MODELING NATuRAL REGENERATION ESTABLISHMENT
IN THE NORTHERN ROCKY MOUNTAINS OF THE U.S~A.
D. E. Ferguson
USDA Forest Service.
Intermountain Research Station
Moscow? Idaho 83843,U.S,A.
ABSTRACT
Retrospective examination of cutover forests enables the development of models that predict
regeneration success as. a function of plot cO:t;l.ditions and time since disturbance. The
modeling process uses a two-state system. In the first state, all plots are analyzed to predict
the probability of stocking (at least one established seedling on the plot). In the second state,
only stocked plots are analyzed to predict seedling density, species composition, and seedling
heights. Outcomes are predicted on a plot basis; therefore, the' model is sensitive to variation
within the stand. Predictions are· then summarized to an area basis. The independent
variables used to predict regeneration success are commonly recorded in forest· inventories.
Study design, model development, model predictions, and model updates are discussed~
INTRODUCTION
When developing a forest growth and yield model for the northern Rocky Mountains, Stage
(1973) envisioned three components of the Prognosis Model. The first part to be coded was
large tree growth, which was driven by periodic diameter increment equations. The second
was growth of small trees, which was driven by periodic height increment equations. Last
was prediction of regeneration establishment following timber harvests.
The Prognosis Model is a distant-independent individual-tree growth and yield model. An
inventory of trees is projected over time by adding incremental growth to trees. At each time
step, growth and mortality are predicted as well as implementation of silvicultural
prescriptions.
An inventory .of trees on one or more plots represents a stand in the Prognosis Model. Each
tree has a density associated with it, \¥hich is a function of the inventory plot size and number
of plots sampled in the stand. For example, each tree sampled on a I-ha plot represents 1
tree/ha, each tree sampled on two 11l0-ha plots represents 5 trees/ha, and each tree sampled
on ten 1I1000-ha plots represents 100 treeslha. Mortality ·in the Prognosis Model is simulated
as a reduction in the treeslha represented by an individual tree record.
The purpose of the Regeneration Establishment Model is to predict new trees that become
established and add them to the inventory in the Prognosis Model, just as would be done if a
regeneration inventory were taken at a future date. The Prognosis Model with the
Regeneration Establishment Model can be used to decide which prescription best meets
reforestation objectives and to link regeneration to long-term predictions of growth and yield.
30
This file was created by scanning the printed publication.
Errors identified by the software have been corrected;
however, some errors may remain.
Linkage to other extensions
succeSSIOn.
10
the Prognosis Model allows predictions of secondary
. The Regeneration Establishment Model has been developed for coniferous forests of the
northern Rocky Mountains of the U.S.A. (Ferguson et al.. "1986, Ferguson and Crookston
1991, Ferguson and Carlson 1993). Regeneration success of ten conifer species is predi~ted
as a function of plot attributes and time since disturbance. Independent variables are those
typically collected during routine stand examinations. This paper discusses the approach
takcm to develop the regeneration model and ideas for developing similar models for other
geographic areas or ecological conditions..
STUDY DESIGN
Predictions of regeneration must be quari.tified in a biologically meaningful and statistically
sound manner. It is important that stands and plots be chosen in an unbiased manner because
unbiased rates of regeneration success are essential for forest planning. A key point of the
study design was to uSe stratified random sampling to retrospectively examine stands that
were commercially harvested 2 to 20 years ago. Stands were classified into categories of
ecological community type, regeneration method, site preparation method, and geographic
location. Stratification' insured that important class variables would be represented in .
sampling. From each stratification category, four to five stands were randomly selected for
sampling.
Stereo aerial photographs were obtained for each stand, and transects were drawn to sample
variability observed on the photos, such as differences in aspect, site preparation, residual
overstory density, and topographic position. About 25 points were distributed equi,distance
along the transects. Each transect point was the centet: of a 11741-ha circular fixed-area plot
for sampling regeneration and a variable radius plot for sampling the residual overstory, if
present. Variables were recorded plot by plot to make them as independeilt as possible.' Plot
variables included habitat type (ecological community type as defined by Cooper et al.
[1991]), slope, aspect, topographic position, and type of site preparation. Residualoverstory
density was recorded on each plot by species, using a variable radius plot. Stand variables
were year of cutting, geographic location, and elevation.
A 11741-ha plot was stocked when at least one conifer was established within its boundary.
The ten conifer species included in the. model are shown in Table 1. The range of sizes for
established trees was between 15 cm tall fot shade tolerant species and 7.5 cm diameter at
breast height. Minimum establishment height for shade intolerant species was 30 cm.
Minimum hei~hts roughly correspond to a 3-year old seedling.
Potential crop trees were sampled on stocked plots. These trees are called "best trees" and
were chosen by the following rules:
1. The two tallest trees on the plot regardless of species.
2. The tallest tree of each additional species on the plot not chosen in rule 1.
3. If rules 1 and 2 do not, result in at least four trees, select the tanest remaining
trees,
.if present, until at least four trees are chosen.
31
Data recorded for best trees were height, age at soil surface, and tree condition (incidence of
damages, diseases, or insects).
.
Table 1. Scientific name, common name, and abbreviation for species in the Regeneration
Establishment Model.
Scientific name
---------------------_.. Pinus monticola
Larix occidentalis .
Pseudotsuga menz{esii
Abies grandis
Tsuga heterophylla
Thuja plicata
Pinus contorta
Picea engelmannii
Abies lasiocarpa
Pinus ponderosa
Common name
Abbreviation
-------------------------
----------------
western white pine
western larch
Douglas-fir
grand fir
western hemlock
western redcedar
lodgepole pine
Engelmann spruce
subalpine fir
ponderosa pine
WP
L
DF
GF
WH
C
LP
ES
AF
pp
MODEL DEVELOPMENT
The 11741-ha plot was the unit of analysis to predict the probability of stocking, density, and
species composition. Equations for predicting seedling heights were developed from height
measurements of best trees. The technique for developing equations follows the example of
Hamilton and BriCkell (1983) for two-state systems. In the first state, a plot is either nonstocked or is stocked with at least one established seedling. All plots are used to predict the
probability of stocking. In the second state, only stocked plots are used to predict the number
of established seedlings on the plot and the species composition of those seedlings.
Steps in the Regeneration Establishment Model are shown in Figure I. Steps 4-8 are the core
of the model. In steps 4-8, the prpbability of stocking is predicted, the number of trees per
stocked plot is chosen, the number of species on stocked plots is chosen, species are assigned
to seedlings, and heights are predicted.
A logistic regression algorithm was used to predict probabilities for dichotomously distributed
dependent variables. The form of the logistic equation is:
(1)
where P is probability, e is the base of natural logarithms, ~i is the vector of regression
coefficients, and xi. is the vector of independent variables. The predicted probability (P) is
continuous and bounded within the interval [0, I].
Table 2 shows how the probability of stocking and attributes of stocked plots are used to
predict regeneration in a stand. Each plot is processed independently, then aggregated to an
area basis.
32
Step
1
Determine plot
site preparation
Compute years since
last disturbance
Calculate the
increment in stocking
2
3
4
Estimate number
of trees
5'
Predict number
of species
6
Calculate probability of
species occurrence
7
8
9
Identify
trees
bes~
10
Accumulate
stand statistics
11
. Pass tr~e records
to prognosis model
12
Yes
Yes
No
Print
regeneration
summary
13
Figure 1. Computer steps in the Regeneration Establishment Model. Predicted regeneration
is added to the inventory of trees in the Prognosis Model.
33
Table 2. Example of using the probability of stocking (P) to scale attribut~s of stocked plots
to an area basis. TPSP is the predicted number of regeneration trees per stocked plot. In this
example, N=5 plots. Species abbreviations are explained in Table 1.
Probability of
stocking (P)
TPSP
--------------- ...,
0.75
-'
0.61
4
2
0.35
0.53
1
0.29
1
Selected
speCIes
Predicted trees/ha
(P*TPSP*741 )!N
----------------
-------------------
GF(2), DF(1)
GF(3), WP(l)
LP(2)
WP(1)
LP(l)
-----------
x = 0.51
333,4
361.6
103.7
78.5
43.0
Species
composition
--------------------------
GF (222.3), DF (111.1)
GF (271.2). WP (90.4)
LP (103.7)
WP (78.5)
LP (43.0)
------------
---------------------------
I = 920.2
I=GF(493.5), DF (111.1)
WP (168.9), LP (146.7)
For some steps in the model, it is important to mimic the distribution of the dependent
variable. For example, the number of seedlings on stocked plots has a reverse l-shape
distribution (Figure 2). The most common occurrence is I tree per stocked plot, followed by
2, 3, 4 trees, etc. Such distributions can be modeled with a Wei bull cumulative density
distribution (Bailey and Dell 1973). Once a Wei bull equation is developed, a uniformly
distributed pseudo-random number in the interval [0,1] can be used to make an unbiased
choice within the distribution.
Percent
35
30
25
20
15
10
5
o
1
2
3
4
5
6
7
8
9
10 11
12 13 14 15 16 17 18 19 20
Number of trees on stocked plots
Figure 2. Distribution of number of seedlings on stocked plots. The tail of this distribution
continues past 20 trees to 213 trees per plot.
34
Use of pseudo-random numbers to make unbiased choices among a number of possibilities
means that rare events could have a large effect on stand averages if there are only a few plots
in the simulation. When the number of inventory plots is less than 50, plots are replicated
(repeatedly doubled) un~il there are at least 50 available for processing. However, model.
users can control plot replications to produce stochasticity in projections (low number of plots
projected) or have predictions that are more deterministic. (high number of plots processed).
Table 3 summarizes, the independent variables used to predict the probability of stocking,
number of trees per stocked plot, number of species per stocked plot, species occurrence, and
seedling heights. Note that these independent variables are routinely· collected by foresters
during stand Cixaminations.
A few examples of model results provide insight into regeneration success in the northern
Rocky Mountains. Figure 3 shows how slope and aspect interact in the probability of
stocking equation. Steep south slopes have the lowest probability of stocking, while stocking
becomes better as south. slopes become less steep. The probability of stocking increases
slightly on north aspects as slope increases, but the increase is not as much as the decrease on
south slopes.
South slopes have the lowest increases in stocking over time and north slopes have the highest
increases in stocking over time (Figure 4). East and west slopes are intermediate between
north and south.
Table 3. Summary of independent variables used to predict dependent variables. P is the
probability of stocking, TPSP is the number of regeneration trees per stocked plot, and SPSP
is the number of species per stocked plot.
.
Independent
variable
P
TPSP
------------------------------------Years since disturbance
Aspect
Slope
Elevation
Residual basal area
Type of site preparation
Habitat type
Geographic location
Topographic position
TPSP
Same species in overstory
Seedling age
Seedling
heightsl
--------------
-----------
./
./
./
./
./
./
./
./
./
./
./
./
./
./
./
./
./
../
../
./
./
./
./
./
./
./
./
./
./
./
./
./
./
../
--------------------------------------------------I
SPSP
--------
Species
occurrence 1
Separate equations developed by speci~s.
35
./
./
Probability
1.0
I
0.8
Slope percent
~~
o·
"G_,,__
~-------
---------
.
"..
0.4
......rr.-..:::
.-..-.- ----...
/.'
..--_.•.._...--.....-:- ..
.-----
___ ~.... ,
.'"
50
0.2
0.0
----
.. :--- -10
. . ::..'--.....
---..
..... ~__ 30
0.6
~:~
..-_._;;;?-"
r------,---.-------,---.-----r--..,------,---'---,-
o
90
45
135
180
225
270
360
315
Aspect in degrees
Figure 3. The interaction of slope and aspect on predicted probability of stocking.
~rObabi~i~ 1
Aspect
N
0.8
- --
!
0.6
E
- -..............
_-----~.-......
0.4
0.2
o~o
~--~----~----------~------~--~--------~
o
5
10
15
Years since disturbance
Figure 4. The effect of aspect and time on·predicted probability of stocking.
36
20
W
S
~~-
~~
~
-~~
--~
An example projection from the Regeneration Establishment Model is shown in Table 4.
Units have been converted to metric equivalents. The 10plots in this projection are on a north
aspect, 30% slope, no residual overstory, an Abies grandis/Clintonia uniflora habitat type,
1070 m elevation, with 30% of the plots mechanically site prepared, and 10 years since
harvest.
~
Grand fir has the highest density followed by Douglas-fir. Western hemlock and western
redcedar do not occur on this habitat type, while subalpine fir is rare. The tallest seedlings are
western larch, Douglas-fir, and western white pine. Seral species such as western larch,
Douglas-fir, and western white pine become established quickly after timber removal and
grow rapidly in full sunlight.
Table 4. Example projection using the Regeneration Establishment Model. The probability of
stocking is O~ 73 80 at 10 years after harvest.
Species
--------
WP
L
OF
GF
WH
C
LP
S
AF
PP
Density of all
regeneration
-------------121
74
477
1139
0
0
22
54
0
22
Density of best
trees (per hal
Average height
of best trees (m)
---------------
121
74
306
788
0
0
22
54
0
22
-.-----
------
1909
1387
1.4
1.6
1.4
1.1
0.7
0.8
1.1
Grand fir and Douglas-fir regenerated in sufficient numbers that plots are overstocked. This is
~ indicated by a drop in density between the column showing all regeneration and the column
showing best trees in Table 4. The column showing best trees reflects the number of trees per
ha by species one could expect to favor in future silvicultural treatments such as thinning.
Predicted regeneration is added to the·tree list maintained in the Prognosis Model. Planting is
simulated by creating tree records that are the species, density, and height specified by the
model user. Equations in the Prognosis Model then predict 5-year periodic height increment
for small trees. When the trees are larger, diameter increment equations predict growth of
trees. Regeneration would be predicted again when harvests are simulated at a future time.
37
DISCUSSION
Modeling regeneration success using the approach, presented in this paper should have
application in other locations and ecological situations. Key points are to use a stratified
random sample to retrospectively examine operationally harvested stands, record plot
variables, and develop the model using a tw~-state technique.
A stratified random sample means that variables of interest are included in the model, while
assuring unhiased selection of sample stands. By using retrospe~tive examinations, results
can be obtained in less time than creating conditions of interest, then waiting 10 to 20 years.
Because operationally harvested stands are sampled, the model should reflect regeneration
success than caD. be expected from routine harvest and site preparation methods.
Recording plot variables helps to insure independence be~ween plots" an assumption of
analysis of variance.. The use of plot variables in the model allows predictions to be sensitive
to variation within the stand. For example, changes in overstory density or type of site
preparation within the stand are accounted for by predicting outcomes plot by plot.
Use of a two-state modeling technique helps decrease the variation that must be explained. In
the first state, all plots are used to predict the probability of stocking (one or more established
seedlings on the plot). _In the second state, only stocked plots are used to predict seedling
density, species occurrence, and seedling heights-. The probability of stocking is multiplied by
the attributes of stocked plots and expanded to an area basis.
-Plot size is a consideration in the study design. The 11741-ha plot used in the Regeneration
Establishment Model is a common size in the northern Rocky Mountains. Choice of the same·
plot size makes predictions easier to understand by model users and their inventory data can
- be processed by the model. Haig (1931) provides ideas for choosmg plot size for sampling
regeneration that are based on densities of mature, fully stocked stands.
Using the same plot size in the model as is used in local inventories -also means that inventory
data can-be used to update, expand, or verify a regeneration model. Future updates may be .
necessary if regeneration success changes due to insects, diseases, advances in technology, or
global climate change. Inventory data can be used to expand a regeneration model to other
geographic areas or ecological situations (Ferguson and Johnson 1988), or it could be used to
verify an existing model and help decide when updates are needed.
The modeling technique used to predjct regeneration in the Prognosis Model may need to be
modifi,ed for situations where pre-harvest conditions strongly influence regeneration success.
Examples are serotinous cones in lodgepole pine, species that sprout from roots or stumps,
and seed stored in the soil. For these cases, features in the model would allow users to include
the information from an inventory or the information could be stored when harvests are
simulated.
Two situations where pre-harvest information is used to predict regeneration success are
included in the Regeneration Establishment Model. First, the history of spruce budworm
(Choristoneura occidentalis) defoliation can be included in predictions of regeneration
38
success. Second, information is stored for species that sprout from roots or stumps.
Computer storage retains the species, size, and number of trees harvested. When regeneration
is predi~ted following the harvest, stored attributes are used to predict the number and size of
sprouts.
An assumption in developing the model is that the influences of soils, diseases, and insects are
represented unbiasedly' through the random selection of stands and the dispersion of harvests
over a number of years. Spanning a number of treatment years is much better than
concentrating treatments in relatively few years. Choosing stands treated in a number of years
also helps average sporadic events like seed crops and weather.
Development of a regeneration model can identify topics for future research. Locations where
stocking isbdow expectations can be investigated to determine the. mechanisms causing
sparse regeneration. Other. topics highlighted during model development might be species
that do not regenerate in adequate numbers or slow growth rates of seedlings.
One recent development that would improve regeneration models concerns independent
fitting of several regression equations from the same dataset. Each equation is usually
considered independent, although this assumption may not be true. An improvement coUld be
made if equations were fit simultaneously as described by Hasenauer et al. (in press).,
Year-to-year variation in regeneration success would be another feature to include in
regeneration models. Most species have cyclic years of cone crops, which interact with the
bioti'C and abiotic environment before seedlings reach establishment size.. Covariances of
probabilities could be .examined to see if it is possible to model year-to-year variation.
REFERENCES
Bailey, RL. & T.R Dell. 1973. Quantifying diameter distributions with the Weibull function.
, Forest Science 19:97-104.
.
Cooper, S.V., K.E. Neiman & D.W. Roberts. 1991. Forest habitat types of northern Idaho: a
second approximation. General Technical Report INT-236. USDA Forest Service,
Intermountain Research Station. 143p..
Ferguson, D.E., A.R Stage & RJ. Boyd. 1986. Predicting regeneration in the grand fir-cedarhe~ock ecosystem of the northern Rocky Mountains. Forest Science Monograph 26.
41p.
Ferguson, D.E. & RR Johnson. 1988. Developing variants for the Regeneration
Establishment Model. In: Forest growth modelling and prediction. General Technical
Report NC~120. USDA Forest Service, North Central Experiment Station. p 369-376.
Ferguson, ·D.E. & N.L. Crookston. 1991. User's guide to version 2 of the Regeneration
Establishnient Model: a part of the Prognosis Model. General Technical Report INT279. USDA Forest Service, Intermountain Research Station. 34p.
Ferguson, D.E. & C.E. Carlson. 1993. Predicting regeneration establishment with the
Prognosis Model. Research Paper INT-467. USDA Forest Service, Intermountain
Research Station. 54p.
Haig, LT. 1931. .The stocked-quadrat method of sampling reproduction stands. Journal of
Forestry 29:747-749.
39
Hamilton, D.A., Jr. & lE. Brickell. 1983. Modeling methods for a two-state system with
continuous responses. Canadian Joumal of Forest Research 13: 111 7-1121 .
.Hasenauer, H., R.A. Monserud & T.G. Gregoire. In press. Cross-correlations among single
tree growth models. In: IUFRO proceedings, symposium on spatial accuracy assessment
in natural resources and environmental sciences. todd Mowrer, ed.
Stage, A.R. 1973. Prognosis Model for stand development. Research Paper INT-137. USDA
Forest Service, Intermountain Fo.rest andRange Experiment Station. 32p.
40
~-.--.---.---
Title:
---
Modelling regeneration success and early growth of forest stands.
. Proceedings from the IUFRO Conference,
held in Copenhagen, 10-:-13 June 1996.
Editors:
J.P. Skovsgaard & V.K. Johannsen.
Publisher:
Ministry of Environment and Energy,
Danish Forest and Landscape Research Institute.
Citation:
Skovsgaard, J.P. & V.K. Johannsen (eds.) 1996: Modelling regeneration.
success and early growth of forest stands. Proceedings from the IUFRO
Conference, held in Copenhagen, 10-13 June 1996. - Danish Forest and
Landscape Research Institute, H0rsholm. 606 pp.
ISBN:
87 -89822-59-5
Printing:
DSR Tryk, DK-1867 Frederiksberg C, Denmark
Number printed:
350
Price:
DKK350
The publication is available from:
Danish Forest and Landscape Research Institute
H0rsholm Kongevej 11
DK-2970 H0rsholm
Denmark
Tel. +4545763200
Fax +4545763233