&

A Term Paper Presentation

On

PROBABILITY AND MODELS OF

TREE MORTALITYJeetendra Gautam

MSc Forestry (General Forestry)

Roll No. 14

TREE MORTALITY

• PLANT DEATH IS A COMPLEX PROCESS, INFLUENCED BY • PHYSIOLOGY,

• ENVIRONMENT

• SUCCESSIONAL DEVELOPMENT,

• AGE, AND,

• CHANCE

- (HARCOMBE, 1987; FRANKLIN ET AL., 1987)

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

• LOW ENERGY INVESTMENT IN PROTECTIVE MEASURES (LOEHIE, 1987)

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

• 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 ABOVE AGENTS

TREE MORTALITY PROCESS(GAP MODEL)

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

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

• TREEHIGH MOR. RATE ~ ONLY 3 OR MORE CONSECUTIVE YEAR OF LOW THRESHOLD GROWTH RATE

• (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

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

GROWTH DEPENDENT MORTALITY

MODEL

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

• 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

EXOGENOUS MORTALITY MODEL

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

• 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.

• 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,

LI IS THE LENGTH OF REMEASUREMENT INTERVAL FOR THE ITH OBSERVATION

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

USES OF MODELS

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

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.

USES OF MODELS

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).

• 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 TO INCLUDE.

• ULTIMATE CAUSE OF TREE DEATH

• INTENSIVELY SAMPLED TREE SEEDLINGS AND SAPLINGS.

CONCLUSION AND RECOMMENDATION

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ANY QUERRIES

ANDSUGGESTION

S ARE

WARMLYWELCOME