2. A Term Paper
Presentation
On
PROBABILITY AND MODELS
OF
TREE MORTALITY
Jeetendra Gautam
MSc Forestry (General Forestry)
Roll No. 14

3. TREE MORTALITY
• PLANT DEATH IS A COMPLEX PROCESS,
INFLUENCED BY
• PHYSIOLOGY,
• ENVIRONMENT
• SUCCESSIONAL DEVELOPMENT,
• AGE, AND,
• CHANCE
- (HARCOMBE, 1987; FRANKLIN ET AL., 1987)

4. TREE MORTALITY
• GENERAL CAUSES
• LACK OF SUFFICIENT RESOURCES TO RESTRAIN STRESS,
INJURIES OR SUSTAIN LIFE, OR KILLED BY EXTERNAL
FACTOR (WARING, 1987)
• NEGATIVE CARBON BALANCE (RESPIRATION >
PHOTOSYNTHESIS)
• INSECT INFESTATION
• PROLONGED DROUGHT UNDER LOW LIGHT CONDITION

5. TREE MORTALITY PROCESS
(GAP MODEL)
• BOTKIN (1993) DEFINES TWO GAP MODELS
• INTRINSIC MORTALITY
• OCCUR IN FAVORABLE ENVIRONMENT  WITH/OUT
COMPETITION
• MIGHT INCLUDE NON EPIDEMIC DISEASE, LIGHTNING,
WIND THROW
• GROWTH DEPENDENT MORTALITY
• OFTEN DUE TO COMPETITION FOR RESOURCES
• ASSUMES: SLOW GROWING  LIKELY TO DIE
• OTHER AGENTS: INSECT OR DISEASE, WIND EVENTS OR
ABIOTIC PERTURBATIONS

6. TREE MORTALITY PROCESS
(GAP MODEL)
• KEANE ET. AL. 2001 DISCUSSES AN ADDITIONAL
CLASS  EXOGENOUS MORTALITY
• WHEN EXTERNAL FACTOR SWEEPS AND
KILLS A PATCH OR STAND OR ALL TREES
• AGENTS: FIRE, PEST OUTBREAKS, SEVERE
WIND
• REPRESENTED AS THE SEVERITY OF THE

7. INTRINSIC MORTALITY MODEL
• AS AN AGE INDEPENDENT MORTALITY ROUTINE( MAX. AGE
DEPENDENT)
• ASSUMES:
• CHANCE PLAYS MAJOR ROLE (MORTALITY ~ RANDOM,
LOCALIZED)
• CONSTANT PROBABILITY OF DEATH
• STANDS END WITH 1% OR 2% OF ALL TREES SURVIVING
• COMMON EQUATION
• ANNUAL MORTALITY RATE ~ SPECIES~ EACH HAS DIFF.
MAX AGE

8. GROWTH DEPENDENT
MORTALITY
MODEL
• SLOWED GROWTH RATE  ENHANCED PROB. OF MORTALITY
• ASSUMES: RATE BELOW THRESHOLD  NEGATIVE CARBON
BALANCE
• 1 YEAR OLD STEM WITH STEM RADIAL GROWTH ,0.1 MM/YR 
AFTER 10 YEARS 30% OF VULNERABLE TREES DID NOT SURVIVE
- BOTKIN 1972
• TREEHIGH MOR. RATE ~ ONLY 3 OR MORE CONSECUTIVE YEAR
OF LOW THRESHOLD GROWTH RATE

9. GROWTH DEPENDENT
MORTALITY
MODEL
• (FORSKA APPROACH, PRENTICE et. al., 1993) ANNUAL
MORTALITY RATE (XM) BASED ON RELATIVE GROWTH
EFFICIENCY (EREL)
• WHERE, U0= INTRINSIC MORTALITY RATE
U1= SPECIES SPECIFIC MORTALITY RATE
q = THRESHOLD VALUE FOR VIGOR INDEX
r = SPECIES SPECIFIC SHAPE PARAMETER

10. GROWTH DEPENDENT
MORTALITY
MODEL
• SORTIE APPROACH PALACE et. al., 1993 CALCULATES
USING RING WIDTH OF LIVE AND DEAD INDIVIDUALS
• WHERE, PM= PROB. OF MORTALITY
d= AVERAGE RIG WIDTH (mm)
u and v= SPECIES SPECIFIC CONSTANTS

11. EXOGENOUS MORTALITY MODEL
• RESULT OF LONG TIME SIMULATED PERIODS
• NOT BEEN IMPLEMENTED IN GAP MODELS DUE TO
1.
IT WAS PREVIOUSLY THOUGHT TO BE UNIMPORTANT TO
THE DYNAMICS OF THE SIMULATED ECOSYSTEM,
2.
THERE WAS LITTLE KNOWN ABOUT THE SPATIAL
MECHANISMS OF THE DISTURBANCE PROCESS
3.
IT WAS DIFFICULT TO SIMULATE BECAUSE OF EXTENSIVE
COMPUTER REQUIREMENTS
4. THERE WERE VERY LITTLE DATA FOR PARAMETERIZATION
AND
5.
THE SIMULATED VARIABLES COULD NOT BE RELATED TO
EXOGENOUS DISTURBANCE EFFECTS

12. EXOGENOUS MORTALITY MODEL
• KEANE ET. AL., (1990, 1996) SIMULATED FIRE MORTALITY
FROM EMPIRICALLY DERIVED STOCHASTIC EQUATION
where, Pfire= PROB. OF FIRE CAUSED MORTALITY
DBH= TREE DIAMETER
bt= SPECIES SPECIFIC BARK THICKNESS
COEFFICIENTS(cm)
CK= PERCENTAGE CROWN VOLUME

13. USES OF MODELS
• (FRIDMAN et.al., 2001)THERE ARE AT LEAST THREE
PRINCIPLES FOR APPLICATION OF THE FUNCTIONS:
• DETERMINISTIC,
• MORTALITY IS EVENLY DISTRIBUTED AMONG PLOTS AND
TREES
• STOCHASTIC
• RANDOM SIMULATION DETERMINES WHAT PLOTS AND
TREES WILL BE AFFECTED.
• STOCHASTIC WITH MONTE CARLO SIMULATION
• CAN BE USED TO DERIVE EXPECTED VALUES AND
DISTRIBUTIONS

14. • GENERAL MODEL USED IN 3 STEP MODELOING OF
SWEDISH FOREST WAS
• THE PERFORMANCE OF THE FUNCTIONS DEVELOPED
INDICATES FAIR PREDICTABILITY IN GENERAL. THUS,
APPLICATION OF THE MODELS IN SWEDISH LONG-TERM
PLANNING SYSTEMS CAN BE RECOMMENDED.

15. USES OF MODELS
• IN ALBERTA MIXEDWOOD FORESTS FOR ASPEN, WHITE SPRUCE AND
LODGEPOLE PINE, THIS MODEL WAS USED:
WHICH IS THE LOGARITHMIC EXTENSION OF THE EQUATION
WHERE ß = (ß 0, ß 1, ..., ß K ) ARE UNKNOWN PARAMETERS,
YI IS THE RESPONSE VARIABLE FOR THE ITH OBSERVATION,
XI IS THE VECTOR OF THE EXPLANATORY VARIABLE FOR THE ITH
OBSERVATION,

16. USES OF MODELS
• FINDINGS IN ALBERTA MIXEDWOOD FORESTS
FOR ASPEN, WHITE SPRUCE AND LODGEPOLE
PINE WAS
• ASPEN IS THE SHORTEST LIVED SPECIES
WITH THE LOWEST SURVIVAL PROBABILITY,
WHILE WHITE SPRUCE IS THE LONGEST
LIVED SPECIES WITH THE HIGHEST OVERALL
SURVIVAL PROBABILITY

17. USES OF MODELS
• HOOD ET. AL. 2007 USES THE FOLLOWING REGRESSION
MODEL TO ESTIMATE DELAYED MORTALITY ON CONIFERS
FOLLOWING FIRE

18. USES OF MODELS
• THE STUDY FOUND THAT PERCENT CROWN LENGTH KILLED AND THE
NUMBER OF QUADRANTS WITH DEAD CAMBIUM SAMPLES TO BE THE
MOST IMPORTANT VARIABLES FOR PREDICTING POST-FIRE
MORTALITY FOR MIXED CONIFER SPECIES IN CALIFORNIA
• FOR FIRES WHERE ASSESSMENTS HAVE BEEN MADE OVER A
LONGER PERIOD OF TIME, THE MAJORITY OF THE MORTALITY
OCCURRED WITHIN THREE YEARS POST-FIRE. DELAYED MORTALITY,
IN TERMS OF CROWN DEATH, MAY TAKE SEVERAL YEARS TO OCCUR
FOR TREES WITH FATAL LEVELS OF CAMBIUM KILL.
• FOR WHITE FIR, CAMBIUM KILL WAS A MORE IMPORTANT VARIABLE IN
THE THREE-YEAR MODEL COMPARED TO THE TWO-YEAR MODEL.

19. CONCLUSION AND
RECOMMENDATION
• DAHLMAN (1985) ~ GAP MODELS ARE POTENTIALLY POWERFUL
TOOLS FOR SIMULATING COMMUNITY-LEVEL RESPONSES TO CO2
INCREASE, BUT ONLY IF PROPERLY PARAMETERIZED AND
VALIDATED. OTHERWISE, ~ JUST EXPLORATORY EXERCISES.
• A QUESTION WHETHER APPROPRIATE MORTALITY DATA ARE
AVAILABLE OR CAN EVER BE COLLECTED TO EXTENSIVELY
VALIDATE THE REPRESENTATION OF PLANT DEATH IN GAP MODELS,
ESPECIALLY SPATIAL GAP MODELS (DEUTSCHMAN ET AL., 1999).

20. CONCLUSION AND
RECOMMENDATION
• STOCHASTIC MORTALITY FUNCTIONS MUST BE DEVELOPED THAT
USE PROCESS BASED, MECHANISTIC RELATIONSHIPS AS
PREDICTIVE VARIABLES.
E.G., FIRE IGNITION PROBABILITIES  CLIMATE-BASED
VARIABLES.
• RESEARCH - EXPANDED - ATTEMPTS TO MECHANISTICALLY
UNDERSTAND THE RELATIONSHIP BETWEEN ECO-PHYSIOLOGICAL
PROCESSES AND PLANT MORTALITY.
• A COMPREHENSIVE FIELD DATABASE IS NEEDED TO DESIGN,
PARAMETERIZE, AND VALIDATE GAP MODEL MORTALITY ALGORITHMS

22. 22