Variance Decomposition of Species-Environment Relationships. Variance Decomposition of Species-Environment Relationships

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1 Variance Decomposition of Species-Environment Relationships P Goal is to decompose the variance in the species data set explainable by logical components of unique and interactive effects of explanatory variables. Total Inertia % species variance explainable by full set of explanatory variables A S P 1 Variance Decomposition of Species-Environment Relationships P The major goal is to determine the relative importance of each type of factor (to the species) and the strength of coordination and confounding among the components. Space P The secondary goal is to determine within each set which variables are most important and how they interact with other variables within and between sets. Veg Abiotic 2

2 Covariables and Partial CCA/RDA P Variance decomposition is accomplished via the use of covariables and partial CCA/RDA/CAP the same as regular CCA/RDA/CAP with the added constraint that each synthetic gradient must be uncorrelated with the covariables - as well as with all other canonical axes. P Partial CCA/RDA is effective to decompose the variance into its logical components of unique and interactive effects. P Requires that covariables and environmental variables are not very highly correlated otherwise the covariables will remove most of the story told by environmental variables. 3 Total Inertia Not accounted for by covariables Covariables Environ variables Variance Decomposition of, Patch, and Landscape Effects on Bird Species in the Oregon Coast Range Patch Landscape 4

3 The Seven Variance Components [Pa] [L] independent plot effect independent patch effect independent landscape effect [PlPa] joint plot and patch, independent of landscape [PaL] [PlL] joint patch and landscape, independent of plot joint plot and landscape, independent of patch [PlPaL] joint plot, patch and landscape. [PlPa] [PlL] [PlPaL] [Pa] [PaL] [L] Patch Landscape The Seven Variance Components 5 Three of the seven components we can calculate directly from partial CCA/RDA/CAP: = Pl PaL [Pa] = Pa PlL [L] = L PaPl The others require some intermediate steps. [PlPa] [PlL] [PlPaL] [Pa] [PaL] [L] We need to run 12 Partial models to isolate all seven components. Patch Landscape 6

4 Analyses Needed to Isolate Variance Components 1. Pl variables explanatory, no covariables 2. Pa Patch explanatory, no covariables 3. L Landscape explanatory, no covariables 4. Pl Pa -- explanatory, Patch covariables 5. Pl L explanatory, Landscape covariables 6. Pl PaL explanatory, Patch and Landscape covariables 7. Pa Pl -- Patch explanatory, covariables 8. Pa L Patch explanatory, Landscape covariables 9. Pa PlL Patch explanatory, and Landscape covariables 10. L Pl Landscape explanatory, covariables 11. L Pa Landscape explanatory, Patch covariables 12. L PlPa Landscape explanatory, and Patch covariables 7 Variance Partitioning Calculations: Step 1 = Pl PaL explanatory, Patch & Landscape covariables Independent Effects [Pa] = Pa PlL Patch explanatory, & Landscape covariables Independent Patch Effects [L] = L PaPl Landscape explanatory, & Patch covariables Independent Landscape Effects [PlPa] [PlL] [PlPaL] [Pa] [PaL] [L] Patch Landscape 8

5 Variance Partitioning Calculations: Step 2 The next step to solve the rest of the puzzle is to calculate the 3- way overlap, [PlPaL]: Three alternatives: P L PlPa + (L-L Pa) + (L-L Pl) -L P Pa PlL + (Pa-Pa Pl) + (Pa-Pa L) -Pa P Pl PaL +(Pl-Pl Pa) + (Pl-Pl L) -Pl The key insight here is that: [Pa] [PlPa] [PlPaL] [PaL] [PlL] [L] L-L Pa = [PlPaL]+[PaL], L-L Pl = [PlPaL]+[PlL], Pa-Pa Pl = [PlPaL]+[PaL], etc.. Patch Landscape 9 Variance Partitioning Calculations: Step 3 Once the 3-way overlap is known, the remaining 3 partitions can be easily derived: [PlPa] = Pl - Pl Pa - [PlPaL], or Pa - Pa Pl - [PlPaL] Joint -Patch Effects [PlL] = Pl - Pl L - [PlPaL], or L - L Pl - [PlPaL] Joint -Landscape Effects [Pa] [PlPa] [PlPaL] [PaL] [PlL] [L] [PaL] =Pa - Pa L - [PlPaL], or L - L Pa - [PlPaL] Joint Patch-Landscape Effects Patch Landscape 10

6 Variance Partitioning Results The 12 Analyses CCA Approach: Total Inertia = 1.84 Sum Can Eigen Percent Species Variance P-value 1 plot patch land plot_cpatch plot_cland plot_cpatchland patch_cplot patch_cland patch_cplotland land_cplot land_cpatch land_cplotpatch Variance Partitioning Results The 7 variance components P Interpreting the relative importance of major factors and the degree of confounding among components Patch Landscape 12

7 Evaluating Stability Across Basins Pl PlPa Pa Pl PlPa Pa Pl PlPa Pa PlL L Drfit PlPaL drift Pl Pa L PlPa PaL PlL PaPlL PlL L PlPaL Lobster lobster Pl Pa L PlPa PaL 0 PlL PaPlL PlL PlL L PlPaL Nestucca nestucca Pl Pa L PlPa PaL PlL PaPlL Evaluating Stability Across Basins Variablility among basins in the size of each partition 14

8 Evaluating Stability Across Basins Pl PlL L PlPa PlPaL Pa variablility across basins for cca mean std coef Pl Pa L E PlPa PaL PlL PaPlL Across the three basins the size of the seven partitions of plot, patch, and landscape effects on the bird community are amazingly stable. effects, as expected are the most important, accounting for over 80% of explained variation. Landscape and Patch factors are also important, but are largely confounded with plot effects. Only approximately 5% of bird variance is explained by Patch factors independent of other explanations, and only approximately 4% of bird variance is explained by landscape factors independently. In contrast, factors in isolation explain between 22 and 27% of bird variance. 15 Hierarchical Variance Decomposition Nested within the first level of the hierarchy are additional partitions of the data set: P Partition: < Biotic Floristics Structure Cover < Abiotic P Patch Partition: < Area < Structure P Landscape Partition: < Composition < Configuration Floristics Abiotic Area Structure Structure Biotic Patch Landscape Cover Configuration Composition 16

9 Hierarchical Variance Decomposition Partitioning of Marginal vs Conditional Effects P Marginal Partition -- Relative contribution of each sub-partition to the parent partition as a whole. P Conditional Partition -- Relative contribution of each sub-partition to the parent partition s independent (i.e., conditional) effects. 17 Hierarchical Variance Decomposition Calculating Second/Third-Tier Partitions P Second/third-tier conditional partitions are computed the same way as the first tier, except that the other first(and second)-tier components are added as covariables. Marginal Partitions: Composition = Lc Ls Joint = L - Lc Ls -Ls Lc Structure = Ls Lc Conditional Partitions: Composition = Lc LsPlPa Joint = L PlPa - Lc LsPlPa -Ls LcPlPa Structure = Ls LcPlPa 18

10 Hierarchical Variance Decomposition Second/Third Tier Results P Partition...Structure not as important as floristics and cover type abundance. P Patch Partition...Patch structure, independent of area, was a better predictor of community structure than patch area for both decompositions. P Landscape Partition...Landscape composition was a more important predictor of community structure than was landscape configuration for both decompositions. 19 Interpreting Relationship among Sites, Species, and Environmental Variables in Variance Partitions P Relationships among sites, species and environmental variables within each partition can be displayed with in a triplot. P Conditional Triplots...The most interesting relationships may be the conditional partitions, which show the independent relationships of a factor after accounting for confounding with other factors; i.e., that variance that can be exclusively associated with a factor. P Cumulative Species Fit...May be most meaningful to display only species that meet some minimum specified threshold in cumulative variance explained; i.e., species that show a strong relationship to the partition. 20

11 Partial Triplots Independent Effects (after accounting for Patch & Land) 21 Variance Decomposition of Species-Environment Relationships Summary and Conclusions P Variance decomposition is a powerful means of separating the species-environment relationships into logical components of unique and interactive effects of explanatory variables. P Suitable for hierarchically organized, multi-level explanatory variables. Veg Space Abiotic 22