Using statistical models to study climate-disturbance-plant interactions Andrew Latimer – amlatimer@ucdavis.edu Adam Wilson – adam.wilson@yale.edu Cory Merow – cory.merow@gmail.com Mediterranean climate • Key features: warm temperate, with cool wet winters and hot dry summers. Climate change effects? The obvious ones: • Warmer winter -> more growth • Hotter summer -> more fire Complications May raise growth rate while hammering other parts of life cycle (e.g. survival) Fire-plant feedbacks can produce rapid shift -> fuel starvation -> flammability Feedback example – Sierra forest • When feedbacks positive, slight shift in disturbance regime can cause state change Moderate fire (-) e.g. Collins et al. (2009) Ecosystems Less fuel, milder fire Intense fire (+) More shrubs, intense fire e.g. Stevens et al. (2013) Can.J.For.Res. Photos: Jens Stevens Fire-plant interaction example: South African fynbos No fire (fire suppressed) Fire No fire (plant growth suppressed) Population size More frequent fire can eliminate populations 8-year intervals between fires 4-year intervals between fires Stevens & Beckage, Oecologia 2010 Climate Growth, Survival etc. Ignition and spread Disturbance Fire Regrowth of Fuel, flammability Plant species, communities Challenges – ecological data • Scales of process can be large – Field data collection is almost always not • Interpolation and extrapolation (worse in projections) Current Future Environment Challenges – environmental data • Highly multivariate environmental measurements – Sensor outputs – Model outputs – Heterogeneous data sources • Multivariate responses – Community: Many species, life stages – Individual: phenotypes, genotypes • What’s important and why? – Q: Are the factors on both sides sparse? Outline 1) 2) 3) 4) A little more introduction Fire return times Biomass regrowth Demography Study system for this talk Cape Floristic Region of South Africa • Fynbos shrubland interfacing with karroo desert • Evolutionary radiation -> very high plant diversity and endemism • Diversity concentrated in ~30 lineages over 0.5-30 MY CFR climate change Historical patterns Recent change (1950-2000) Total Spring/Summer Precipitation Change per Year (mm) (mm) Change per decade High : 10.97 Low : -10.06 Climate change projections CMIP5 multimodel average 2081-2100 -- RCP8.5 Stippling: ≥ 8/11 models agree on sign Downscaled projections: Adam Wilson Thomas et al. (2004) Nature. Midgley et al. (2006). Diversity & Distributions. Example 1: Fire occurrence What affects fire frequency? Climate Growth, Survival etc. Ignition and spread Disturbance Fire Regrowth of fuel Plant species, communities Cape region fire data Cape Nature Fire Database (1927-2005) 18°0'0"E 18°30'0"E 19°0'0"E 19°30'0"E 20°0'0"E 20°30'0"E 21°0'0"E 21°30'0"E 22°0'0"E 22°30'0"E 23°0'0"E 31°30'0"S 32°0'0"S 34°30'0"S 34°30'0"S 34°0'0"S 34°0'0"S 33°30'0"S 33°30'0"S 33°0'0"S 33°0'0"S 32°30'0"S 32°30'0"S 32°0'0"S 31°30'0"S Fire_Code SWBG/12/1988/01 Reserve_NME Swartberg Date 12/1998 Perimeter 38,326 meters Area 3,606 hectares Veld_Age 8 years Cause Unknown 18°0'0"E 0 1020 40 18°30'0"E 60 19°0'0"E 80 100 Kilometers 19°30'0"E 1:2,500,000 20°0'0"E 20°30'0"E 21°0'0"E 21°30'0"E 22°0'0"E 22°30'0"E 23°0'0"E Thanks to Helen DeKlerk Fire data preparation • • • • Overlay ~2km x 2km grid on reserve areas Seasonal time resolution (3 months) Cell considered “burned” if >50% area burned Voxels of weather data: – 80 seasons x 2611 cells = 208,880 voxels Issues… • Very multivariate weather data • Approach: reduce dimensionality by biological intuition, hypothesis • Chris Wikle: “Sensible science-based parameterizations or dimension reductions” Issue: highly multivariate environmental data Mean Precipitation in December (mm) −31 80 70 −32 60 50 −33 40 30 −34 20 10 18 20 22 24 Weather station data Daily, point locations Included in WorldClim (50) Available Stations (523) Bayesian kriging with covariates (Adam Wilson) Gridded weather data Daily, ~2km grid 1.290 1.280 f(ppt.year.lag1) 1.282 f(ppt.year.mean) 1.280 1.270 150 Meetings (many…) Soil moisture model 1.278 200 -32 1.284 50-year average maximum drought length -1 0 1 2 -1 0 ppt.year.mean -33 1 2 ppt.year.lag1 1.29 1.31 1.0 1.25 1.27 f(gdd.grseas.mean) 1.6 1.4 50 -34 1.2 f(ppt.year.anom) 1.8 100 -1.5 -0.5 0.5 1.0 1.5 2.0 -2 -1 0 0 20 22 24 Indices -- i.e. hypotheses Seasonal to yearly Lon Choice of methods ppt.year.anom gdd.grseas.mean Modeling 1 Fire history data Timeline for one grid cell 6 years 14 years ? ? 1980 (beginning of record) Other hypothetical fire histories: . fires 2000 (end of record) Nonparametric survival model Zi = observed time between a pair of fires in cell I Pit : P(Zi > t | Zi > t-1) i.e. probability of “surviving” season t without a fire Climate: Long-term mean Probit(P) = XTβ + e Weather: anomalies in each grid cell * season Climate index (AAO) Random effects: season, sub-region Note Alan Gelfand’s 2013 paper adding spatial random effects Dealing with censoring • Left censoring: no previous fire observed in record Unobserved pit predicted from XTβ {Unobserved fire times} ~ Multinom(1-pit, t in [1950-1979]) Gives length distribution of unobserved fire intervals # Note may inflate fire frequency because a few cells will have failed to burn in these 30 years ? Wilson et al. (2010) Ecological Modelling Cumulative fire probabilities Wilson et al. (2010) Ecological Modelling Expected fire return times Wilson et al. (2010) Ecological Modelling Importance of large-scale atmospheric circulation patterns • Importance of AAO brings us back to complex multivariate problem (why AAO??) • But in this case pretty clear how it works • Note trends in ozone depletion (ozone hole) associated with positive AAO – Manatsa et al. (2013) Nature Geosci. Abram, et al. (2014) Nature Climate Change doi:10.1038/nclimate2235 Part 2: modeling postfire regrowth Climate Growth, Survival etc. Ignition and spread Disturbance Fire Regrowth of fuel Plant species, communities Remote sensing: Watching plants grow from space • MODIS terra NDVI data Model • Functional form that can match recovery pattern • Parameters – αi : minimum NDVI – γi : difference between min and max NDVI – λi: recovery rate parameter – Αi : amplitude of seasonal variation Wet, coastal ~4 years Dry, interior ~8 years Wilson et al. in prep Spatial variation in regrowth rates Regrowth rate based on Threshold NDVI value (95% of max NDVI) Wilson et al. in prep Tying this back to demographic models Factors related to regrowth rate Wilson et al. in prep Projected change in recovery time Years longer shorter Comparing recovery time to observed fire return intervals Some correspondence Slowest growing areas may be burning too often Conclusions on fire • Climate change likely to shorten fire return times • And also increase regrowth rates in many areas – But: Lower warm-season precipitation in the west, hotter summers • Big shifts possible – Frequent fire in slow-recovery areas – Fuel starvation and fynbos contraction (?) Example 3: Demography Tradeoff: -- More biological detail -- MUCH less data Climate Growth, Survival etc. Ignition and spread Disturbance Fire Regrowth of fuel Plant species, communities Focal species: Protea repens Data: Protea Atlas Project Tony Rebelo of SANBI Goal: model population performance across region • Measure across gradients • Demographic rates: – Growth & Fecundity – Mortality (dead adults) – Recruitment (seedlings per parent) Issue: recruitment sites limited by fire occurrence Analysis issues • Misalignment – Growth and seed production measured at different sites from seedling recruitment • Missing some steps in life cycle – Seedling emergence and survival Scaling issues raised by Jim and Alan Integral projection model (IPM) n t+1 = A n t nt+1 (z) = t z z' nt(z) nt+1(z’) K(z’,z) ò all sizes K(z', z) nt (z)dz = time = size at t = size at t+1 = size distribution of individuals at t = size distribution of individuals at t+1 = projection kernel (Matrix) (IPM ) Life History: Perennial shrub nt+1 (z') = ò “kernel” W [ P(z', z) + F(z', z)] state vector nt (z) dz P(z’,z) = (survival) * (growth) F(z’,z) = (mean # flowers/plant) * (mean # seeds/flower) (establishment probability)* (offspring size) mean = b0 + b1size + b2 size + b3 Rain + b4Temp 2 0.06 0.08 4 0.04 2 0.02 8 6 2 8 4 0.00 6 0.06 Size (t) 8 Size (t) 0.04 0.06 0.08 0.00 8 0.02 8 6 6 0.08 4 4 Size (t+1) 0.04 2 2 Size (t) 4 6 8 0.00 2 0.02 Size (t) 0.02 0.04 4 0.04 4 0.06 6 0.08 8 0.06 6 Size (t+1) Size (t+1) 0.02 2 0.00 8 6 8 6 4 Size (t+1) 6 4 4 Size (t+1) 2 0.00 2 2 2 0.08 8 Vital Rate Regression: Growth Size (t) Maps of mean model-estimated demographic rates Jump into the bog of elasticity Merow et al. 2014 Ecography Mean modeled pop growth rate If we treat this as species distribution model And assume presence predicted where λ ≥ 1.0 Merow et al. 2014 Ecography Predictions Forecasts Merow et al. 2014 Ecography Conclusions • Multivariate data hard to escape – Not really enough to rely on intuitions – Still left with the question: what are the interesting parts of big data sets • Building some mechanism into model isn’t enough to reliably get at key transitions – Problems of underfitting and extrapolation – Can get individual processes but not their interactions Acknowledgments UC Davis: Jens Stevens, Melis Akman Other US: John Silander (Uconn) Alan Gelfand (Duke) South Africa Tony Rebelo (SANBI) Jasper Slingsby (SAEON) Helen de Klerk (CapeNature) Field crew members: Rene Wolmarans, Bianca Lopez, Lisa Nupen Funding Sources: NSF Dimensions of Biodiversity grant DEB 10-45985 UC Davis Dept of Plant Sciences IPM models: Danish Research Council (via Signe Normand) Predicting community response to extreme drought event • Resample 3 kinds of plots – Long environmental gradients (spatial variation) – Time series data (15 years in 80 plots at one site) – Experimental water manipulations • What kinds of responses can we predict? – Abundance of different kinds of species – Shifts in plant type or function • Which kinds of data predict best? Vital rate models Growth Average growth/year Survival % Survival ~ ~ Environment Size + Environment Fecundity Flowering Probability # Flowers/Individual Seeds/Flower = Germination = ~ Size + Environment ~ Size + Environment 74 1.1% Offspring size Size ~ Environment Forecasts Merow et al. 2014 Ecography Predictions – uncertainty Map of collection sites Jane Carlson, Nicholls State U. Common garden experiment • Collected seed from 19 source populations across gradients for a widespread species (Protea repens) • Planted ~800 seedlings in common garden • Measured leaf traits, working on wood traits Genetic variation in growth rate 90 height (cm) Plant Height_cm_2013 80 70 60 50 40 30 0 2 4 julmint 6 Mean daily minimum temperature in winter (C) 8 Anysberg: small stature probably reflects both genetic and plastic responses Eight-year old P repens Anysberg, interior dry CFR Photos: Adam Wilson Big evolutionary questions • What drives high diversity? – Ecological speciation – Isolation on habitat islands – archipelago-like patterns – Climatic and geological stability Photo: Adam Wilson Wilson et al. in prep Demographic model Seed release Germination & first-year survival Germinant & seedling Pre-Repro Reproductive Large Repro Seedling survival Growth & Juv. Surv. Recruitment Adult survival Adult success Data Predictor variables Mean annual precip. Min. July temp. Max. January temp. Precipitation seasonality Winter soil moisture days fecundity/ % High fertility soil % Fine texture soil % Acidic soil Feedback example – Sierra forest • When feedbacks positive, slight shift in disturbance regime can cause state change Moderate fire (-) e.g. Collins et al. (2009) Ecosystems Less fuel, milder fire Intense fire (+) More shrubs, intense fire e.g. Stevens et al. (2013) Can.J.For.Res. Photos: Jens Stevens Example vital rate model: seed production Seedheadsi,j,t ~ Poisson(λi,j,t) log(λi,j,t) = β0 + β1*sizei,j,t + β2*size2i,j,t + β3*Precipj,t Mediterranean climate features temperature precipitation Very dry! Less dry Priors