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- 1. EURO-‐BASIN, www.euro-‐basin.eu Introduc)on to Sta)s)cal Modelling Tools for Habitat Models Development, 26-‐28th Oct 2011
- 2. 2 Index• Introduction to species habitat and some concepts in community ecology• Statistical methods dealing with communities • Analysis of β-diversity: Similarity and distance matrices & Mantel and partial Mantel test Practical session “Community Ecology with R” • Direct Ordination Methods (CCA and RDA) • Variation partitioning Practical session “Community Ecology with R” • 4th corner method
- 3. 3 Hypothesis• Which are the main factors that determine the distribution (or the habitat) of species? • Environmental factors (e.g. temperature, nutrients, …) → Adaptation processes versus • Dispersal limitation factors (reproduction and mortality rate, growth, migration,…) → Historical processes • for a species, but species compete for resources (hence, for space) • for an assemblage (or community) of species, within a guild A guild (or ecological guild) is any group of species that exploit the same resources: e.g. zooplankton, phytoplankton, trees
- 4. 4 Hypothesis Site 1 Site 2 Site 1 Site 2 A E B D A F B C E F C G G D Shared species ↓ Shared species ↑• Which are the main factors that determine the species composition of acommunity in a region?• What are the factors that determine the maintenance of local and regionaldiversity?
- 5. 5 diversities… γ-diversity / Landscape α-diversity / β-diversity /Within an homogeneous habitat Environnemental gradient Whittaker (1960, 1977)
- 6. 6 Habitat theories 1. Environmental factors ⇔ Niche ⇔ « Environmental patchiness »Abundance a b c d e Environmental Gradient 2. Geographic Distance ⇔ Dispersal limitation ⇔ « random walk » (Neutral theory, Hubbell 2001) Shared species Distance between sites Neutral community: all individuals have the same rates of reproduction and mortality
- 7. 7 Niche model• The Hutchinsonian niche views niche as an multi-dimensional hypervolume, where the dimensions are environmental conditions and the resources that define the requirements of an individual or a species (E. Hutchinson, 1957).• The full range of environmental conditions (physical and biological, i.e. the resources) under which an organism can exist describes its fundamental niche. Unidimensional niche Two dimensional niche Abundance Variable Three dimensional niche
- 8. 8 Dispersal-limited model • Species composition fluctuates in a random, autocorrelated way. Site 1 Site 2 Site 1 Site 2 A E B D A F B C E F C G G D Similarity ↓ : β-diversity↑ Similarity ↑: β-diversity ↓ Distance decay β-diversity Metacommunity: a set of local communitiesShared that are linked by dispersal of multiple,species Metacommunity A potentially interacting species Metacommunity B Geographical distance
- 9. 9 TerminologyA metapopulation is a group of spatially separated populations of the samespecies which interact at some level m1 n2 n1A metacommunity is a set of local communities that are linked by dispersal ofmultiple, potentially interacting species na2 ma1 mb1 nb1 nb2 na1 nc1 na3
- 10. 10 The theory of island biogeography (MacArthur and Wilson, 1967)• The number of species found on an undisturbed island is determined by immigration and extinction.• Immigration and emigration are affected by the distance of an island from a source of colonists (distance effect).• Large islands => lower extinction• Near islands to continents => higher immigration rateMacArthur, R. H. and Wilson, E. O. 1967. The Theoryof Island Biogeography. Princeton, N.J.: PrincetonUniversity Press.
- 11. 11 Dispersal limited model Variance partitionning β-diversityCondit et al. Science, January 25, 2002. Duivenvoorden et al. Science, January 25, 2002.
- 12. 12 Spatial Autocorrelation species Shared Environmental Gradient Geographic distanceLegendre, P. (1993) Spatial autocorrelation: trouble or new paradigm. Ecology, 74, 1659–1673.• Environmental variables and species distributions tend to be spatially autocorrelated: • Species distributions are most often aggregated because of contagious biotic processes such as local dispersal • But also, environment is structured primarily by climate and geomorphological processes on land that cause gradients and patchy structures.• Therefore values of these variables are not stochastically independent from one another. This may lead to misinterpretation of patterns using classical statistics when ecologists conclude that species– habitat associations are statistically significant.• To evaluate the relative importance of environmental segregation and limited dispersal in explaining species distributions, spatial structure must be considered.• Spatial autocorrelation can be a problem for explaining species ecological niche, however, it can improve habitat modelling
- 13. 13Some statistical methods to analyse distribution patterns of species communities • Similarity and distance matrices & Mantel and partial Mantel test (Analysis of β-diversity) Practical session “Community Ecology with R” • Direct Ordination Methods (CCA and RDA) • Variation partitioning • Practical session “Community Ecology with R” • 4th corner method
- 14. 14 Analysis of β-diversity:Similarity and distance matrices & Mantel and partial Mantel test
- 15. 15 Similarity and distance matrices Species Matrix: m sites x n species β-diversity e.g. n = 5 sites x11 x12 ... x1n 1 s12 s13 s14 s15 (Jaccard, …) . 1 s23 s24 s25 x ... . . S = 21 S sim = . . 1 s34 s35 : . . . . . . 1 s45 x xmn . . m1 . . . . 1 Similarity Coefficient / Distance x11 x12 ... x1q 1 s12 s13 s14 s15 . 1 s23 s24 s25 x21 ... . . AMB = AMB (Euclidean, …) sim = . . 1 s34 s35 : . . . . . . 1 s45 x . m1 . . xmq . . . 1 Environmental Matrix: m sites x q variables Environmental similarity
- 16. 16 (Dis)Similarity and distance indices Site 1 Site 2Similarity indices (for species data): 0 → 1 B F A E • Jaccard index (for presence-absence data) is the C number of species shared between the two plots, D divided by the total number of species observed. 0 (no shared species) → 1 (all species shared) Jaccard = 4 / 6 • Bray-Curtis index (for abundance data) is defined by 2W/(A+B), where W is the sum over all species of the minimum abundances between the two stations of sp1 sp2 min each species, and A and B are the sums of the St1 3 4 →3 abundances of all species at each of the two stations. St2 5 2 →2 • Bray-Curtis is also known as Steinhaus dissimilarity, Sørensen index, or Czekanowski W= 5 •…Distance indices (for variables): var1 var2 • Euclidean : d St1 32.3 0.2 •… St2 34.6 0.3 d1=2.32 d2=0.12
- 17. 17 Species Matrix β-diversity x11 x12 ... x1n 1 s12 s13 s14 s15 (Jaccard, …) . 1 s23 s24 s25 x ... . . S = 21 S sim = . . 1 s34 s35 : . . . . . . 1 s45 x . . m1 . . xmn . . 1 Similarity Coefficient / Distance Mantel Test x11 x12 ... x1q 1 s12 s13 s14 s15 . 1 s23 s24 s25 x21 ... . . AMB = AMB (Euclidean, …) sim = . . 1 s34 s35 : . . . . . . 1 s45 x . m1 . . xmq . . . 1 Environmental Matrix Environmental similarity
- 18. 18 Species Matrix β-diversity e.g. 5 sites x11 x12 ... x1n 1 s12 s13 s14 s15 (Jaccard, …) . 1 s23 s24 s25 x ... . . S = 21 S sim = . . 1 s34 s35 : . . . . . . 1 s45 x xmn . . m1 . . . . 1 Similarity Coefficient / Distance Mantel Test x1 y1 0 d12 d13 d14 d15 x2 ... . 0 d23 d24 d25d = . d = . . 0 d34 d35 xy Euclidean . . . . 0 d45 . . . . 0 xm ym Site location: x,y Geographic distance
- 19. 19 Case Study 1: Tree rainforest in PanamaFloristic data: 708 tree species (> 10 cm dbh) 53 sites of ~1 ha Precipitation Gradient Floristic Composition Environmental Variables: • Precipitation • Elevation • Slope • Water accumulation flow • Geology • Fragmentation
- 20. 20 Case Study 1: Tree rainforest in Panama Jaccard Geographical Distance (GD) 0.637Fraction species shared Dispersal-related factors ln(GD) 0.696 β-diversity Cross-plot forest fraction 0.323 Elevation 0.424 Slope 0.318 Runoff 0.078 Environmental factors Precipitation 0.572 Dry season 0.461 Geologic types 0.126 Band 1 0.305 Band 2 0.117 Band 3 0.127 Spectral data Distance (km) Band 4 0.258 Band 5 0.148 Condit et al. Science, January 25, 2002. Band 7 0.160
- 21. 21 Identification of complementary areas of diversity Site 1 Site 2 Site 1 Site 2 A E D A F B C E F C G D• Problem of the minimal area Minimise the total surface while preserving all species• Problem of the maximal coverage Maximise the number of species within a fixed surface Optimising γ-diversity
- 22. 22 Identification of complementary areas Step 1. Hierarchical agglomerative clustering Similarity 0% 8% 20%Cluster 3.1 3.2 3.3 3.4 3.5 2.1 2.2 1.1 1.2Plots 1,3,4,21,22, 2,S0,S1,S3,S2,S4, 34 40 41 31,32 36 35 37 29,23,27,24, SH,25,26,5,17,13, 33 28,30,C1, 10,11,18,14,P1, C4,C2,C3 P2,6,7,12,15,16,8, 9, 20,19,G1,G2 Step 2. Multiple Regression Model between distance matrices
- 23. 23 Identification of complementary areas Step 1. Hierarchical agglomerative clustering Similarity 0% 8% 20%Cluster 3.1 3.2 3.3 3.4 3.5 2.1 2.2 1.1 1.2Plots 1,3,4,21,22, 2,S0,S1,S3,S2,S4, 34 40 41 31,32 36 35 37 29,23,27,24, SH,25,26,5,17,13, 33 28,30,C1, 10,11,18,14,P1, C4,C2,C3 P2,6,7,12,15,16,8, 9, 20,19,G1,G2 Step 3. Step 2. Multiple Regression Model Extrapolation between distance matrices of the model and cluster 1.0 assignation Jaccard similarity 0.8 Ŝ(pixel i, site 1) • Log(GD) 0.6 Ŝ(pixel i, site 2) • Elevation • Bands 1-4 0.4 : R2 = 0.57 (p < 0.001) Ŝ(pixel i, site 53) 0.2 0.2 0.4 0.6 0.8 1.0 Predicted
- 24. 24 Predicted floristic types: identification of complementary areas Non-rain forest Water surfaces Cluster 1.1 Cluster 1.2 Cluster 2.1 Cluster 2.2 Cluster 3.1 Cluster 3.2 Cluster 3.3 Cluster 3.4 Cluster 3.5Chust, G., J. Chave, R. Condit, S. Aguilar, S. Lao, & R. Pérez (2006) Determinants and spatial modeling of beta-diversity in a tropical forest landscape in Panama. Journal of Vegetation Science 17: 83-92.
- 25. 25 Case Study 2: zooplankton in the Bay of Biscay47 20 10 0 267 Zooplankton 0m m samples collected from46 May 2-16, 2004 Bay of Biscay45 Cap Ferret Canyon Gironde Estuary 24 most abundant copepods Arcachon Bay44 Cap Breton Canyon Adour river43 -7 -6 -5 -4 -3 -2 -1 0 Copepod Calanus helgolandicusIrigoien, X., G.Chust, J.A. Fernandes, A. Albaina, L. Zarauz (2011) Factors determiningmesozooplankton species distribution and community structure in shelf and coastal waters.Journal of Plankton Research 33: 1182-1192.
- 26. 26 Case Study 2: zooplankton in the Bay of BiscaySpecies similarity indices against geographic distance 1.0 Species similarity (Bray-curtis) 0.8 0.6 Species similarity 0.4 0.2 0.0 0 50 100 150 200 250 300 350 Distance (km) 0.8 Species similarity (Jaccard) 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350 Distance (km) Distance (km)
- 27. 27 Case Study 2: zooplankton in the Bay of BiscaySpecies similarity indices against environment:• 15 environmental variables (bottom depth, temperature, salinity and density at surface and bottom, difference in density between surface and bottom, Frequency of Brunt- Vaisala, integrated fluorescence, depth of the maximum fluorescence, fluorescence at the maximum, abundance of chaetognath, jellyfish and fish eggs)• 32767 possible subsets were compared ! • ∑ , where n: number of var., k: combinations ! !• The best subset of environmental variables selected so that explain the maximum variation of the species similarity were 4: Frequency of Brunt-Vaisala, salinity at surface, density at bottom and jellyfish abundance (for Bray-Curtis index)
- 28. 28 Model Selection Aim: to select the best subset of environmental variables, so that distances of (scaled) environmental variables have the maximum correlation with community dissimilarities Environmental Matrix Environmental similarity x11 x12 ... x1q 1 s12 s13 s14 s15 . 1 s23 s24 s25 x21 ... . . AMB = AMB (Euclidean, …) sim = . . 1 s34 s35 : . . . . . . 1 s45 x . m1 . . xmq . . . 1 x11 x12 x ... AMB = 21 : . x . m1 n combinations of q variables → n Environmental similarity matrices
- 29. 29 Case Study 2: zooplankton in the Bay of Biscay Mantel r p-value Terms selected for Environmental variablesBray-Curtis × Environment 0.54 0.001 Frequency of Brunt-Vaisala, Salinity at surface, Density at bottom, Jellyfish abundanceBray-Curtis × Distance 0.43 0.001Bray-Curtis × Environment (Distance partially out) 0.50 0.001Jaccard × Environment 0.44 0.001 Temperature at bottom, Density at surface and at bottom, Fish abundanceJaccard × Distance 0.47 0.001Jaccard × Environ selec (Distance partially out) 0.34 0.001 ENV Conclusion: mesozooplankton communities in DIS the Bay of Biscay are subjected to balanced degree of dispersal limitation and niche segregation.
- 30. 30 Case Study 2: a comparison of estuarine intertidal communitiesSaltmarsh and seagrass plants Macroalgae Macroinvertebrates rM = 0.625 rM = 0.316 rM = 0.064 Slope = -0.0021 Slope = -0.0020 Slope = -0.0003
- 31. 31 Software for Similarity/distance indices and Mantel tests• R: vegan package (Oksanen et al. 2011, see Docs)• PRIMER (Clarke & Gorley 2006; http://www.primer-e.com/)• …
- 32. 32Practical session 1 “CommunityEcology with R: vegan package”
- 33. 33 ANALYZING BETA DIVERSITY: PARTITIONING THE SPATIAL VARIATION OF COMMUNITY COMPOSITION DATA (Legendre et al. 2005, Ecological Monographs)• The variance of a dissimilarity matrix among sites (rM2) is not the variance of the community composition,• hence, partitioning on distance matrices should not be used to study the variation in community composition among sites.• Partitioning on distance matrices underestimated the amount of variation in community composition explained by the raw-data approach.• The proper statistical procedure for partitioning the spatial variation of community composition data among environmental and spatial components, and for testing hypotheses about the origin and maintenance of variation in community composition among sites, is canonical partitioning.• The Mantel approach is appropriate for testing other hypotheses, such as the variation in beta diversity among groups of sites. Regression on distance matrices is also appropriate for fitting models to similarity decay plots.
- 34. 34Direct (constrained) Ordination Methods & Variation partitionning
- 35. 35 Constrained (Canonical) Ordination Methods One species q environ. var. (Occurrence, abundance) x1 x11 x12 ... x1q x x21 ... . . • Univariate: e.g. (multiple) regression model S = 2 × AMB= : . . . : x x m m1 . . xmq • Multivariate response data: e.g. Canonical Ordination Species composition data. q environ. var. x11 x12 ... x1n x11 x12 ... x1q x21 ... . . x21 ... . . S = : . . . × AMB = : . . . x . . xmn x . . xmq m1 m1 • Residual variation of multivariate response data: e.g. Partial ordination Species composition data. q environ. var. Spatial terms x11 x12 ... x1n x11 x12 ... x1q x1 y1 x2 ... x21 ... . . x21 ... . . S = : . . . × AMB = : . . . × d xy = . . x x xmq x m1 . . xmn m1 . . m y m
- 36. 36 Constrained (Canonical) Ordination Methods• Ordination methods such as principal component analysis (PCA) are used toreduce the variation in community composition in an ordination diagram.(PCA uses an orthogonal transformation to convert a set of observations of possibly correlatedvariables into a set of values of uncorrelated variables called principal components) x11 x12 ... x1n x11 x12 ... x1q pc1 pc 2 ... pc 3 x21 ... . . x21 ... . . S = → ... PCA = ... . . × AMB = : : . . . : . . . . . . ... ... x . . xmn . . x . . xmq m1 m1 • Constrained (Canonical) Ordination: is a combination of ordination andmultiple regression. It extracts continuous axes of variation from species abundancedata in order to explain which portion of this variation is directly explained byenvironmental variables. The axes are constrained to be linear combinations ofenvironmental variables. The orthogonal directions in PCA is particular and otherdirections may well be better related to env. var. Canonical Ordination is a solutionfor this. Response models Indirect Direct Multivariate Linear PCA Constrained Ordination: RDA Unimodal Constrained Ordination: CCA
- 37. 37 Constrained (Canonical) Ordination MethodsCanonical Correspondence Analysis (CCA): species are assumed to have unimodalresponse surfaces with respect to compound environmental gradient. It is related toCorrespondence Analysis and it is based on Chi-squared distance. Abundance a b c Environnemental GradientRedundancy Analysis (RDA): species are assumed to have linear response surfaces withrespect to compound environmental gradients. Thus, RDA is a direct extension of multipleregression to the modelling of multivariate response data. It is related to PCA and it is basedon Euclidean Distances. c a Abundance b Environnemental Gradient
- 38. 38 Spatial terms for Canonical Ordination Methods: trend surfaceGeographic distance Trend surface modelfor Mantel approaches Linear 30 x, y 25 d 20 Z Data 15 10 5 5 4 ta 3 Da 0 X 4 2 3 x y Y Da ta 2 1 1 . . . . . . Cubic 100 x, y, xy, x2, y2, x2y, y2x, x3, y3 50 0 Z Data -50 5 -100 4 ta 3 Da -150 X 4 2 3 2 Y Da 1 ta 1
- 39. 39 Variation Partitionning 2 variable types Example 3 variable types UNA = 50% UNA UNA: Not explained ENV ENV ENV ANT d a 30% a b g c 10% e f b 10% c DIS DIS DIS e.g. Environment ENV, Distance DIS, e.g. Environment, Distance, Anthropogenic ANT UNA: unaccounted (not explained) Steps (just algebra): 1. Canonical Ordination (CO) between Species and ENV → a+c 2. pCO between Species and ENV, partially out SPA→ a; → c = (a+c)-a 3. CO between Species and (ENV & Distance) → a+b+c; i.e. 1-UNA Thus, b = (a+b+c) – a – c Or 3bis. CO between Species and DIS → b+c → Thus b = (b+c) – c ; UNA = 1 – [a + b + c] © AZTI-TecnaliaChust, G., et al. (2003). Conservation Biology 17 (6): 1712-1723.
- 40. 40Software for Canonical and Redundancy analysis, and Variation Partitioning: • R: vegan package (Oksanen et al. 2011, see Docs) • CANOCO (ter Braak and Smilauer 1998; http://www.pri.wur.nl/uk/products/canoco/) • …
- 41. 41 Case Study 1: Tree rainforest in Panama Based on Mantel test Based on Canonical Correspondence Analysis Shared Spatial terms 17% 25% Environment 10% 46%Duivenvoorden et al. Science, 2002. Not explained Chust et al. 2006. JVS* Conclusion: The distribution of Panamanian tree species appears to be primarily determined by dispersal limitation, then by environmental heterogeneity *Chust, G., J. Chave, R. Condit, S. Aguilar, S. Lao, & R. Pérez (2006) Determinants and spatial modeling of beta-diversity in a tropical forest landscape in Panama. Journal of Vegetation Science 17: 83-92.
- 42. 42Practical session 2 “CommunityEcology with R: vegan package”
- 43. 434th Corner Method
- 44. 44 4th Corner Method (Legendre et al. 1997) • The fourth-corner tests for the association between biological traits to habitat at locations where the corresponding species are found. • How do the biological and behavioral characteristics of species determine their relative locataions in an ecosystem? • e.g. are the modes of dispersion related to habitat fragmentation? A B C Presence/Absence × Traits × Environment 245 sp × 78 sites 3 life form Fragmentation 4 types of dispersion A( sp × sites ) B ( sp × trait ) D = C * A’ * B C (var× sites) D(var× trait ) • test F (global) • Correlation rLegendre, P., Galzin, R. & Harmelin-Vivien, L. (1997) Relating behavior to habitat: solutions to the fourth-cornerproblem. Ecology, 78, 547–562.
- 45. 45Case study 1: Coral reef fish data• Biological and behavioural traits• Environmental variables: Bottom type Depth … Legendre et al. 1997
- 46. 46 Case study 2: Plant traits 3 life forms Habitat fragmentation4 types of dispersion
- 47. 47 Case study: Plant traits Test FFragmentation Correlation Interpretation: The effects of fragmentation of scrubland on scrub species community are related to the dispersal type Interpretation: Wind- dispersed species are positively related to the defragmentation
- 48. 48 Case study: Plant traits Woody plants Annual herbs Interpretation: Wind- Number of species in scrublands dispersed and annual species are positively related to the defragmentation of scrublands Animal-dispersed Wind-dispersed 0-33 34-66 67-100 Fraction of scrubland (%) FragmentationChust, G., A. Pérez-Haase, J. Chave, & J. Ll. Pretus. (2006) Linking floristic patterns and plant traits of Mediterranean communities infragmented habitats. Journal of Biogeography 33: 1235–1245.
- 49. EURO-‐BASIN, www.euro-‐basin.eu Introduc)on to Sta)s)cal Modelling Tools for Habitat Models Development, 26-‐28th Oct 2011

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