Download presentation
Presentation is loading. Please wait.
1
Mathematical Biology Group
Statistical framework for deep analysis of spatiotemporal community data Gleb Tikhonov Spring Symposium 7 March 2017
2
Any consequences for ecology?
Yes!
3
Automatized data collection techniques
Camera traps Sound recorders for birds/bats Underwater sonic recorders
4
Automatized data collection techniques
Panthera onca 24.12W, 48.42S 10:57 07/03/17 auto Movement identification & image recognition Tapirus terrestris 24.34W, 47.54S 22:31 06/03/17 auto Puma concolor 23.87W, 48.03S 04:28 04/03/17 manually ... Tons of HD information!!!
5
cat *
6
… or some less radical solutions
Simplify or aggregate data e.g. drop temporal component by summation Stop! Thus we will miss all temporal signal in the data! Spatiotemporal analysis approach Spatio-temporal single species distribution models Cannot assess potential interactions (co-associations) between species Community analysis approach Join species distribution models (JSDM) So far only very restricted spatiotemporal joint species smoothing models exist We need something like… Spatiotemporal JSDM
7
Joint species distribution model
(on example of Multivariate Generalized Linear Model) 𝑌 𝑖𝑗 ~𝐷( 𝑔(𝐿 𝑖𝑗 ), 𝜙 𝑗 ) 𝐿 𝑖𝑗 = 𝐿 𝑖𝑗 𝐹 + 𝐿 𝑖𝑗 𝑅 𝐿 𝑖𝑗 𝐹 = 𝑥 𝑖 𝛽 𝑗 𝐿 𝑖𝑗 𝑅 ~𝑁(0,Σ) 𝑖 – sampling unit, 𝑗 – species 𝐷 – distribution function 𝜙 𝑗 – dispersal parameter 𝑔 – link function 𝐿 𝑖𝑗 -linear predictor Σ 𝐿 𝑖𝑗 𝐿 𝑖𝑗 𝑅 Similar to SDM, but explicitly accounting for correlation between species atop of response to environment
8
Both 𝜂 𝑖 and 𝜆 𝑗 must be estimated
Latent factors model 𝑌 𝑖𝑗 ~𝐷( 𝑔(𝐿 𝑖𝑗 ), 𝜙 𝑗 ) 𝐿 𝑖𝑗 = 𝐿 𝑖𝑗 𝐹 + 𝐿 𝑖𝑗 𝑅 𝐿 𝑖𝑗 𝐹 = 𝑥 𝑖 𝛽 𝑗 𝐿 𝑖𝑗 𝑅 ~𝑁(0,Σ) 𝐿 𝑖𝑗 𝑅 = 𝜂 𝑖 𝜆 𝑗 𝜂 𝑖 ~𝑁(0,I) 𝜂 𝑖 - latent factors 𝜆 𝑗 - latent loadings 𝐿 𝑖𝑗 𝜂 𝑖 Λ Λ T Covariance matrix Both 𝜂 𝑖 and 𝜆 𝑗 must be estimated
9
Hierarchical Model of Species Communities (HMSC)
↓ 𝑐𝑜𝑣 𝜂 𝑖 1 , 𝜂 𝑖 2 =exp − 𝛼 𝑠 −1 𝑑 𝑠 𝑖 1 , 𝑖 2 exp − 𝛼 𝑡 −1 𝑑 𝑡 𝑖 1 , 𝑖 2 𝑌 𝑖𝑗 ~𝐷( 𝑔(𝐿 𝑖𝑗 ), 𝜙 𝑗 ) 𝐿 𝑖𝑗 = 𝐿 𝑖𝑗 𝐹 + 𝐿 𝑖𝑗 𝑅 𝐿 𝑖𝑗 𝐹 = 𝑥 𝑖 𝛽 𝑗 𝐿 𝑖𝑗 𝑅 = 𝜂 𝑖 𝜆 𝑗 𝜂 𝑖 - latent factors 𝜆 𝑗 - latent loadings Time units Space units 𝜂 𝑖 1 𝜂 𝑖 2 𝑑 𝑡 𝑖 1 , 𝑖 2 𝑑 𝑠 𝑖 1 , 𝑖 2 𝛼 𝑡 𝛼 𝑠 𝛼 𝑠 and 𝛼 𝑡 - spatial and temporal scales of autocorrelation 𝑑 𝑠 𝑖 1 , 𝑖 2 and 𝑑 𝑡 𝑖 1 , 𝑖 spatial and temporal distances between sampling units 𝑖 1 and 𝑖 2 + Development of Bayesian full conditional Gibbs sampler Numerical optimization of the algorithm Implementation, debugging and testing
10
38 camera traps, 120 days one hour resolution
Example with real data Brazil, São Paulo 30 x 30 km area 38 camera traps, 120 days one hour resolution 17 mammal species
11
Example with real data Omnivore Carnivore medium Carnivore large
Eira barbara Leopardus guttulus Puma yagouaroundi Cerdocyon thous Procyon cancrivorus Leopardus pardalis Leopardus wiedii Dasypus novemcinctus Carnivore large Puma concolor Panthera onca Herbivore Medium Large Cuniculus paca Mazama bororo Tapirus terrestris Canis familiaris Homo sapiens Dasyprocta azarae Mazama guazoubira
12
Results Activity pattern Question What kind of daily activity patter do different species follow? Activity pattern Hour Hour
13
Results Co-associations matrix Space units Time units (hours)
14
Perspectives Space units Time units (hours) Space units
15
Thank you for your attention! Questions?
Mathematical Biology Group Thank you for your attention! Questions? 𝜂 𝑖 ~𝑁 0,I ↓ 𝑐𝑜𝑣 𝜂 𝑖 1 , 𝜂 𝑖 2 =exp − 𝛼 𝑠 −1 𝑑 𝑠 𝑖 1 , 𝑖 exp − 𝛼 𝑡 −1 𝑑 𝑡 𝑖 1 , 𝑖 2 Time units Space units 𝜂 𝑖 1 𝜂 𝑖 2 𝑑 𝑡 𝑖 1 , 𝑖 2 𝑑 𝑠 𝑖 1 , 𝑖 2 𝛼 𝑡 𝛼 𝑠
16
Joint species distribution model
(on example of Multivariate Generalized Linear Model) Pollock et al, 2014 Co-occurrence pattern due to known environment Associations atop of environment (interactions) Σ = Mode is determined be response to environment 𝑚 𝑖𝑗 = 𝑥 𝑖∙ 𝛽 ∙𝑗 Σ = Σ – number of estimated parameters ~ square of community size Σ = 1 −0.75 −0.75 1 Pollock et al, 2014
17
Data typically acquired by community ecologists
Code Question FQ1 How much variation in species occurrence is due to environmental filtering, biotic interactions, and random processes? FQ2 How does the answer to FQ1 vary across spatial and temporal scales? FQ3 How does community similarity depend on environmental similarity and/or geographic distance? FQ4 How does community structure change over time due to predictable succession or stochastic ecological drift? FQ5 Do temporal community dynamics vary with environmental conditions or spatial location? FQ6 What are the structures of species interaction networks? FQ7 How does the abiotic environment influence the answer to FQ6? FQ8 How do species’ traits influence ecological niches? FQ9 Do phylogenetic relationships correlate with ecological niches, beyond that explained by traits? FQ10 Are there signals of niche conservatism or niche divergence? FQ11 How do traits and phylogenetic constraints influence species interactions? AQ1 Which processes have been central in determining the response of a community to environmental change AQ2 How can species be classified in terms of their response to abiotic environment? AQ3 How can geographic areas be classified into communities of common profile? AQ4 Do some species indicate the presence of others? AQ5 How is community structure predicted to change under various scenarios of e.g. environmental change Y Occurrence X Environment Spatio-temporal context 1980 2000 2020 ? sampling units sampling units species covariates C Phylogeny T Traits species species species traits
18
The statistical framework in a nutshell:
Hierarchical Modelling of Species Communities (HMSC) Parameters Data 𝛀 𝐗
19
C. Variance partitioning D. Species associations
A. Study design B. Predictive power Presence-absence of 50 fungi surveyed in 2800 resource units (large beech logs) belonging to 230 sampling plots in 8 natural (green) and 20 managed (red) forests. Forest Plot Sampling unit Level UC C Forest 18% 20% Plot 21% Sampling unit 1% 3% Predictive power Prevalence Prevalence Prevalence C. Variance partitioning Proportion of variance Species D. Species associations The photos exemplify negative and positive associations at the sampling unit level: Diatrype disciformis often fruits alone, whereas Biscogniauxia nummularia and Stereum ostrea are often found to fruit together. Forest Plot Sampling unit Species Species Species Species
20
C. Variance partitioning D. Species associations
A. Study design B. Predictive power C. Variance partitioning Presence-absence of 55 butterflies in 10 x 10 km grid covering Great Britain. The map shows variation in species richness. Non-spatial Spatial 7% 43% Proportion of variance Latitude Predictive power Longitude Prevalence Species D. Species associations E. Community similarity Community correlation Species Latitude Species Longitude Distance
21
B. Variance partitioning
A. Study design B. Variance partitioning Species: Little grebe Black-winged stilt Little-ringed plover Moorhen Mallard Common shelduck Common coot Presence-absence of 7 waterbirds surveyed for 7 years on 215 irrigation ponds in southeast Spain. 2 6 Proportion of variance Species C. Species associations Influence of previous year Pond-year Pond Year Focal species Influencing species Species Species Species
22
B. Variance partitioning C. Species associations
A. Study design B. Variance partitioning Presence-absence of 60 bryophyte species surveyed on 208 aspen trees within 14 natural forest sites and 14 logging sites. A retention aspen on a logging site. Proportion of variance Species C. Species associations Site Tree Species E. Species classification The photos exemplify species that are re-colonizing (Radula complanata) or old-growth favouring (Neckera pennata). RC OG D. Scenario simulations D Influence of time since logging Species richness Community similarity LB Stand age (years) Stand age (years) Preference for natural forests
Similar presentations
