Geostatistical assessments in the NSERC Ca Incorporation of Auxiliary Information in the Geostatistical Simulation of

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1 Assessment of evidence and impacts of calcium decline in fresh-water lakes and soils: Geostatistical methods and ecosystem modeling 1) Spatial inferences for 3 lakes in the EB Muskoka watershed region ) Integration with soil databases (CANSIS): The role of geostatistics and GIS in identifying areas of increased risk or longterm instability 3) It takes a (species) community to tell an ecosystem s story: Fisher s species- abundance distribution (SAD) and the MAXENT modeling framework in macroecology Why geostatistics? or Will geostatistics do anything beyond assembling already existing information and producing beautiful maps? or Can geostatistics alert us to something that we didn t see in the data already? An example from the recent literature Geostatistical assessments in the NSERC Ca Incorporation of Auxiliary Information in the Geostatistical Simulation of decline project: Implementation and first steps Soil Nitrate Nitrogen S. Grunwald, P. Goovaerts et al. Vadose Zone Journal () 1) Previously assembled dataset: Bythothrephes (spiny waterflea) invasions in 311 lakes of the Watershed EB region (Allegra Cairns, Norman Yan et al.) ) The geostatistical tool set: A) Statistical concepts i) (Semi-)Variogram ii) Kriging iii) Kriging covariates: B) Software: GeoR package (Diggle et at.) for Statistics in R Ca concentrations in lakes: Data summary (I) Ca concentrations in lakes: Data summary (II) 1

2 Ca concentrations: Empirical cloud variogram Sample variogram for Ca concentrations in lakes γ(u) = (1/N(u)) x,y: x-y ~u [s(x)-s(y)] Spatial inference of lake Ca concentrations in the EB Watershed region by simple kriging (I) Spatial inference of lake Ca concentrations in the EB Watershed region by simple kriging (II) Spatial inference of lake Ca concentrations in the EB Watershed region by simple kriging (III) Spatial inference via simpale kriging for other chemical variables: Na (I)

3 Spatial inference via simpale kriging for other chemical variables: Na (II) Spatial inference via simpale kriging for other chemical variables: Na (III) lakes: phosphorus (PPUT1) Spatial inference via simple kriging: phosphorus (I) Spatial inference via simple kriging: phosphorus (II) Spatial inference via simple kriging: phosphorus (III) 3

4 lakes: acidicity (ph value) Spatial inference via simple kriging: ph value (I) Spatial inference via simple kriging: ph value (II) Simple kriging spatial inferences: Geostatistical covariates of Ca concentrations (I): The elevation effect ph value Ca concentrations R = -.35

5 Geostatistical covariates of Ca concentrations (II): Na concentrations Geostatistical ANOVA: Detrending the sample variogram against covariates R=.79 Ca with covariates Ca/ detrended against Altitude Ca/ detrended against Na Spatial inference using covariate information (I): Simple kriging with trend parameter Altitude Spatial inference on Ca concentrations using information from covariates (I): Simple kriging with trend parameter Altitude Lake Ca concentrations: Covariate kriging identifies systematic effects. Spatial inference on Ca concentrations using information from covariates (II): Simple kriging with trend parameter Na Kriging with Altitude covariate Kriging without covariate 5

6 Kriging with covariate Na Kriging without covariates Macroecology: Minimal assumption (null) models of species abundance and community composition MAXENT: Constrained entropy maximisation Morphometry, area & climate constraints Metabolic rates & relative growth rates constraints Stoichiometry in soils/ aquatic environments Aggregate and quantitative variables in macroecology/ community ecology, derivable through MAXENT: - species-area relationship (SAR) : number of different species in a given area - species-abundance distribution (SAD): fraction of species with specified abundance - abundance-energy relationship (AER): number of individuals of a given species with specified energy requirement Example: SAD empirically follows the log-series distribution (Fisher 193): Φ(n) ~ (1/n) x n, where x is a constant < 1. Shipley, Science, J. Harte et al., Ecology, Dataset: 7 years of bimonthly seasonal measurements in 7 Ontario lakes collected at the Dorset Center/ ~19 individual observations/ Data organized by and obtained from Norman Yan Abundance distribution in octaves: Oct.1: 1 Oct.: -3 Oct.3: -7 Oct.: -15 Oct.5: 1-31 Oct.: 3-3 Oct.7: -17 Oct.: Number of species 5 Species-abundance distribution/ Plastic Lake/ / Octaves: No. of individuals 1-Oct- B. FREYI, LIEDERI OR LONGIROSTRIS 7 1-Oct- DAPHNIA (HYALODAPHNIA) GALEATA MENDOTAE 5 1-Oct- EUBOSMINA (NEOBOSMINA) TUBICEN 5 1-Oct- HOLOPEDIUM GLACIALIS 5 1-Oct- DIAPHANOSOMA BIRGEI 1 1-Oct- CALANOID COPEPODID 19 1-Oct- LEPTODIAPTOMUS MINUTUS 1-Oct- CALANOID NAUPLIUS 3 1-Oct- CYCLOPOID COPEPODID 19 1-Oct- CYCLOPS SCUTIFER 1 1-Oct- TROPOCYCLOPS PRASINUS MEXICANUS 5 1-Oct- CYCLOPOID NAUPLIUS most frequent species Number of species species-abundance distribution/ Plastic Lake/ /7 Octaves: No. of Individuals A changing pattern in species abundance distribution: A more robust indicator of ecosystem stress? No. of species species-abundance distribution/ Plastic Lake/ / 11-Jun-7 B. FREYI, LIEDERI OR LONGIROSTRIS 7 11-Jun-7 DAPHNIA (DAPHNIA) AMBIGUA 9 11-Jun-7 EUBOSMINA (NEOBOSMINA) TUBICEN 9 11-Jun-7 HOLOPEDIUM GLACIALIS 11-Jun-7 DIAPHANOSOMA BIRGEI 1 11-Jun-7 CALANOID COPEPODID 11-Jun-7 LEPTODIAPTOMUS MINUTUS 11-Jun-7 CALANOID NAUPLIUS 1 11-Jun-7 CYCLOPOID COPEPODID 11-Jun-7 CYCLOPS SCUTIFER 11-Jun-7 MESOCYCLOPS EDAX 1 11-Jun-7 CYCLOPOID NAUPLIUS 3 most frequent species No. of individuals 3-Jun- DAPHNIA (DAPHNIA) AMBIGUA 3 3-Jun- EUBOSMINA (NEOBOSMINA) TUBICEN 5 3-Jun- HOLOPEDIUM GLACIALIS 7 3-Jun- POLYPHEMUS PEDICULUS 1 3-Jun- EUBOSMINA (EUBOSMINA) LONGISPINA 3-Jun- DIAPHANOSOMA BIRGEI 3-Jun- DAPHNIA SP. 1 3-Jun- BOSMINA (BOSMINA) FREYI 7 3-Jun- CALANOID COPEPODID 3-Jun- LEPTODIAPTOMUS MINUTUS 3-Jun- CALANOID NAUPLIUS 3 3-Jun- CYCLOPOID COPEPODID 9 3-Jun- CYCLOPS SCUTIFER 5 No dominant species/ several species with intermediate abundances 3-Jun- MESOCYCLOPS EDAX 13 3-Jun- CYCLOPOID NAUPLIUS 7

7 Species-abundance distribution/ Plastic Lake/ / species-abundance distribution/ Plastic Lake/ /7 No. of species Species-abundance distribution/ Plastic Lake/ / 5 Number of species 5 Octaves: No. of individuals Number of species Octaves: No. of Individuals No. of individuals -Jun-5 DAPHNIA (DAPHNIA) AMBIGUA 13 -Jun-5 DAPHNIA (DAPHNIA) CATAWBA 1 -Jun-5 EUBOSMINA (NEOBOSMINA) TUBICEN -Jun-5 HOLOPEDIUM GLACIALIS -Jun-5 POLYPHEMUS PEDICULUS 1 -Jun-5 EUBOSMINA (EUBOSMINA) LONGISPINA -Jun-5 DIAPHANOSOMA BIRGEI 1 -Jun-5 DAPHNIA SP. 3 -Jun-5 BOSMINA (BOSMINA) FREYI 1 -Jun-5 CALANOID COPEPODID 19 -Jun-5 LEPTODIAPTOMUS MINUTUS 5 -Jun-5 CALANOID NAUPLIUS 5 -Jun-5 CYCLOPOID COPEPODID 1 -Jun-5 CYCLOPS SCUTIFER 5 -Jun-5 MESOCYCLOPS EDAX -Jun-5 CYCLOPOID NAUPLIUS -Jun-5 TROPOCYCLOPS EXTENSUS 1 No dominant species/ several species with intermediate abundances No. of species species-abundance distribution/ Plastic Lake/ / No. of individuals No. of species Species-abundance distribution/ Plastic Lake/ / 5 No. of individuals /5: no dominant species, many species with intermediate abundances Species-abundance distributions in Plastic Lake 19- Species-abundance distributions in seven lakes 19-: A statistically significant pattern change Abundance segments Plastic Blue Chalk Chub Crosson Dickie Harp Heney 19 Time Few species in abundance segment Many species in abundance segment Abundances are normalized: Total number of individuals is constant (~35) over all lakes and time points. Abundance distributions are significantly different between the periods 3- and 19-: Plastic Lake Number of species/ medians 1 to 3 to 7 to 15 1 to 31 3 to 3 to 17 1 to 55 Blue Chalk 19 to to p-value E-5.31E-.37E- 7.E-3 NA Chub 19 to 3 3 to 1 3 p-value E-5.7. NA SAD Octaves: to to p-value e-3 7.7E E- 1.3E-3 NA p-values are from Wilcoxon rank-sum statistics: Test on differences in frequencies of octave abundancy segments, separately for each octave Crosson 19 to to p-value e-5..7 NA Dickie 19 to to p-value E NA Harp 19 to to p-value 9.E-5.1.1E-5.3.E- 1.7E-3.1 NA Heney 19 to to p-value E NA Plastic 19 to to p-value e-3 7.7E E- 1.3E-3 NA 7

8 Future steps/ directions: - include further covariates and soil type information in geostatistical analysis - resolve georeferencing difficulties in GIS/ CANSIS soil databases - compare and validate different kriging methods (especially indicator kriging and derivation of critical threshold probability maps) - Macroecology and constrained Entropy Maximisation Method: Establish reference null models for community composition (needed: data on metabolic rates, growth rates, size distributions), with special reference to calcium sensitivity He handed me a white lump the size of a softball, but chalky, as though he head been saving blackboard dust for half a century. Hold it, he said. See how heavy it is. It sank in my hand like a shotput. Now that has hardly any organic matter in it, hardly any nutrients, he observed slowly, choosing his words. But it is certainly a soil. It was also my introduction to the pygmy forest, and Jenny s understanding of ecosystem evolution. The heavy chalky lump I hefted was, he told me, ancient, Methusalan. With a ph just this side of lemon juice and a subsoil as hard as a frying pan, the soil it came from grew nothing but a few stunted pines and heath plants acid lovers like manzanita... What most startled me was that this soil was not from a parched desert but from the area widely regarded as unmatched for scenic beauty on the whole California coast. This white dust was from Mendocino. The Soil Man (Hans Jenny), in Dirt The ecstatic skin of the earth, by William Bryant Logan, 1995.