- Forest growth and yield models are used to predict future timber growth and distribution based on past and present data - There are different approaches to growth and yield modeling including stand table projection, whole stand modeling, and individual tree modeling - Whole stand modeling relates growth and yield to stand-level variables like basal area, age, and site index while individual tree modeling simulates growth at the tree level accounting for size, competition, and site factors

1. UNIT-8
Growth and Yield

2. • Stand Table is a table showing the distribution of stems
by diameter classes for each of the series of crop
diameters.
• A stand table gives number of trees in each diameter
class. Future stand tables can be predicted from current
stand tables using a stand table projection method
• Stand table projection use a current diameter distribution
(stand table) and recent past growth (usually from stump
analysis) to project or estimate future diameter
distribution.
Stand Table Projection
DBH class present no of stems
6 522
8 352
10 179
12 88
14 40
16 11
18 10
20 8

3. Stand Table Projection……….
After 10 years
Present
Predicted
DBH class present no of stems
expected mortality
(%) 10 yr dbh growth
6 522 40 2.2
8 352 35 2.3
10 179 25 2.4
12 88 20 2.2
14 40 15 2.4
16 11 10 2.6
18 10 10 2.1
20 8 20 1.8
Total 1210

4. Stand Table Projection
After 10 years
Present
Predicted
DBH class
present no of
stems
expected
mortality
(%)
10 yr dbh
growth
Expected survival
% (after 10 yr)
Expected survival
no (after 10 yr)
6 522 40 2.2 60 313
8 352 35 2.3 65 229
10 179 25 2.4 75 134
12 88 20 2.2 80 70
14 40 15 2.4 85 34
16 11 10 2.6 90 10
18 10 10 2.1 90 9
20 8 20 1.8 80 6
Total 1210 805

5. Stand Table Projection
DBH
class
present no
of stems
expected
mortalit
y (%)
10 yr
dbh
growth
Expected
survival
% (after 10 yr)
Expected
survival no
(after 10 yr) G/i
6 522 40 2.2 60 313 1.10
8 352 35 2.3 65 229 1.15
10 179 25 2.4 75 134 1.20
12 88 20 2.2 80 70 1.10
14 40 15 2.4 85 34 1.20
16 11 10 2.6 90 10 1.30
18 10 10 2.1 90 9 1.05
20 8 20 1.8 80 6 0.90
Total 1210 805

6. Stand Table Projection
DBH
class
present
no of
stems
expe
cted
mort
ality
(%)
10 yr
dbh
grow
th
Expected
survival
% (after
10 yr)
Expected
survival
no (after
10 yr) G/i
6 522 40 2.2 60 313 1.10
8 352 35 2.3 65 229 1.15
10 179 25 2.4 75 134 1.20
12 88 20 2.2 80 70 1.10
14 40 15 2.4 85 34 1.20
16 11 10 2.6 90 10 1.30
18 10 10 2.1 90 9 1.05
20 8 20 1.8 80 6 0.90
Total 1210 805
no of stem moving up by
dbh class
g/i*100
no
change 1 class 2 class
110 0% 90% 10%
115 0% 85% 15%
120 0% 80% 20%
110 0% 90% 10%
120 0% 80% 20%
130 0% 70% 30%
105 0% 95% 5%
90 10% 90% 0%

7. Stand Table Projection
DBH
class
present no
of stems
expecte
d
mortalit
y (%)
10 yr
dbh
growth
Expected
survival
% (after 10
yr) G/i g/i*100
no
change 1 class 2 class
Future
stand
6 522 40 2.2 313 1.10 110 0 282 31 0
8 352 35 2.3 229 1.15 115 0 194 34 282
10 179 25 2.4 134 1.20 120 0 107 27 226
12 88 20 2.2 70 1.10 110 0 63 7 142
14 40 15 2.4 34 1.20 120 0 27 7 90
16 11 10 2.6 10 1.30 130 0 7 3 34
18 10 10 2.1 9 1.05 105 0 9 0 14
20 8 20 1.8 6 0.90 90 1 6 0 13
22 0 0 0 0 0 0 0 6
Total 1210 805 696 110 805

8. Numerical 2:
• Based on the following information prepare stand table for the year 2026
Diameter class
(cm) No. of stem in 2015
Expected mortality (%)
for 5 years
Diameter growth (cm) for
the period 2010-2015
25 400 30 5.75
30 280 25 5
35 125 20 4.5
40 150 10 4

9. Solution:
Diamete
r class
(cm)
No. of
stem in
2015
Expected
mortality
(%) for 5
years
Diameter
growth (cm)
for the period
2010-2015
Expect
ed
surviv
al in
2026 G/i
G/i*10
0
No
change1 class 2 class
25 400 30 5.75 280 1.15 115 0% 85% 15%
30 280 25 5 210 1 100 0% 100% 0%
35 125 20 4.5 100 0.9 90 10% 90% 0%
40 150 10 4 135 0.8 80 20% 80% 0%
45 0 0 0 0 0 0 0% 0% 0%
Total 955 725

10. Solution:
Diame
ter
class
(cm)
No. of
stem in
2015
Expected
mortality
(%) for 5
years
Diameter
growth
(cm) for the
period
2010-2015
Expe
cted
survi
val
in
2026 G/i
G/i*1
00
No
chan
ge
1
class
2
class
No
chan
ge
1
class
2
class
Futu
re
stan
d
25 400 30 5.75 280 1.15 115 0 85 15 0 238 42 0
30 280 25 5 210 1 100 0 100 0 0 210 0 238
35 125 20 4.5 100 0.9 90 10 90 0 10 90 0 262
40 150 10 4 135 0.8 80 20 80 0 27 108 0 117
45 0 0 0 0 0 0 0 0 0 0 0 0 108
Total 955 725 725

11. Numerical 3:
• Based on the following information, prepare future i.e 5 years stand table
Diameter class
No. of
present stem Mortality % Diameter growth (cm) in 5 year
15 700 20 3.3
18 500 16 3.6
21 500 12 3.85
24 320 12.5 3
27 200 10 2.7
30 150 10 2.4

12. Numerical 3: solution
Diamete
r class
No. of
present
stem
Mortali
ty %
Diameter growth
(cm) in 5 year
Expecte
d
survival G/i G/i*100 No change 1 class 2 class
Future
stand
15 700 20 3.3 560 1.10 110 0 90% (504)
10%
(56) 0
18 500 16 3.6 420 1.20 120 0 80% (336)
20%
(84) 504
21 500 12 3.85 440 1.28 128 0 72% (317)
28%
(123)
336+56
=392
24 320 12.5 3 280 1.00 100 0
100%
(280) 0%
317+84
= 401
27 200 10 2.7 180 0.90 90 10% (18) 90% (162) 0%
18+280
+123=4
21
30 150 10 2.4 135 0.80 80 20% (27) 80% (108) 0%
27+162
=189
33 0 108
Total 2370 2015 2015

13. Numerical 4:
• Based on the following information, prepare future i.e 10 years stand table
Diameter (inch) No. of present stem
Expected Mortality
%
Diameter growth (cm) in 10
year
24 744 40 2.2
26 432 35 2.3
28 271 25 2.4
30 180 20 2.2
32 75 15 2.4

14. Numerical 4: solution
Diameter
(inch)
No. of
present
stem
Expected
Mortality %
Diameter
growth (cm)
in 10 year
Expecte
d
survival G/i G/i*100
No
chan
ge 1 class 2 class
Future
stand
24 744 40 2.2 446 1.1 110 0 90% (402) 10%(45) 0
26 432 35 2.3 281 1.15 115 0 85% (239) 15%(42) 402
28 271 25 2.4 203 1.2 120 0 80%(163) 20%(41) 283
30 180 20 2.2 144 1.1 110 0 90%(130) 10%(14) 205
32 75 15 2.4 64 1.2 120 0 80%(51) 20%(13) 170
34 0 0 0 0 65
36 0 13
1138 1138

15. Numerical 5:
• Based on the following information, prepare future i.e 10 years stand table
Diameter (inch) No. of present stem
Expected Mortality
%
Diameter growth (cm) in 10
year
10 531 41 2.2
12 352 35 2.3
14 189 30 2.4
16 100 25 2.6
18 45 15 2.3
20 30 10 2.2
22 20 10 2
24 10 10 1.8

16. Numerical 5: Solution
Diamete
r (inch)
No. of
present
stem
Expected
Mortality
%
Diameter
growth (cm) in
10 year
Expected
survival G/i G/i*100
No
change 1 class 2 class
Future
stand
10 531 41 2.2 313 1.1 110 0 90%(282) 10%(31) 0
12 352 35 2.3 229 1.15 115 0 85%(194) 15%(34) 282
14 189 30 2.4 132 1.2 120 0 80%(106) 20%(26) 226
16 100 25 2.6 75 1.3 130 0 70%(53) 30%(23) 140
18 45 15 2.3 38 1.15 115 0 85%(33) 15%(6) 79
20 30 10 2.2 27 1.1 110 0 90%(24) 10%(3) 55
22 20 10 2 18 1 100 0 100%(18) 0% 30
24 10 10 1.8 9 0.9 90 10%(1) 90%(8) 0% 22
26 0 0 0 0 0 0 0 0 0 8
Total 842 842

17. • Forest and natural resource management decisions are often based on information collected
on past and present resource conditions.
• This information provides us with not only current details on the timber we manage (e.g.,
volume, diameter distribution) but also allows us to track changes in growth, mortality, and
ingrowth over time.
• We use this information to make predictions of future growth and yield based on our
management objectives.
• Techniques for forecasting stand dynamics are collectively referred to as growth and yield
models. Growth and yield models are relationships between the amount of yield or growth
and the many different factors that explain or predict this growth.
Growth and yield model

18. • Yield: total volume available for harvest at a given time
• Growth: difference in volume between the beginning and end of a specified period of time
(V2 – V1)
• Annual growth: when growth is divided by number of years in the growing period
• Model: a mathematical function used to relate observed growth rates or yield to measured
tree, stand, and site variable
Growth and yield model

19. 1. Stand table projection
2. Whole stand modeling
3. Individual tree modeling
i. Distance dependent
ii. Distance independent
Different growth and yield modeling approach

20. • Forest volume growth and yield are often viewed as functions of site quality,
age, and some measure of stand density, as well as interactions among these
variables
• Whole stand models may or may not contain density as an independent
variable.
• In this modeling, growth and yield mostly are used as dependent variables and
site quality, crown classes or stand density, number of trees, quadratic mean
diameter, stand mean age, basal area, volume and crown class proportion of the
stand trees are used as independent variables
Whole stand modeling

21. • Y = 1.6689 + 0.041066BA – 0.00016303BA2– 0.076958A + 0.00022741A2 +
0.06441S
where
Y = periodic net annual basal area increment
BA = basal area, in square feet per acre
A = age, in years
S = site index
Whole stand modeling

22. • Approaches to predicting stand growth and yield which use individual tree as
the basic unit are referred to as individual tree models.
• Individual tree models work by simulating the growth of each individual tree in
diameter, height, and crown and deciding whether it lies or dies, calculating it's
growth and volume, and growth rates.
• The components of tree growth in tree models are commonly linked together
through computer program which simulates the growth of each tree and then
aggregate these to provide estimate of stand growth and yield.
Individual tree modeling

23. • DBH increment = f (size, competition, site)
• Mortality (%) = F (size, competition, site)
• Ingrowth (trees/ha) = F (competition, site)
• Height (m) = F (size, site) or
• Height increment (size, competition, site)
• Individual tree models further divided into two classes:
i. Distance Dependent Model
ii. Distance Independent Model
Individual tree modelling......

24. Distance independent model

25. Distance independent model
• The distance-independent model
uses a competition index that
does not require the spatial
information of trees

26. Distance dependent model

27. Distance dependent model
• Each tree is modeled separately and its competitive position is determined by its individual
diameter, ht. and condition to its stand characteristics, such as basal area and average
diameter
• Distance-independent models only require information about tree characteristics as inputs.
These models predict tree growth based on initial tree characteristics and general
expressions of competition (eg. Stand density index, total basal area, basal area of larger
trees, relative height).
• Distance-independent models are more common than distance-dependent models primarily
because detailed information about tree locations is relatively unavailable

28. Application of Growth & Yield Models
• To model the flows of timber and other resources for forest management planning .
• To assess tree and stand responses to silviculture treatments
• Selection of appropriate treatments
• To predict changes in tree and stand values for periods between successive inventories.
• To evaluate the impact of management policies on the sustainable use of forests
• To understand the general tree growth responses in relation to habitat characteristics
• To examine relationships between stand growth and structural diversity
• To forecast the development of both pure even-aged and mixed-species uneven-aged stands
• To make decisions for feasible investment options

29. Yield Table
• Yield table is a tabular statement which summarizes on per unit area basis all the
essential data relating to the development of a fully stocked and regularly thinned even
aged crop at periodic intervals covering the greater part of its useful life.
• yield tables gives different parameters of a crop such as number of trees, crop height,
crop diameter, crop basal area, volume of standing crop, volume removed in thinning,
MAI, CAI etc. It gives all the quantitative information regarding development of a crop.
• This also denotes growth prediction tables based upon age and site for fully stocked,
even aged stand.
• Yield tables are in the form of growth charts, tables or formulas,

31. Kinds of yield tables:
Yield tables are further classified on the basis of the grades of thinning and whether the outturn
is expressed in volume or value.
A. On the basis of the number of grades of thinning used:
a. Single yield table: It is a yield table in which parameters have been given only for one
grade of thinning which is usually c grade.
b. Multiple yield tables: These are yield tables in which data are given for different grades
of thinning.

32. Thinning Grade Intensity Thinned tree
A slightly thinning 4D
B Medium thinning A+ Dwarf+ large and small branched tree
C intensive thinning A+B+ large tree with_ no large spacing
D Very intensive thinning A+B+C+ equal spaced

33. b. Empirical Yield Table:
• In contrast to normal yield tables, Empirical yield tables are based on average rather
than fully stocked stands.
• The resulting yield tables describe stand characteristics for the average stand density
encountered during the collection of field data
3. Variable Density yield table:
The limitations listed above for normal and empirical yield tables led to the development of
techniques for compiling tables with three independent variables, stand density being included
as the third variables: hence the term variable density yield tables.
 Basal area/area, mean diameter or other stand density indices are used to define the density
classes.
 Such yield tables are particularly useful for abnormal stands e.g. abnormal due to early
establish

34. Application and use of yield table:
1. Determination of site quality .
2. Estimation of total yield or growing stock.
3. Determination of increment of stand.
4. Determination of rotation
5. Preparation of stock map by site qualities.
6. As a guide to silvicultural thinning
a. Number of stems corresponding to a given age
b. Number of trees corresponding to a given crop diameter

35. Thank You