better to new areas, and be more effective for climate change modeling than indirect predictors. Provides more info for conservation management Data sets widely available in GIS Low cost, ease of collection Can be effective predictors, ie elevation in mountainous areas Encompasses a range of correlated variables so should: result in parsimonious models if variable selection applied, recording fewer variables Strength Variables require greater effort to record Data sets may need to be estimated for large spatial extents (using indirect variables reducing overall accuracy Weakness Correlation with direct variables tend to be location specific Limited interpretation – biological meaning inferred, resulting in increased uncertainty Specifics: variable selection DirectIndirect

16. Example of how direct/indirect variables may affect a plant species Click to enlarge

17. Variables and their selection • Species only select their habitats in the broadest sense (Heglund 2002), and distribution patterns are the cumulative result of a large number of fine scale decisions made to maximize resource acquisition. • The more accurately these fine-scale resources can be approximated and access quantified, the better the model should perform if all models were equal. • Predictions at broad scales can use broader environmental variables, often associated with the fundamental niche, • Finer scale predictions need to concern themselves more with those variables that determine the realized niche. (Pearson & Dawson 2003)

18. Process, ie habitat selection, reproduction Pattern, eg habitat occupancy Theoretical models Specific models General empirical models (from Van Horne 2002) • Variable selection determines generality vs specificity of modelled output

19. Environmental Variables • MAP, Psummer, Pwinter • MAT, Tmin, Tmax, Tmin06 • Soil (pH, texture, organic C, fertility) • Avoid indirect measures of a variable which is a challenge • project into the future e.g. slope, aspect, altitude • Difficult variables – Solar radiation, wind

20. Derived Variables • Growing degree days (e.g. base 5°C) • PET – Thornthwaite, Priestly-Taylor, Linacre • Water Balance – Crudely defined as MAP – PET • Favourable soil moisture days– Modelled using e.g. ACRU, WATBUG • Palmer Drought Stress Index – PDSI Program

21. Use variables that show direct relationship with organism Improved predictive ability, especially over large geographical extents or predicting responses to environmental change Improved predictive ability, greater biological validity (modeling of realized niche), greater explanatory power and ease of interpretation Consideration of interacting species Improved predictive ability with new data because model does not need to extrapolate beyond conditions under which model was constructed; explanatory conclusions more widely applicable ID complete geographical region of interest prior to sampling (Thuiller et al 2004) Improved predictive ability, greater explanatory understanding, more relevant to cons planning Multiscale approach to sampling Aim to sample at least 10 sites for every environmental variable considered More reliable model development and explanatory analysis, improved predictive ability Aim to model spatial autocorrelation, where present; test to ensure adequate stats power for autocorrelation analyses in design of sampling scheme (Keitt et al 2002, Dungan et al 2002. More background Legendre 2002, Perry et al 2002) Facilitated detection, characterization and subsequent modeling of autocorrelation, improved understanding of mechanisms generating distribution pattern, greater predictive accuracy Essential to test models, increase scientific rigour and observational analyses. Idea of model generality and predictive ability. Collect independent evaluation data; environmental stratification used in process. Recommendations for variable selection RecommendationPotential advantages Environmental stratification, with equal samples between strata Improved predictive ability, more accurate explanatory analysis Aware of effects of prevalence in pres/abs modelling (Manel et al 1999, 2001)

22. Species distribution datasets Data sources and their typical scales Locality Type 1-1000m 1-5km 1-15 minutes 0.25- 1 degree 1-5 degree Museum Specimens Presence Herbaria Specimens Presence Expert Atlas Presence/Absence Survey Atlas Presence/Absence Fieldwork Presence/Absence • Museum/Herbarium data e.g. Precis (Sabonet) • Survey Atlas data e.g. Protea Atlas • Expert Atlas e.g. Birds of Africa • Field data e.g. Ackdat or TSP databases • Presence / Absence data • Georeference accuracy e.g. GPS / QDS • Taxonomy affects numbers • Taxonomic updates of older museum data

23. Species distribution datasets…2 Using existing data • Ad hoc museum data – presence only (Brotons et al 2004) • Atlases – may be presence/absence. Scaling down of atlas data: not a good idea to attempt without due caution and model validation (Araujo et al 2005) • Flagship/Indicator species: depends on objective of model – ecosystem function vs biodiversity vs change detection • Adaptation response depends on selected flagship species, ie Proteas in CFR

24. Species distribution datasets…3 Collecting new data to model • Gradsect sampling – maximizing samples across gradients (Wessels et al 1998) • Focussed vs random (Hirzel & Guisan 2002): ‘Regular’ and ‘equal-stratified’ sampling strategies is more accurate and more robust. Improve sample design: • (1) increase sample size, • (2) prefer systematic to random sampling and • (3) include environmental information in the design

25. How do we choose a model type?

26. Different types of models • BioClimatic envelope e.g. Bioclim • Ordinary Regression e.g. incl. in Arc-SDM • Generalised additive models (GAM) e.g. GRASP • Generalised linear models (GLM) e.g. incl. in Biomod • Ordination (e.g. CCA) e.g. ENFA • Classification and regression trees (CART) e.g. incl. in Biomod • Genetic Algorithm e.g. GARP • Artificial neural networks e.g. SPECIES • Bayesian e.g. WinBUGS

27. Principles • What question do you want to answer? • Data considerations • What environmental data do you have access to? • What is the resolution and extent of this data? • Categorical or continuous data? • Scale considerations. (Thuiller et al 2003 – GAMs better at performing consistent across scales because of ability model to complex response curves) • Different variables important at different scales (Pearson& Dawson 2003) • Good example of an informed modeled solution: Gibson et al 2004 • Different models compared: summary of such studies in Segurado & Araujo 2005, Thuiller et al 2003.

28. Various decision trees from the literature Click to enlarge. (Guisan and Zimmerman, 2000)

29. Decision trees from the literature (2) (Segurado & Araujo 2005)

30. In conclusion • In general, neural networks and GAM (possibly with an autocorrelation coefficient) are the most robust. • Neural networks are black boxes: biological interpretation is hard to do • Two options: • Choose an expert system (e.g. BIOMOD) that compares models automatically, and selects the best one, or choose a model that is generally robust. • Choose a method particularly suited to the questions asked, i.e. ENFA when presence-only data is available. • However, GAM with pseudo-absence may outperform presence-only techniques (Brotons et al 2004).

31. Model calibration and evaluation Once you have decided on a model type, then you need an methodology to select the best model from a suite of potential models, all with different combinations of the selected environmental variables. Stepwise selection of variables: order doesn’t matter in GAM, does with GLM Click magnifying glass to enlarge table. (from Johnson & Omland 2004, Rushton et al 2004).

32. Models and their selection - BioClimatic Envelope Species Distribution Frequency Value classes Environmental Variables IF Tann =[23,29] °C AND Tmin06=[5,12] °C AND Rann=[609,1420] AND Soils=[1,4,5,8] THEN SP=PRESENT

33. Models and their selection - GAM modeling For linear regression there is a dependent variable Y and predictor variables X1 … Xp such that Additive models replace the linear function Bj with a smoothed non-linear function fj Owing to the binomial nature of the dependent variable we need to use the “Logit” family (non-linear transformation)

34. Models and their selection - GARP Atomic rules IF TANN=23 degC AND GEO=4 THEN SP=PRESENT BIOCLIM rules IF TANN=(23,29]degC AND TMNCM=(10,16]degC AND TMXWM=(35,38]degC AND TSPAN=(19,27]degC AND TCLQ=(21,23]degC AND TWMQ=(29,30]degC AND TWETQ=(24,32]degC AND TDRYQ=(19,26]degC AND RANN=(609,1420]mm AND RWETM=(156,319]mm AND RDRY=(1,1]mm AND RCV=(101,123]mm2 AND RWETQ=(460,874]mm AND RDRYQ=(0,9]mm AND RCLQ=(1,16]mm AND RWMQ=(272,532]mm THEN SP=PRESENT Range rules IF GEO=(6,244]c AND TMNEL=(285,1480]masl THEN SP=ABSENT Logit rules IF 0.1 - GEO*0.1 + TMNEL*0.3 THEN SP=ABSENT

35. Output data = probability values • Observed data = presence – absence data How to compare? Actual Predicted How good are the predictions? (Fielding & Bell 1997, Guisan and Zimmerman, 2000) • Need a probability threshold to derive a misclassification matrix (MM)

36. Kappa statistic • Based on the MM • Take into account chance agreement • Estimation of Kappa for a range of threshold and keep the best • Ke = [(TN+FN)x(TN+FP) + (FP+TP)x(FN+TP)]/n² • Ko = (TN + TP)/n • K = [Ko – Ke] / [1 – Ke] • Scales between 0 and 1; >0.7 good, 0.4 – 0.7 fair, <0.4 poor (Thuiller 2004, pers comm.)

37. 1 0.8 0.6 0.4 0.2 0 0.0 0.2 0.4 0.6 0.8 1.0 1 - specificity Receiver operating characteristic analysis (ROC) • Sensitivity TP/(FN+TP) (true positive fraction) • Specificity TN/(FP+TN) (true negative fraction) • Plot sensitivity and specificity for a range of thresholds • Calculate Area-under-curve (AUC): • 0.8 good, 0.6 – 0.8 fair, 0.5 random, <0.6 poor

38. How good are the predictions? • Testing and training data sets (30:70) • Comparison across models, or across var’s with same model. • Number of explanatory variables. • Model development and improvement is iterative process • Delineating the predictive ability of predictor variables (Lobo et al 2002) • Evaluate model output against historical data (Hilbert et al 2004) • Use of modelled data in conservation planning (Hannah et al; Cabeza at al, 2004; Loiselle et al 2003)

39. Check your understanding of Chapter 6 PASS MARK 80% Please do not proceed further until you have PASSED Chapter 6: test yourself

40. Next Links to other chapters Chapter 1 The evidence for anthropogenic climate change Chapter 2Global Climate Models Chapter 3 Climate change scenarios for Africa Chapter 4 Biodiversity response to past climates Chapter 5 Adaptations of biodiversity to climate change Chapter 6 Approaches to niche-based modelling Chapter 7 Ecosystem change under climate change Chapter 8 Implications for strategic conservation planning Chapter 9 Economic costs of conservation responses I hope that found chapter 6 informative, and that you enjoy chapter 7.