1. 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

2. Mediterranean climate Key features: warm temperate, with cool wet winters and hot dry summers.

5. Climate change effects? The obvious ones: Warmer winter -> more growth Hotter summer -> more fire

6. 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

7. Feedback example – Sierra forest When feedbacks positive, slight shift in disturbance regime can cause state change Moderate fire Less fuel, milder fire Intense fire More shrubs, intense fire (-) (+) e.g. Collins et al. (2009) Ecosystems Photos: Jens Stevens e.g. Stevens et al. (2013) Can.J.For.Res.

8. No fire (fire suppressed) No fire (plant growth suppressed) Fire-plant interaction example: South African fynbos Fire

9. More frequent fire can eliminate populations 8-year intervals4-year intervals Population size between fires Stevens & Beckage, Oecologia 2010

10. Fire Climate Plant species, communities Growth, Survival etc. Ignition and spread Disturbance Regrowth of Fuel, flammability

11. Challenges – ecological data Scales of process can be large – Field data collection is almost always not Interpolation and extrapolation (worse in projections) Environment Current Future

12. 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?

13. Outline 1)A little more introduction 2)Fire return times 3)Biomass regrowth 4)Demography

14. 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

15. CFR climate change Change per decade (mm) Historical patterns Recent change (1950-2000)

16. Climate change projections CMIP5 multimodel average 2081-2100 -- RCP8.5 Stippling: ≥ 8/11 models agree on sign Downscaled projections: Adam Wilson

17. Thomas et al. (2004) Nature. Midgley et al. (2006). Diversity & Distributions.

18. Example 1: Fire occurrence What affects fire frequency? Fire Climate Plant species, communities Plant species, communities Growth, Survival etc. Ignition and spread Disturbance Regrowth of fuel

19. Cape region fire data Thanks to Helen DeKlerk

20. 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

21. Issues… Very multivariate weather data Approach: reduce dimensionality by biological intuition, hypothesis Chris Wikle: “Sensible science-based parameterizations or dimension reductions”

22. Issue: highly multivariate environmental data Weather station data Daily, point locations Gridded weather data Daily, ~2km grid Indices -- i.e. hypotheses Seasonal to yearly Modeling Bayesian kriging with covariates (Adam Wilson) Meetings (many…) Soil moisture model Choice of methods

23. Fire history data Timeline for one grid cell 1980 (beginning of record) 2000 (end of record) 14 years 6 years ? ?. fires Other hypothetical fire histories:

24. Nonparametric survival model Z i = observed time between a pair of fires in cell I P it : P(Z i > t | Z i > t-1) i.e. probability of “surviving” season t without a fire Probit(P) = X T β + e Climate: Long-term mean 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

25. Dealing with censoring Left censoring: no previous fire observed in record Unobserved p it predicted from X T β {Unobserved fire times} ~ Multinom(1-p it, 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

26. Wilson et al. (2010) Ecological Modelling ?

27. Cumulative fire probabilities Wilson et al. (2010) Ecological Modelling

28. Expected fire return times Wilson et al. (2010) Ecological Modelling

29. 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

30. 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

31. Part 2: modeling postfire regrowth Fire Climate Plant species, communities Plant species, communities Growth, Survival etc. Ignition and spread Disturbance Regrowth of fuel

32. Remote sensing: Watching plants grow from space MODIS terra NDVI data

33. Model Functional form that can match recovery pattern Parameters – α i : minimum NDVI – γ i : difference between min and max NDVI – λ i : recovery rate parameter – Α i : amplitude of seasonal variation

34. Wilson et al. in prep Wet, coastal Dry, interior ~4 years ~8 years

35. Spatial variation in regrowth rates Wilson et al. in prep Regrowth rate based on Threshold NDVI value (95% of max NDVI)

36. Tying this back to demographic models Factors related to regrowth rate Wilson et al. in prep

37. Projected change in recovery time Years shorter longer

38. Comparing recovery time to observed fire return intervals Some correspondence Slowest growing areas may be burning too often

39. 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 (?)

40. Example 3: Demography Fire Climate Plant species, communities Growth, Survival etc. Ignition and spread Disturbance Regrowth of fuel Tradeoff: -- More biological detail -- MUCH less data

41. Focal species: Protea repens Data: Protea Atlas Project Tony Rebelo of SANBI

42. 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

43. 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

44. Integral projection model (IPM) t = time z = size at t z' = size at t+1 n t (z)= size distribution of individuals at t n t+1 (z’)= size distribution of individuals at t+1 K(z’,z)= projection kernel

45. Life History: Perennial shrub P(z’,z) = (survival) * (growth) F(z’,z) = (mean # flowers/plant) * (mean # seeds/flower) (establishment probability)* (offspring size) “kernel” state vector

46. Vital Rate Regression: Growth

47. Maps of mean model-estimated demographic rates

48. Jump into the bog of elasticity Merow et al. 2014 Ecography

49. Mean modeled pop growth rate Merow et al. 2014 Ecography If we treat this as species distribution model And assume presence predicted where λ ≥ 1.0

50. Predictions

51. Forecasts Merow et al. 2014 Ecography

52. 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

53. 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)

54. 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?

55. Vital rate models Growth Average growth/year ~ Environment Survival % Survival ~Size + Environment Fecundity Flowering Probability~Size + Environment # Flowers/Individual ~Size + Environment Seeds/Flower =74 Germination = 1.1% Offspring size Size~Environment

56. Forecasts Merow et al. 2014 Ecography

57. Predictions – uncertainty

58. Map of collection sites Jane Carlson, Nicholls State U.

59. 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

60. Genetic variation in growth rate Mean daily minimum temperature in winter (C) Plant height (cm)

61. Photos: Adam Wilson Eight-year old P repens Anysberg, interior dry CFR Anysberg: small stature probably reflects both genetic and plastic responses

63. Big evolutionary questions What drives high diversity? – Ecological speciation – Isolation on habitat islands – archipelago-like patterns – Climatic and geological stability Photo: Adam Wilson

64. Wilson et al. in prep

65. Demographic model Germinant & seedling Pre-Repro Repro- ductive Large Repro Seed release Germination & first-year survival Seedling survival Growth & Juv. Surv. Adult survival Recruitment Adult success

66. Data Predictor variables fecundity/ Mean annual precip. Min. July temp. Max. January temp. Precipitation seasonality Winter soil moisture days % High fertility soil % Fine texture soil % Acidic soil

67. Feedback example – Sierra forest When feedbacks positive, slight shift in disturbance regime can cause state change Moderate fire Less fuel, milder fire Intense fire More shrubs, intense fire (-) (+) e.g. Collins et al. (2009) Ecosystems Photos: Jens Stevens e.g. Stevens et al. (2013) Can.J.For.Res.

68. Example vital rate model: seed production Seedheads i,j,t ~ Poisson(λ i,j,t ) log(λ i,j,t ) = β 0 + β 1 *size i,j,t + β 2 *size 2 i,j,t + β 3 *Precip j,t

69. Mediterranean climate features Very dry! Less dry temperature precipitation

70. Priors