Source of species with climate change

1
Source of species with climate change?
2
Temporal scale

• Mean annual variation small
• Monthly variation large

3
Germination response
4
Sensitivity varies among species at each life
history stage
5
Background

• Scalable Landscape Inference and Prediction - The
  SLIP model, Govindarajan et al SoCG 2004
• Individual based, spatially explicit
• Efficient approximation algorithms
• Handles large landscapes
• Resolution of 1sq. m. on a 1sq. km. landscape

128 x 128m landscape 4 species
6
SLIP Overview

• Landscape
• Population

• Yearling One year old plants
• Seedling plant height lt 50cm
• Sapling 50cm ? plant height ? 2m
• Adult plant height gt 2m

7
SLIP Overview - Submodels

• Dynamics
• Establishment and Growth
• Mortality
• Seed Dispersal
• Resources
• Light, Temperature,
• Moisture, Carbon dioxide
• Each Modeled separately
• Light and Seed Dispersal submodels
  computationally most expensive

Yearling growth (m)
Light
8
Hierarchical Bayes model
Data
CO2 treatment
Climate
Diameter data
Canopy data
Maturity obs
Seed traps
TDR
Survival
Soil moisture
Light
Dispersal
Diameter growth
Diameter
Maturation
Mortality risk
Fecundity
Processes
Observation errors
Process uncertainty
Parameters
Heterogeneity
Hyperparameters
No cycles spatio-temporal
p(unknownsknowns)
9
Growth
Data
CO2 treatment
Climate
Diameter data
Canopy data
Maturity obs
Seed traps
TDR
Survival
Soil moisture
Light
Dispersal
Diameter growth
Diameter
Maturation
Mortality risk
Fecundity
Processes
Observation errors
Process uncertainty
Parameters
Heterogeneity
Hyperparameters
10
Merging data, process, and structure
i individual j stand t year
Data from multiple sources
Diameter data
Increment data
Dij,t
Process annual change in diameter
Dij,t-1
Dij,t1
Parameters
Diameter error
Mean growth
Individual effects
Year effect ?t1
Year effect ?t-1
Increment error
Year effect ?t
Process error
Hyperparameters spatio-temporal structure
Population heterogeneity
Clark, Wolosin, Dietze, Ibanez (in review)
11
Prediction two data sources
i individual j stand t year
Clark, Wolosin, Dietze, Ibanez (in review)
12
Resources canopy light availability
Data
CO2 treatment
Climate
Diameter data
Canopy data
Maturity obs
Seed traps
TDR
Survival
Soil moisture
Light
Dispersal
Diameter growth
Maturation
Mortality risk
Diameter
Fecundity
Processes
Observation errors
Process uncertainty
Parameters
Heterogeneity
Hyperparameters
13
Light availability ground to remote data
Wolosin, Agarwal, Chakraborty, Clark, Dietze,
Schultz, Welsh
Light models from allometry/solar geometry
Remote sensing
Ground observations
14
Estimates combine three data types
error
GLM
Bias, error
Cumulative logit
Wolosin, Agarwal, Chakraborty, Clark, Dietze,
Schultz, Welsh
15
Synthetic modeling
Data
CO2 treatment
Climate
Diameter data
Canopy data
Maturity obs
Seed traps
TDR
Survival
Soil moisture
Light
Dispersal
Diameter growth
Maturation
Mortality risk
Diameter
Fecundity
Processes
Observation errors
Process uncertainty
Parameters
Heterogeneity
Hyperparameters
16
Long term census data

• Mapped stands
• All life history stages
• Seed rain
• Seed banks
• Seedlings
• Saplings
• Mature trees
• Interventions
• Canopy gaps
• Nutrient additions
• Herbivore exclosure
• Fire
• Environmental monitoring
• Canopy photos
• Soil moisture
• Temperature
• Wireless sensor networks

• Trees
• Seed traps

17
Inference
Qij,t
i individual j stand t year
v

• Maturation status

qij,t
Maturity obs
Seed traps
qij,t
sj,t
Maturation
Diameter
Qij,t
Dij,t
18
Inference
i individual j stand t year

• Seed prediction from estimated fecundity

Seed traps
Dispersal
Maturation
Qj,t
Fecundity
fj,t
19
Inference
i individual j stand t year

• Seed prediction from estimated fecundity

Seed traps
Dispersal
Maturation
Qj,t
Fecundity
fj,t
20
Inference

• Multivariate regression Fixed and random
  individual effects

i individual j stand t year
Diameter data
Canopy data
?ij,t
Diameter growth
Light
Diameter
Dij,t
Fecundity
fij,t
dij,t
aij
Random effects
Year effects
bt
21
Inference
st

• Year effects

bt
ft
22
Sources of variability/uncertainty in fecundity
bt
bij
?ijj
Clark, LaDeau, Ibanez Ecol Monogr (2004)
23
Resources

• Fecundity increases with exposure
• No evidence of growth response

24
Inference
Increases with diameter Dij,t
Declines with growth rate dij,t

• Semiparametric mortality

zij,t
Survival
dij,t
Diameter growth
Mortality risk
Diameter
Dij,t
i individual j stand t year
25
Allocation among individuals

• Growth ?
• mortality risk
• fecundity

26
Allocation within individuals

• Little evidence of interannual tradeoffs

27
SLIP Overview

• Landscape
• Population

• Yearling One year old plants
• Seedling plant height lt 50cm
• Sapling 50cm ? plant height ? 2m
• Adult plant height gt 2m

28
SLIP Light Model

• Light computation explicit each m2
• Individual trees
• Graphics hardware based algorithm

8100 Solar grid points
29
Detail where it matters
Gap in Duke Forest Approximated by a square
A 20X20 gap
30
Event based modeling of gap formation
Average run time for with different update periods
31
Approximation fine
Update period 5 years
SLIP Model
32
Modeling Seed Dispersal

• Fecundity

fi,t fecundity of tree i at time t ?0, ?1
species specific constants Di,t DBH of tree i at
time t bi Individual effect for tree i
33
Modeling Seed Dispersal

• Dispersal Kernel (Clark et.al. Ecology 1990)

• Expected seeds dispersed at center of
  
• grid cell j Cj from all trees of location li
  at
• time t

gj(Cj) ?ifi,t Kern ( Cj?li u, p)
34
SLIP Dispersal Algorithm

• Monopole Approximation (destination based)

35
SLIP Dispersal Algorithm

• Quad tree data structure

T
v

• Computational Complexity O((A logAn)/?2)
• n number of fecund individuals
• ? monopole coefficient
• A area of the landscape

36
Tradeoff speedup vs error
How much can we stand?
37
Mean seed density
cv (over years)
38
Drawbacks

• Fecund individuals sparse
• Does not exploit temporal correlations
• Difficult to dynamize

Red Maple
Tulip Poplar
Time series of number of fecund trees in 515X512
landscape
39
Source Based Algorithm

• Computational Complexity O((A n/?2)logA)
• n number of fecund individuals
• ? monopole coefficient
• A area of the landscape

Destination Based Dispersal Complexity O((A
logAn)/?2)
40
Switch, depending on density
Complexity
source
destination
Density
41
Temporal Dispersal Model

• Calculate for whole landscape at fixed intervals
• 1st order approximation (in t) for change in
  sources
• Extrapolate linear approximations to update
  dispersal values for the intermediate periods
• Update for new or dead fecund individuals

42
Spatial Distribution of Seeds for Red Maple (Acru)
Approximate (source based)
Exact
lt 5
5-10
10-15
15-20
20-25
25-30
30-35
43
Approximation fine
Temporal Dispersal (Update 20 yrs)
SLIP dispersal
44
Competitive exclusion
Species 1 goes extinct slower growth higher
low-light survival
tulip poplar red maple
45
with random effects
RITEs only for fecundity, seedling growth
tulip poplar red maple
46
Collaborators

• lab participants
• Jim Clark
• Benoit Courbaud
• Mike Dietze
• Sean McMahon
• Mike Wolosin

• Computer Sciences
• Pankaj Agarwal
• Sathish Govindarajan
• Sukhendu Chakraborty
• Hi Yu