Forest Ecology and Management, 1 8 (1987 ) 1 - 34
Elsevier Science Publishers B.V., Amsterdam- Printed in The Netherlands
1
Biogeographical Distribution Limits of Douglas­
Fir in Southwest Oregon
ROBERT K. CAMPBELL
Pacific Northwest Research Station, Forest Service, U.S. Department of Agriculture, Corvallis,
OR 97331 (U.S.A.)
(Accepted 15 J uly 1986 )
ABSTRACT
Campbell, R.K. , 1987. Biogeographical distribution limits of Douglas- fir in southwest O regon. For.
Ecol. Manage., 1 8: 1 -34 .
Two methods for estimating the distribution limits of Douglas-fir ( Pseudotsuga menziesii
(Mirb. ) Franco) in southwest O regon, U.S. A. , were attempted using a cover-dominance model
and a niche- habitat model. The cover- dominance model was based on estimates from 435 plots of
cover and frequency of Douglas- fir and other tree species. The niche-habitat model was based on
common-garden estimates of 1 35 genotypic values of Douglas- fir parent trees from 80 locations.
Both models indicated that closest proximity to the species edge was in the dry southeastern areas
with high sun exposure at low elevations. There was no clear way to choose between models. The
niche-habitat model suggested that special problems with natural and artificial regeneration can
be expected in the margin near the biogeographical limits. The niche-habitat model also indicated
that, to ensure a uniform distribution of adapted crop trees in the margin, a large number of
planted seedlings per hectare would be needed. The number increased exponentially from the inner
to the outer edge of the margin. The number can be decreased by successful initial establishment,
no early thinning, or fewer crop trees per hectare.
INTRODUCTIO N
In some areas of southwest Oregon, Douglas-fir (Pseudotsuga menziesii
( Mirb. ) Franco ) has many of the characteristics ofa species near its adapta­
tional limits - difficult regeneration, a distribution influenced by topography,
and all-aged stands in a species that, in the central part of its range, is com­
monly represented by even-aged stands. This paper treats the problem of iden­
tifying geographic features that are associated with limits of adaptation of
Douglas-fir in southwest Oregon.
Meteorological stations indicate strong environmental gradients in south­
west Oregon. Annual precipitation decreases west to east from about 160 to 50
em, and from north to south along the west side of the Cascade Range from
2
about 100 to 50 em ( Franklin and Dyrness, 1973 ) . Precipitation occurs mainly
in winter - at Medford, in a nonforested interior valley in the southeast quarter
of the region, 3.6 em is the average for June through August. Both the annual
and dry-season precipitation decrease substantially with decreasing elevation
( Froehlich et al., 1982; McNabb et al., 1982 ) . Temperature also follows gra­
dients within the region. January mean minimum temperature ranges from
2.5 o C to - 5.0 o C from west to east. July mean maximum grades from 24.5 o C
to 3 1 .0°C northwest to southeast ( Franklin and Dyrness, 1973 ) . The response
of vegetation to precipitation and temperature is modified locally by geology,
soils, and topography, which are highly variable.
Vegetation in the region has been classified into three zones at elevations
below 1400 m ( Franklin and Dyrness, 1973 ) . The Mixed-Conifer Zone ( west­
ern slopes of the Cascade Range ) and the Mixed-Evergreen Zone ( Siskiyou
Mountains ) extend down to about 750 m and are separated by the Interior
Valley Zone, which occurs in the Rogue and Umpqua River valleys. Douglas­
fir is the most abundant species in plant communities dominated by trees, but
it decreases in importance froin north to south within the Mixed-Conifer Zone
and is absent in many plant communities in the Interior Valley Zone. Vegeta­
tion in the region has been influenced by humans for several generations, hence
it is sometimes difficult to determine if the present vegetation is "natural".
At lower elevations in the Mixed-Conifer and Mixed-Evergreen Zones,
Douglas-fir sometimes encounters conditions that limit its ability to reproduce
in competition with more drought-tolerant species. This internal "species edge",
far within the boundaries of the species range, may be abrupt where soils become
shallow, or gradual where moisture becomes critical along a gradient. In either
case Douglas-fir is replaced by drought-tolerant brush or tree species.
There is an intrinsic relationship between individuals and environments near
the species edge ( Emlen, 1973 ) that suggests special problems in natural and
artifical regeneration. It would therefore be helpful to estimate a margin near
the species edge in which these problems might occur for Douglas-fir in south­
west Oregon. Not only would delineation draw attention to areas where adap­
tational limitations may underlie regeneration failures, but delineation would
also provide a basis for allocating regeneration research to problem sites.
This paper presents the rationale for assuming that regeneration within the
margin will become increasingly more difficult as the species edge is approached.
Two models are then used to estimate proximity of the species edge in south­
west Oregon. Finally, an application is provided to suggest the relative degreee
of difficulty expected in regenerating sites within the margin.
MODELS FOR ESTIM ATING THE DISTRIBUTIO N LIMITS
Two models of estimating species limits were compared. The first ( the cover­
dominance model ) was based on estimates from temporary plots of cover and
3
frequency of Douglas-fir and other tree species. The second ( the niche-habitat
model ) was based on an evaluation of genotypes of individual Douglas-fir trees
sampled throughout the area. Variations of the first method traditionally have
been used for describing distribution of vegetation ( Daubenmire, 1956; Whit­
taker, 1967 ) . The second method is a new application of the mapping of genetic
variation. This section of the paper gives the basis for using genetic-variation
trends to estimate the species margin by the niche-habitat model.
Recently a general, deterministic, epidemic model has been proposed to
explain biogeographical distribution limits ( Carter and Prince, 1981 ) . The
model defines the rate of spread of a species as a function of the number of
susceptible sites in an area ( unoccupied sites in which the species could grow ) ,
the number of occupied sites from which the species disseminates seeds, an
infection rate dependent on the probability of establishment of the species in
susceptible sites, and a removal rate dependent on the length of time sites
remain occupied. The model was useful in examining many poorly understood
characteristics of species limits. The niche-habitat model proposed here has a
more limited purpose than the epidemic model. The niche-habitat model is
used to describe an area ( the margin ) near the species edge in which lack of
susceptible sites may hinder regeneration. The niche-habitat model is there­
fore concerned primarily with indicating probability of establishment in sus­
ceptible sites rather than with explaining biogeographical limits.
Probability of establishment depends on the requirements of the species for
conditions and resources, the prevalence of these factors in the environment,
and the number of seeds produced. Douglas-fir is genetically highly variable in
many morphological, physiological and isozyme traits, including those affect­
ing survival. Genetic variation in resistance to drought and cold exists, for
example, among local populations, among families in populations, and among
individuals ( Ferell and Woodard, 1966; Heiner and Lavender, 1 972; Griffin
and Ching, 1977; Rehfeldt, 1 979; Larsen, 1981 ) . Each population undoubtedly
consists of individuals with requirements that vary around an average require­
ment. Conditions and resources of the environment are also highly variable.
In mountainous regions average conditions usually change along complex gra­
dients, but variation in soil color, organic matter, stoniness, shade, and surface
roughness can create a local mosaic of microsites that range from favorable to
unfavorable for seedling survival ( Isaac, 1938; Hertnann, 1 963; Eiche, 1966;
Heatly, 1967 ) . As conditions deteriorate along the gradient approaching the
species edge, the entire range of microsites must become less favorable. If so,
then the proportion of favorable to unfavorable sites changes along the gra­
dient. At the outer edge of a margin near the species edge, most microsites may
be near the physiological limits of the species. It is reasonable to speculate that
at the outer edge only the especially hardy individuals can survive, and then
only in the most favorable of microsites ( this limitation is dynamic, of course,
because conditions in microsites vary in time as well as in space ) . At the inner
4
edge of the margin near the central population, most sites may be suitable for
most individuals in the population and survival of an individual may depend
largely on that individual's ability to compete with other Douglas-fir.
Unlike animals, plants cannot migrate to suitable sites; establishment of a
plant within a microsite therefore depends on the close matching of an indi­
vidual with a microsite that can fulfill its requirements. This chance will vary
within the margin. At the outer edge, the probability may be almost zero within
a single, normal seed year; near the inner edge the probability may be almost
as large as within the central population. In extraordinarily good seed crops or
over a period of many seed crops, the probabilities will be universally higher,
but never will be as high at the outer edge as at the inner edge.
The study reported here assumed a species margin of variable width in which
the proportion of seedlings that are adapted to available microhabitats becomes
smaller and smaller as the species edge is approached. The procedure for delin­
eating the margin of Douglas-fir in southwest Oregon was based on an appli­
cation of three concepts: (1 ) the realized niche, ( 2 ) the one-to-one
correspondence of realized ni'c he and an appropriate microhabitat, and ( 3 )
the equivalence of realized niche and genotype. Some explanation of concepts
is necessary to make the application more understandable.
The word "niche" has been used variously, often without definition. It has
become a vague concept that can refer to properties of the organism, or of the
environment, or to properties of both. An organism is a function of two sepa­
rable properties- its genetically mandated requirements, and its environ­
ment. In this paper the niche is a property only of the organism, and the
microhabitat only of the environment. This seems to be the original meaning
of Hutchinson ( 1957 ) , who defined the niche of a species as the geometric
representation, in n-space, of the combination of all conditions under which a
species can perpetuate itself. The number of dimensions in n-space corre­
sponds to the number of conditions and resources affecting the survival, growth,
and reproduction of the species. An individual cannot use all resources it is
capable of using or tolerate all conditions it is capable of tolerating because of
competition with other individuals or species. Fundamental and realized niches
are therefore distinguished. The realized niche lies within and is coequal to or
smaller than the fundamental niche in all dimensions. Demes ( local popula­
tions; Gilmour and Gregor, 1939; Briggs and Walters, 1969 ) and individuals
within demes vary in their required conditions. Each has a realized and fun­
damental niche within the realized and fundamental niche of the species
( Pianka, 1974; Roughgarden, 1974 ) .
The realized niche of an individual measures the conditions and resources
by which a genotype can survive and perpetuate itself in competition with its
neighbors. This niche is an abstraction in the same sense that the blueprint of
a house is an abstraction. For the house to be built, prescribed conditions must
be met and material and labor must be furnished. For a tree to live, physical
5
resources and conditions must exist as a habitat in which the genotype reacts
with that habitat to produce the phenotype; that is, a tree cannot exist unless
a habitat is available to satisfy the conditions of the tree's niche.
Little is known about the limiting conditions near a species edge ( Carter
and Prince, 1981 ) , but near the edge there likely will be few microhabitats that
can satisfy available niches. The chance of the niche of an individual being
matched by a microhabitat may be almost zero. This probability should increase
across the species margin until niches and habitats can be matched with high
probability in the range center. The delineation of the margin thus depends on
the estimation of niches and microhabitats.
In this paper niches and microhabitats are estimated by predicting the gen­
otypic values of individuals that are expected to occur in association with top­
ographic and geographic features in southwest Oregon. Hyp_othetically, this is
also a prediction of niches of individuals and of the corresponding microhabi­
tats. In the species margin, microhabitats will be predicted for which no suit­
able niches were found in a sample of Douglas-fir in southern Oregon. These
are assumed to represent microhabitats for which no matching niches have
evolved in nearby Douglas-fir demes.
The matter of whether variation in genotypes can be used to estimate vari­
ation in niches and microhabitats hinges on several things. Pianka ( 1974 ) has
defined the niche as "the sum total of the adaptations of an organismic unit",
so it seems reasonable to take the genotypic value of a tree as a consistent
estimate of its niche - the genotype, too, is the sum total of the adaptations of
an organism. But for variation among genotypes to be also a measure of vari­
ation among microhabitats, the adaptations must have a foundation that is
mainly genetic, as opposed to phenetic ( somatically plastic ) .
The case that Douglas-fir's adaptations are mainly genetic rests primarily
on theory and some evidence from nontree species. Species show different
strategies for maintaining fitness in a heterogenous environment ( Levins, 1963;
Emlen, 1975 ) . Some rely on somatic plasticity. Others, such as Douglas-fir,
generate many genotypes and a large amount of genetic variability. Levene's
( 1953 ) analysis indicates that genetic variation within populations can be
maintained by disruptive selection among microhabitats. The condition
assumed in this paper - that the fraction of adults that come from any type of
microhabitat is proportional to the fraction of that microhabitat in the envi­
ronment- contributes to the "easy" generation of genetic variation ( Rough­
garden, 1979 ) .
Emlen ( 1975 ) proposed that natural selection optimizes the generation of
variability so as to maximize fitness. For large amounts of genetic variation to
have a selective advantage, however, one of two conditions must hold: ( 1 ) either
the variation among microhabitats is large, which in turn, requires quite dif­
ferent niches among individuals in a progeny to ensure matching of niche and
habitat, or ( 2 ) the dimensions of the realized niche of an individual are small
6
in relation to variation among microhabitats. In either case, the implication is
that within -genotypic variation ( phenetic ) is small in relation to variation
among microhabitats. Emlen's analysis (1975) suggests that selection pres­
sures on a population in which the variation in adaptive traits is mainly phe­
netic leads to the variation becoming more phenetic; where the variation in
the population is mainly genetic, it tends to become still more genetic. Large
genetic variation within populations of Douglas-fir suggests that the variation
has arisen by disruptive selection, by the selection of trees with niches that are
strongly controlled by genotype.
Douglas-fir's reproductive system - the episodic production of many pro­
pagules with highly diverse genotypes - accommodates intense competition
among individuals within populations and at the same time it offers an oppor­
tunity for the matching of niches and microhabitats by disruptive selection. In
most stands of Douglas-fir, the resources of microhabitats are probably almost
completely utilized. The microhabitat of a tree is more and more restrictive as
the tree grows and competes with its neighbors. The surviving individuals in a
stand- the ones "selected" - are the phenotypically best adapted to the micro­
habitats. Selection is "soft" ( Wallace, 1968, 1975 ) , that is, it depends on the
number and nature of the phenotypes of all competing individuals as well as
on the physical conditions and resources of the microhabitats. If adaptations
of Douglas-fir are mainly genetic, as hypothesized, the niches of individuals at
maturity will have been closely packed into all available microhabitats by dis­
ruptive selection. The niches of trees and the microhabitats will be completely
interdependent.
There is far less evidence in tree species than in other species that the selec­
tion among individuals by competition and other conditions of the microha­
bitat is, in fact, disruptive. In tree species, selection has been reported to reduce
genetic variability from the juvenile to the adult population ( Hamrick and
Libby, 1972 ) . Furthermore, the selection that reduces variation within popu­
lations cannot be attributed just to the stabilizing selection caused by elimi­
nation of the inbred individuals resulting from self-pollination ( Shaw, 1980 ) .
There is also evidence that the selection near the species edge is not stabilizing.
Selection in the juvenile population apparently had more effect on gene fre­
quencies in a low-density pine stand at a low elevation forest-grassland ecotone
than in a more central, higher density stand ( Farris and Mitton, 1984 ) .
In nontree species, many types of breeding systems have been shown to pro­
vide for the preservation of diverse genotypes within small local populations
( Harper, 1977 ) : in apomicts ( Solbrig and Simpson, 1974 ) , in exclusive
inbreeders ( Kannenberg and Allard, 1967 ) , in partial outbreeders ( Clegg and
Allard, 1973 ) as well as in mainly outbreeders. The coexistence of these many
genotypes within local populations "suggests disruptive selection in which there
are perhaps many adaptive optima" ( Harper, 1977 ) . Harper reviewed evi­
dence from several studies and proposes "that there are nearly as many adap­
7
tive optima within a habitat as there are individuals" and that for long-lived
outbreeders "the few survivors from each generation may represent the variety
of adaptive optima present within the habitat". In the terminology of this paper,
niches of surviving individuals apparently are tightly packed in all available
microhabitats by disruptive selection. Selection among microhabitats is strong
enough to preserve diverse genotypes within populations even in exclusive
inbreeders ( Kannenberg and Allard, 1967 ) . It therefore seems reasonable to
use variation among genotypes as a measure of variation among niches. Also,
if niches are available for all suitable microhabitats ( niches are solidly packed ) ,
if all resources in microhabitats are used, and furthermore, if niches and micro­
habitats are interdependent, the variation in niches should be a reasonable
estimate of the variation in microhabitats.
M ATERIALS AND M ETHODS
Estimation of limits by the cover-dominance model
The area sampled was in southwest Oregon, from 0 to 140 km north of the
California border ( 42 o north latitude ) and from 30 to 160 km east of the Pacific
Ocean. Within the area, 435 plots were measured at 400 locations. In addition
to latitude and distance from the ocean, several variables were used to describe
plot locations. For these variables the distribution of plots were:
( 1 ) Elevation, uniformly from 350 m to 1460 m.
( 2 ) Aspect, uniformly distributed from 0 o to 360 o azimuth.
( 3 ) Slope percent, from 0 to 85, but uniformly distributed from 0 to 60.
( 4 ) Direction of flow in nearest drainage, uniformly distributed in degrees
azimuth.
( 5 ) Vertical distance to the top of slope above plot, from 0 to 600 m, but con­
centrated at < 1 10 m.
( 6 ) Vertical distance to bottom of slope below plot, from 0 to 910 m, but con­
centrated at < 160 m.
( 7 ) Horizon sum, calculated as the sum of the vertical angles from the plot
center to a horizon taken at 22.5° intervals of azimuth from oo to 360°. The
sums ranged from 6 to 428 but were concentrated between 81 and 260.
( 8 ) Sun exposure, 9 February. The above vertical angles from segments east
( 90 o ) to west ( 270 o ) were plotted to provide a graph of the horizon across the
southern sky. Using this graph and the graphed path of sun height throughout
the day 9 February, the number of minutes of direct sun exposure at the plot
center was calculated. Values ranged from 0 to 789 and were strongly centered
around 420 min.
( 9 ) Sun exposure, 3 April. Values ranged from 477 to 846 and were strongly
centered around 690 min.
At each location, the diameters of trees bf all species were measured in vari­
8
able-radius plots ( Grosenbaugh, 1958 ) . In variable-plot sampling, a tree whose
diameter is large enough to subtend the critical angle of a wedge prism is con­
sidered to be in the plot. By determining the number and diameter of the "in"
trees, the basal area and number of trees per hectare were calculated ( Dilworth
and Bell, 1979 ) . At each plot, the prism chosen to determine "in" trees had a
basal area factor small enough to ensure the sampling of 12 to 15 trees. In
variable-plot sampling, each tree carries equal weight in computing basal area
per hectare, regardless of tree diameter ( Grosenbaugh, 1958 ) .
Data from each plot were summarized in four "response" variables; the num­
ber and basal area of Douglas-fir trees per hectare, and number and basal area
of Douglas-fir trees as a percentage of the number and basal area of all trees in
the plot.
Frequency and cover of Douglas-fir was determined for single plots at 365
locations, and for two plots at an additional 35 locations. Variability among
plots was first analyzed to partition variation into components of variance
( and covariance ) indicating differences among locations and among plots
within locations. The model was:
Yij
=
u + Lj + e ij
where Yij is the plot mean for the jth plot in the ith location ( L), u the overall
mean, and e the plot error. To partition variance ( and covariance ) into com­
ponents, mean squares in the analysis of variance were equated to their expec­
tations and the resulting equations were then solved.
Frequency and cover estimates may form a highly correlated, multivariate
system. The second step involved a principal component ( PC ) analysis of the
four response variables ( Morrison, 1967 ) . Input for the analysis was the matrix
of components of variance and covariance for locations. The principal com­
ponent analysis transforms the original set of variables into a new set. Not
only does the new set include all the variation in the original set, but one or
two of the new variables ( PCs ) usually accounts for most of the variation in
the original set.
After PCs were chosen, a new variable ( factor-score ) was created for each
plot. These were obtained for each significant PC by:
where Yin = factor score for the ith PC ( i = 1 , .. . , 4 ) , the nth plot ( n = 1 , . . . ,
435 ) , and eigenvectors having coefficient aik• for the ith PC and kth response
variable ( xk; k=1, . . . , 4 ) .
Factor scores of plots for the significant principal components were analyzed
in a preliminary model by multiple regression. The model included linear terms
for all location variables, and quadratic terms and interaction terms when pre­
vious experience had indicated that such effects were possible. Because the
9
habitat factors that restrict the range of Douglas-fir at high and low elevations
may be different, two analyses were done for each PC; one for plots below 915
m ( 252 plots ) and one for plots above 915 m (183 plots ) . In each of these
analyses, an equation in which all variables significantly reduced sums of
squares in factor scores was selected from the preliminary model by backward
elimination ( Draper and Smith, 1966, p. 167 ) . Lack of fit of data to the selected
equation was tested using data from the two plots measured at 35 locations as
repeats ( Draper and Smith, 1966, p. 76 ) .
Estimation of margin by the niche-habitat model
The procedure for estimating the margin of Douglas-fir from genetic varia­
tion patterns in southwest Oregon involved eight steps: ( 1 ) obtaining seed
from parent trees at locations sampling the area, ( 2 ) growing open-pollinated
families in common gardens to estimate genotypic values of parents for several
seedling traits, ( 3 ) determining structure of variation in the set of correlated
seedling traits by principal component analysis, ( 4 ) transforming the original
set of traits into a smaller set of new variables ( PCs ) with an estimated gen­
otypic value ( factor score ) for each parent for each significant PC, ( 5 ) cal­
culating the components of variance in factor scores for source and for families
in source, ( 6 ) determining the relation of source variation to location varia­
bles, ( 7 ) predicting the distribution of genotypes and microhabitats over the
range of location variables in southwest Oregon, and ( 8 ) using predicted dis­
tributions to estimate the proportion of microhabitats for which there are
matching genotypes at selected locations in southwest Oregon.
Procedures for most steps will be sketched briefly. Steps 1 through 6 are
covered in detail elsewhere ( Campbell, 1986 ) . Steps 3 through 6 are analogous
to steps used in the analysis of cover and frequency in the previous section of
this paper. The final two steps will be described in some detail because they
relate more directly to estimating
the species margin.
I
The sampled area was approximately square with west and east boundaries
58 and 192 km respectively from the Pacific Ocean. The southern and northern
boundaries were on the northern California border and on the parallel at 43 o
north latitude, respectively.
Cones were collected from 135 parent trees, from two trees separated by
more than 133 m at each of 55 locations, and from one tree at another 25
locations. Parents were chosen mainly to sample the extreme mild and harsh
environments for Douglas-fir. The origin of parent trees was described by seven
location variables: elevation, latitude, distance from the ocean, vertical height
of the mainslope, vertical distance to the bottom of the slope below the parent
tree, slope percent, and sun exposure on 3 April. The distributions of the loca­
tions of parent trees were quite similar to the distributions of sample plots used
in the cover and frequency study.
10
To evalute genotypes of parent trees, open-pollinated offspring were planted
as newly germinated seed in two nursery environments. Each family was rep­
resented by a five-seedling row plot, with families allocated randomly in each
of four replications in an environment. Thirteen traits expressing timing of
the vegetative cycle and growth potential ( e.g., bud burst and bud set, second
flushing, height, and diameter ) were measured for two growing seasons. For
each trait the genotypic value of a parent tree was estimated by the mean of 20
seedlings.
Genotypic values were analyzed in the same steps and procedures used to
analyze plot means in the cover and frequency study above: first, an analysis
of variance ( and covariance ) to estimate components of variance ( and cov­
ariance ) associated with parent-tree location ( a; ) and with trees within loca­
tion ( a¥(sJ ) ; second, a principal component analysis to consolidate the 13
correlated traits into fewer uncorrelated ones; third, a calculation of factor
scores for each significant principal component for each parent; and fourth , a
regression analysis to determine the association of factor scores ( genotypic
values ) of parents with location variables.
The estimation of the species margin starts with the prediction of average
genotypic values for locations. For reasons covered in a previous section, the
predicted distribution of genotypes at a location also gives the distribution of
niches of Douglas-fir and of corresponding microhabitats.
The distribution of the genotypes within southwest Oregon was defined by
the mean and standard deviation of factor scores calculated for many points
systematically located within the region. The mean of the deme at a point was
estimated by solving the regression equations for factor scores of the signifi­
cant principal components. Predicted values for each PC for each point were
obtained from an array of the location variables that had been shown to describe
genetic variation in southwest Oregon. The standard deviation of individual
genotypes within the deme at the point was estimated from the additive genetic
variance taken as 3a¥(s) . This standard deviation was used to calculate the
distribution of niches within the deme. The multiplier 3 presupposes 0.33 as
the genetic correlation among offspring of open-pollinated parents; it reflects
the greater likelihood of pollination by adjacent related parents ( Squillace,
1974 ) and an average of 7% production of seed by self-fertilization in Douglas­
fir ( Sorensen, 1973 ) .
The standard deviation of genotypes in a deme is assumed to be the same in
all demes in southwest Oregon although the evidence is indirect. If there is
more additive genetic variation among trees at one location than at another,
this should appear as increased variation among individuals within families
( two-thirds of the additive variance at a location is found within families ) . In
analyses of many seedling traits of Douglas-fir in this and other studies
( Campbell, 1979 ) , differences among sources in within-family ( within-plot )
standard deviations have seldom been found. When found, they have been
extremely small.
11
The second step i n delimiting the margin involved calculating the distribu­
tion of genotypes in the edgemost hypothetical deme of the central population.
Any species with a continuous range can be divided into more-central and less­
central demes. In the more centrally located demes of Douglas-fir, the array of
realized niches in the deme can occupy the available range of microhabitats
( Fig. 1a ) . But, as harsher sites are sampled nearer the species edge, some gen­
otypes cannot survive some conditions, or the available resources are limiting
to some genotypes. Niches appropriate to some microhabitats either have not
evolved or are represented in only a small proportion of individuals. In this
study, a concerted effort was made to sample parent trees from the most
droughty and harsh environments that can support Douglas-fir in southwest
Oregon. The most extreme factor score ( at the "droughtiness" end of the range )
found in the sample of 135 families for each of the significant PCs was there­
fore assumed to indicate the edgemost genotype in the central population. The
distribution of genotypes in the edgemost deme of the central population was
then taken as having a mean 2.5 standard deviations central to the edgemost
genotype ( Fig. 1b ) . In such a deme, fewer than 1 % of individuals would have
a genotype more extreme than any found in the sample of genotypes evaluated
in this experiment
The final step in delimiting the margin was to evaluate the degree of mis­
match among niches and microhabitats within the margin. A normal distri­
bution of niches and microhabitats was assumed because the distribution of
genotypic values for factor scores was approximately normal.
From the regression equations for factor scores, predictions were continued
along gradients of the topographic variables beyond the edgemost deme ( Fig.
1c ) . Distal to this deme, genotypes were predicted for which there were no
matching genotypes in the adjacent Douglas-fir deme. These are taken as rep­
resenting microhabitats for which there are no matching niches within the
edgemost population of Douglas-fir. The mismatch between Douglas-fir niches
and microhabitats is indexed as the part of the distribution of microhabitats
that does not overlap the distribution of niches. The index ranges from approx­
imately zero at the proximal edge of the margin ( Fig. 1b ) to approximately
one at the distal edge ( Fig. 1d ) .
Principal components represent different aspects of the genotypic value ( e.g.,
growth vigor vs. growth timing ) and thus different aspects of the niche. A
seedling exposed to the microhabitat might risk poor adaptation in respect to
one aspect of its niche, another aspect of its niche, or both. Therefore, the
mismatch of niches and microhabitats was calculated for factor scores from
each significant principal component. When the variation of niches is equal to
the variation of microhabitats, the proportion of overlap in the two curves is
calculated as:
V=1 - 2a
12
b
Niches-1
Microhabitats-1
Limiting
niche
c
Microhabitats-2
d
Niches-2 Microhabitats-3
Niches-2
Microhabltats-4
Fig. 1. Conceptual mode l for estimating position within the spe cies margin: (a) Hy pothe tical
distribution of niches (1 ) and of corresponding microhabitats (1 ) of a deme in the ce ntral popu­
lation. Niches vary along a gradient of some critical res ou rce or condition from le ft to right. The
limiting niche in respect to the critical factor is represented by the vertical line. (b) Distribution
of niches (2 ) and microhabitats (2 ) at the inner edge of the spe cies margin. (c) Microhabitats
(3) in the inne r half of the species margin. The cross-hatched area represents microhabitats that
are available in greater proportions than are niches adapted to such microhabitats. The mismat ch
inde x is M=0.42 . (d) Microhabitats (4 ) in an area near the ou te rmost edge of the spe cies margin
(M= 0.97 ) .
where a = P [ 0 < z < ( x/2 ) /JA 1 , the area under the standard normal curve from
zero to z ( e.g., Snedecor and Cochran 1967, p. 548, table A3 ) and z=x/ ( 2aA);
in which x is the difference between mean factor scores at seed origin and
plantation; aA the standard deviation of the additive genetic variation of factor
scores within sources; and z the standardized factor score.
For each PC, the nonoverlapping proportion ( the hatched area in Fig. 1c
and d ) , and by inference, the proportion of planted seedlings unlikely to
encounter microhabitats to which they are optimally preadapted is:
Pro = 1 - V=2a
Not all seedlings are preadapted to all microsites even at locations within
the central population, but for this procedure they are so considered. Any cal­
culated proportions of poorly preadapted seedlings in the margin is therefore
relative to the proportion expected in the central area. The mismatch ( M) ,
taking into account the nonoverlapping proportion ( Pro ) for each of two PCs
( 1 and 2 ) , is:
M = Pro ( 1 )
+ Pro ( 2 )
-
[Pro ( 1 ) X Pro ( 2 ) 1
13
RESULTS
Cover-dominance model
Slightly more than two-thirds of the variation in the cover of Douglas-fir in
plots was associated with plot location ( 75% for Douglas-fir basal area; 68%
for Douglas-fir as a percentage of the basal area of all trees - Table 1 ) . The
other one-third represents variation in cover among plots within locations.
Frequency of Douglas-fir in plots was somewhat less closely related to location
( 69% for number of Douglas-fir; 60% for number of Douglas-fir as a percentage
of number of all tree species - Table 1 ) .
The different measures of frequency and cover were correlated so that when
the variation was reduced to its PCs, about 90% of the variation could be attrib­
uted to two statistically significant PCs. The structure of the variation in fre­
quency and cover was very similar whether measured in plots above or below
915 m. Loadings ( the correlation between factor scores and measurement of
cover variable ) were almost identical in the two sets of plots ( Table 2 ) . In
each set, the first PC ( PC-1 ) reflected the dominance of Douglas-fir in the
stand in respect to cover. For plots with large factor scores of PC-1, basal area
of Douglas-fir was large, most of the basal area in the plots was contributed by
Douglas-fir, and a large percentage of trees in the plots were Douglas-fir. The
second principal component mainly reflected the number of Douglas-fir trees
per hectare. Large factor scores of PC-2 indicated a large number of Douglas­
fir trees, usually associated with a small percentage of the basal area per hec­
tare. Plots with large factor scores of PC-2 also had higher percentages of
Douglas-fir but the relationship was not strong ( Table 2 ) . Factor scores of
both PC-1 and PC-2 therefore were smaller when Douglas-fir was a smaller
component of the stand, and the factor score was zero in plots having no Doug­
las-fir.
The relation of topographic indices of environment to factor scores was ana­
lyzed by multiple regression for two classes of plots: high elevation ( > 915 m )
and low elevation ( < 915 m ) . I n all cases, a highly significant ( P < 0.00001 )
amount of variation in factor scores was fitted to equations ( Tables 3 and 4 ) .
In each case, a different subset of topographical variables gave the best pre­
dicting equation.
Equations were complex and relationships could not be easily evaluated by
examining coefficients. Interpretation was facilitated by solving equations and
graphing results. The interpretation below should not be taken too literally,
but rather as an indication of broad trends. The null hypothesis of lack-of-fit
was not disproved; that is, one or more genuinely relevant environmental var­
iables may have been left out of the model or may not have been measured.
.....
"'"
TABLE 1
Compone nts of variance (a2) and pe rce ntage of variance (% ) for cove r and freque ncy meas urements and for factor s cores derived from principal
components
Source of
variation
Locations
Plots within
locations
Signifi cance of
locations P < . . .
Douglas-fir
basal area
pe r hectare
Douglas-fir
number pe r
he ctare
Pe rcent of
basal area as
Douglas -fir
Pe rcent of
number as
Douglas-fir
First
principal
component
(J2
%
(J2
%
(J2
%
(J2
%
(J2
%
(J2
%
399
973
75
1 85 822
69
669
68
781
60
0.695
70
0.772
78
34
322
25
81 840
31
315
32
515
40
0.302
30
0.22 1
22
Degrees
of
freedom
0.0000
0.0000
0.0000
0.0005
0.0000
Second
principal
component
--
0.0000
15
TABLE2
L oadings, communalities, and the pe rce nt of variation e xplained by principal components after
varimax rotation
Douglas -fir
basal
area per
he ctare
Douglas-fir
numbe r
per
he ctare
Percent
of basal
area as
Douglas-fir
Pe rcent
of numbe r
as
Douglas-fir
Percent
of
variation
0 .910
0 .02 6
0 . 82 9
0.118
0 .970
0.954
0.932
0.195
0.907
0.749
0.510
0.822
65 .7
22 .1
Plots > 915 mb
0 .92 7
PC-1
PC-2
0.017
0.859
Communality
0 . 157
0.974
0.975
0 .933
0 .22 3
0 .92 1
0 . 82 6
0 .419
0 . 85 8
69 .1
2 1 .2
Principal
components
Plots < 915 m•
PC-1
PC-2
Communality
"Based o n2 52 plots be low a n elevation of 915 m. bBased on 1 83 pl ots above an e levation of 915 m. Also, predictions of individual curves or of the species edge may be quite impre­
cise. Even in the best case, the analysis of PC-1, the regression equations
described only about one-quarter of the variation in factor-scores ( R 2 0.24,
0.30, Tables 3 and 4 ) . For PC-2, the description was even less perfect (R2 = 0.15,
0.15, Tables 3 and 4 ) ; the relationships of factor scores of PC-2 to environ­
mental indices are consequently not described here.
For the high-elevation plots, the environment that influenced cover domi­
nance of Douglas-fir ( as reflected in factor scores of PC-1 ) was indexed by a
complex mix of topographic and geographic features. Percentage of slope was
one of the more important ones, as judged by standardized coefficients ( Table
3 ) . It would be misleading, however, to imply that slope itself ( T ) is a major
factor in the dominance of Douglas-fir because the relation depends also on
the components of environment indexed by sun exposure ( OT) and latitude
=
(LT).
The trend is for Douglas-fir to decrease in importance with flatter mountain
slopes at highest elevations in the northern part of the sample region. The
model indicates that the lowest elevation at which the species edge ( factor
score = O ) might be encountered is about 1040 m ( Fig. 2a ) . This could occur
at the farthest north latitude ( 43.2 o ) on flat land with 840 min of sun expo­
sure. This condition can be expected only on high ridges not surrounded by
higher mountains. The species edge ascends rapidly from this lowest point,
especially with steepening slopes ( Fig. 2a ) and decreasing sun exposure ( Fig.
2b ) , and also with decreasing latitude ( Fig. l2c ) and slightly with distance from
0>
TABLE 3
Regressi on analyses of factor scores derived fr om frequency and cover measureme nts of Douglas-fir in plots of elevati on
Variable"
T
OT
LG
EL
LT
G
D
02
(CONST)
Variable"
First principal component (PC-1)
Partial
coeffi cient
Signi fi cance
P< . . .
Standardb
coe fficie nt
-8.5595
0.1035E-01
2. 1503
-0.4140E-03
3.1 316
-1 . 3616
-0.6 216E-0 2
-0 .3165 E-05
4.9346
0.02
0.040
0.000
0.001
0.002
0.002
0.001
0.029
0.000
-1.64
1.34
0 . 70
-0.66
0.49
-0. 33
-0 . 29
-0. 28
Lack of fit for PC-1 indicated at P < 0 .0004 ; R2
Lack of fit for PC-2 indicated at P < 0.005; R2
For other notations see Table 4.
0 . 24.
0 . 15.
=
=
IG
10
LO
2
E
(CONST)
>
915 m
Second pri ncipal component (PC-2)
Partial
coe fficient
Signi ficance
P< . . .
Standard
coefficie nt
-0.5319E-02
0.6156E-05
0.8560E-03
-0.3784E-07
1 .4231
0.007
0.008
0.001
0.001
-0. 29
0. 29
-0. 24
-0. 23
TABL E 4
Regre ssi on analyses o f factor scores derived from frequency and cover measurements of Douglas-fir in plots o f elevation < 915 m
Variable "
0
02
I
IO
L
LO
OD
LD
E
IT
GU
(CONST)
Principal component 1
Principal component 2
Variable "
Partial
coefficie nt
Significance
P< . . .
Standard
coefficient
-0.7531E-01
0.42 66E-04
-0.3529E-01
0.5479E-04
-5.4957
0. 7953E-02
-0 .1842 E-04
0.1109E-01
0.4578E-03
0.2895E-02
0.3449
30. 3316
0.015
0.02 1
0.005
0.004
0.009
0.011
0.000
0.002
0.000
0.040
0.009
0.008
-4.91
4.13
-2 .81
2 .44
-1.67
1.64
-0.60
0.52
0.33
0.19
0.15
D
OD
GT
OT
LO
LD
EI
E
LT
IG
(CONST)
Partial
coeffi cient
Significance
P< . . .
Standard
coe ffi cie nt
0.3647E-01
-0.4007E-04
-4.4339
0.5256E-02
0. 312 7E-02
-0.1 379E-01
-0.2 495E-05
0.6846E-03
-2 .56 1 1
0.6994
-1.5036
0.001
0.012
0.001
0.000
0.000
0.001
0.003
0.002
0.008
0.005
0.001
1.65
-1.31
-0.69
0.69
0.65
-0.64
-0.54
0.49
-0.40
0 . 39
Lack of fit for PC-1 indicated at P < 0.01; R2 = 0.30.
Lack of fit for PC-2 indicate d at P < 0.003; R2=0.15.
"E=elevation (0. 3047 m).
I= horizon sum (the sum of the vertical angles from the plot ce nter to horizon taken at 22 .5 intervals of azimuth from 0 to 360 )
L= lati tude (degreesN-42 ). 0 =sun exposure in minutes exposed to direct sun on 3 April. G=posi tion on slope (vertical height above bottom/total height of slope ). I= slope (slope percent/100). U=cosine of aspect (degrees azimuth). D =west to east distance from ocean (km). CO NST= constant. bStandardized coeffi cients are some times used (ignoring sign) as measures of relative importance of variables (Snede cor and Cochran, 1967).
o
o
o
•
.....
-l
·-·­ ·
- ·­
·-·
-
r
· - . ,o
_?:,_
b
·- .
.....
.
T
.... _ - _
r -a
·- . .
. . .
-·-·.0-.
-. .
- 59o
...
....
....
...
_
_
-..r...__
-
.... _
--
-..._
....
....... ·
-.
....
0
·-
·-
- -7rs
-
--
d
L
420
f-·-·-·-·-·-·-·-·
-- - _:. 2,._
-­
--
L
--
4<a
--
-·-·- ·- ·-·- . -·-
-------
-
- L
-....4..;;,.___ 32
-------.-----r-----.-- - 0 -aoo 102s 11so 121s 1400 1525
Elevation (m)
r--·
- ·- .
t' - -
-.. G
r-.-.. -2 -f}25
I
eoo
0
--.;,...
-.
-
--- -
1025
-?
-
o ?s
-.
-
-
1150
-
- ·
-
-
-
1275 1400 1525
Elevation (m)
Fig. 2. Comparative e ffe cts of site variable s on cover dominance at higher elevations ( > 915 m) .
Douglas-fir varies from being abse nt (factor score=0) to being predominant (factor score= 3) .
In each subfigure the i nitial conditions (bottom line) are: T=slope (zero percent) , 0 = minutes
of sun exposure (840 ) , N=latitude (43.2° north) , G= bottom of slope (zero) , D=km from the
Pacific coast (160 ) , and U= north aspe ct (1 ). Subfigure s indi cate the decreasing dominance of
Douglas-fir, as affected by: (a) slope, (b) sun e xposure, (c) latitude, and (d) position on slope.
the ocean ( not shown ) . At high elevation, Douglas-fir decreases slightly in
dominance if it is near the bottom of a slope as compared to being near the top
( Fig. 2d ) .
Results are consistent with the common idea that Douglas-fir is limited at
high elevations by cold. Radiation cooling may be excessive on high, flat areas
not surrounded by mountains, and cold air may pool in high drainages.
The model indicated that conditions limiting Douglas-fir ( factor score = 0 )
at elevations < 915 m are encountered only in the southeastern quarter of the
region on very exposed sites at lowest elevations on southern aspects. Of the
indices of environmental influence at low-elevation plots, those measuring sun
exposure ( 0), horizon prominence (I), and the combination of the two ( JO),
were most important ( Table 4 ) . At lower levels of sun exposure, cover domi­
nance at an exposed (I= 80 ) southern location ( 42.1 o north latitude ) , 120 km
from the coast, at 460 m elevation, on nearly flat ground of southern aspect,
19
3
a
Gl
0 2
u
1/1
..
...
"
"1-'Q"' / ' /
/
t-')'1/
/
/
/
b
/
AO ,.
...,.,
7.-'00 \),..,.,.
..
0
u
....
IV
u.
1
26!
A2 i
"---
0
3
"
d
/
.,.
g20(f\
,.,....
£_
,.,.,...
260
-IJ,'Oo('(l
,.
'2.-t;:,O
/
......
..-
..
:.
.,
.,
c
Gl
..
0 2
u
1/1
0
....
u
......
...
1
zoo
----I
5 ,.
o1-.:._ -
,.
...
,.
/
0 ?5
0
575
825
875
72 5
775
Sun exposure on April 3 (minutes)
575
825
875
725
775
Sun exposure on April 3 (minutes)
Fig. 3. Comparative effects of site variables on cover dominance at lower elevations ( < 915 m).
Douglas-fir varies from being absent (factor score= O) to being predominant (factor score=3).
In each subfigure the conditions of the lowermost solid line are: I=horizon sum of 80, L = 42 .1
north latitude, D =120 km from the Pacific coast, E = elevation of 460 m, T=slope of 0% and
U =south aspect (-1). Subfigures indicate the combined effects of horizon sum (I) and sun expo­
sure as modified by extremes in: (a) latitude, (b) distance from the ocean, (c) elevation, and (d)
slope.
o
was about the same as at an enclosed (I= 260 ) location, farther north ( Fig.
3a ) , or closer to the coast ( Fig. 3b ) , or at higher elevation ( Fig. 3c ) , or on a
steep slope ( Fig. 3d) , or on a north aspect ( not shown - the difference between
north and south aspect was almost identical to that shown for elevations in
Fig. 3c ) . In contrast, at higher levels of sun exposure the model indicated some
substantial differences between the two types of locations. At the exposed
southern location, cover dominance decreased with increasing sun exposure.
But cover dominance increased with increasing sun exposure when the enclosed
locations were farther north ( Fig. 3a ) , or farther west ( Fig. 3b ) , or of higher
elevation ( Fig. 3c ) , or on a steeper slope ( Fig. 3d ) , or on a north aspect ( not
shown ) . These high -elevation northern locations represent conditions in which
moisture is less likely to be critical than at low-elevation, southeastern locations.
Results indicate that the orientation of the mountains may be a major factor
in cover dominance of Douglas-fir at specific locations in southwest Oregon.
20
Although a location with a large sun exposure will usually have a low horizon
sum ( r
0. 77 ) , large values for both are simultaneously possible where
mountains are absent east or west of the location. The longer growing seasons
associated with more sun exposure may be a disadvantage where lack of sum­
mer precipitation can severely limit growth. When moisture is less critical,
longer growing seasons are likely to enhance the growth potential of Douglas­
fir.
Results support the hypothesis that Douglas-fir is limited by moisture defi­
ciency at low elevations. Growing season precipitation in southwest Oregon
decreases with distance from the ocean, with lower elevation, and from north
to south. Decrease in cover dominance follows the same progression. The two
exposure indices (I and 0) apparently index environmental factors that mag­
nify problems with reproduction, growth, and survival that are associated with
moisture deficiency.
=
-
Niche-habitat model
The data used to estimate species margin by using genotypic values to index
niche variation were used previously for delimiting seed-transfer zones. Part
of this section is therefore a summary of a more detailed analysis presented
elsewhere ( Campbell, 1986 ) .
Analyses indicated significant genetic variability in all traits. Averaged over
the 13 traits, the variation related to differences among locations ( sources )
accounted for 65% of the total variance ( Table 5 ) . The remaining 35% rep­
resented variation among trees at a location ( families ) .
Components of variance and covariance for sources were used as input for
principal component analysis because variation among sources more clearly
pertains to adaptational differences than does variation among families. The
first two principal components were statistically significant ( P < 0.00 1 ) and
explained 96% of the variation in all traits ( Table 6 ) . The variance in factor
scores derived from PC-1 (eigenvalue = 9.77) is more than three times the
variance in factor scores for PC- 2 ( eigenvalue = 2.69 ) .
Generalized relationships between factor scores and trait scores can be iden­
tified by examining the loadings in Table 6. The first principal component
( PC-1) expresses mainly growth vigor ( height, diameter) and the second ( PC­
2 ) expresses aspects of growth timing not correlated with seedling size. The
smaller the factor score of PC-1, the earlier the bud set and the smaller the
seedling. Also, the smaller the factor score, the fewer the seedlings that flush
twice and the less the variation in height among seedlings within families. The
smaller the factor scores of PC-2, the earlier the bud burst and bud set.
In factor scores derived from PC-1, 78% of variation was associated with
parent-tree source and 22% with families. In factor scores from PC-2, corre­
sponding values were 61% and 39% ( Table 5 ) .
21
TABLES
Analyses of variance and distribution of components of variance among sources and families in
sources for traits and principal components
Trait"
Components of variance (percent
of total)
Source variance
Family variance
69**
47**
52 **
83**
69**
100**
56**
53**
30**
80**
74**
70**
57*
78**
6 1**
31**
5 3**
48**
17**
31**
0
44**
47**
70**
20**
2 6**
30*
43*
22 b
39 b
as2
C bud set 1
C bud burst 2
C bud set 2
C height 2
C diameter 2
C second flushing 2
Wbud set 1
Wbud burst 2
Wbud set 2
Wheight2
Wdiameter 2
Wsecond flushing 2
Wheight variability 2
Principal component - 1
Principal component -2
2
af(s)
"Trait code: C bud set 1 day-of-year when 50% of seedlings have set bud in an untreated nursery bed (C) in the first growing season (1); W bud set 2 - day-of-year to 50% bud set in a heated nursery bed (W) in the second growing season (2 ); height and diameter- total height and diam­
eter at the end of the second growing season; second flushing - percent of seedling with terminal lammas growth; height-variability- standard deviation of height in second year among individ­
uals in a family plot. bNo F-test possible. *P 0.05. **P O.Ol. -
The regression equations relating factor scores to indices of environmental
variation were complex. The regression equations of PC-1 accounted for 68%
of the sums of squares in factor scores (R2 0.68 ) . Regression coefficients of
the environmental indices were highly significant ( Table 7 ) and had small
standard errors - consistently about 25% the size of coefficients.
Some of the variation among sources was not explained by the regression
equation. In analyses of variance, variation among sources accounted for 89%
of the sums of squares for all families. Regression explained only 68% of the
total sums of squares for all families and therefore only 76% of the sums of
squares for sources ( 0. 76 0.68/0.89 ) . The remaining 24% represents source
variation that may or may not be associated with indexing variables not con­
sidered. Residuals, however, did not reveal any weaknesses in the model and
lack of fit was not statistically significant ( Table 7 ) .
=
=
22
TABLE 6
Principal components (PC) with seed- source trait loadings, eigenve ctor coefficients, and
eigenvalues
Trait"
PC-2c
C bud set 1
C bud burst 2
C bud se t 1
C height 2
C diameter 2
C second flushing 2
Wbud set 1
Wbud burst 2
Wbud set 2
Wheight 2
Wheight variability 2
Wdiameter 2
Wsecond flushing 2
Communality
L oading
Coe fficient
L oading
Coefficient
0.983
-0.123
0.759
0.974
0.928
0.896
0.971
-0. 324
0.790
0.958
1 .031
0.947
1 .026
0.010
-0.004
0.082
0.099
0.093
0.092
0. 100
-0 .025
0.087
0.097
0. 106
0.096
0. 105
-0.084
1 .008
0.542
-0. 100
-0.171
-0.006
0.037
0.933
0.660
-0 . 100
0.0 1 1
-0.096
-0.023
-0.034
0.375
0.200
-0.040
-0.066
-0.004
0.0 1 1
0.348
0.244
-0.040
0.002
-0.038
-0.0 1 1
0.973
1 .031
0.870
0.959
0.890
0.803
0.944
0.976
1 .060
0.928
1 .065
0.906
1 .053
" Trait code: see Table 5 . b Eige nvalue, 9 . 770; percent variation, 75 .2. cEigenvalue, 2.685; per ce nt variation, 20.7. The regression equations of PC-2 accounted for 48% of the total sums of
squares in factor scores. Standard errors of regression coefficients averaged
26% of the size of regression coefficients. Because source variation made up
82 % of the total sums of squares, the regression equations explained only 59%
( 0.59 0.48/0.82 ) of sums of squares for sources. An examination of residuals
and a test of lack-of-fit did not indicate any serious departures from the model.
The factor scores of the two PCs for a parent tree represent uncorrelated
aspects of its genotypic value. Niches for individuals are, hypothetically, func­
tions of the entire genotype, so the species edge and margin were estimated by
using equations of both PC-1 and PC-2. In the first step, the equation of PC-1
was solved for a graded series of the environmental indices. This provided the
mean genotypic value ( and by extrapolation, the mean niche and mean micro­
habitat ) for each point in the series of indices. In the second step, the mis­
match of microhabitats and niches was calculated for each point in the graded
series. This was done by comparing the distribution of microhabitats for each
point with the distribution of individual niches in the edgemost deme of the
central population of Douglas-fir. The same steps were then followed using the
equations of PC-2. Finally, the combined mismatch of niches and microhabi­
tats was calculated for each step in the graded series. The mismatch (M) ranged
from zero to one, with zero representing the central population, and one rep­
resenting the predicted edge of the species.
=
23
TABLE 7
Regression analyses of factor scores from principal components
Variable'
Partial
coefficient
E
LD
VE'
DE'
ED
OV'
EL
D
DO
CONST
Variable'
Principal component 1
Significance
P< . . .
Standard
Partial
coefficient
coefficient
0.5470E-01
0.002
33.53
0.8847E-01
0.000
39.44
0.6821E-10
0.000
0.46
- 0.6983E-08
0.000
- 2.76
0.7302E-04
0.000
5.13
- 0.57441E-09
0.000
- 0.37
0.1358E-02
- 3.9728
0.5719E-04
21 .4381
Principal component 2
0.002
- 3.49
0.000
- 42 . 1 1
0.027
0.51
E
ED '
EDT
ET
DV
ED
DVO
DO
CONST
Significance
P< . . .
Standard
coefficient
0.3888E-02
0.000
4.43
0.2973E-06
0.000
4.46
0.2662E-04
0.001
1.44
-0.1832E-02
0.001
- 1 .48
0.6842E-04
0.000
2.83
- 0.6814E-04
0.000
- 8.72
- 0.1032E-06
0.000
- 3.07
0.6881E-04
0.000
1.13
2.5275
0.004
0.000
'E= elevation ( 0.3047 m ) . L = latitude in degrees. D = west to east distance from the ocean (1.6 km ) . 0 = sun exposure in minutes exposed to direct sun on 3 April. V = vertical height of the major slope ( 0.304 7 m) . T = slope ( degrees/45) . CONST = constant. Probability of lack of fit for PC-1 is 0.055; R 2 = 0.68. Probability of lack of fit for PC-2 is 0.090; R ' = 0.48. The complex pattern of predicted microhabitats and niches within the region
made straightforward mapping of M impossible. If Ms were mapped on a
mountain, for example, the M at a given point on the mountain would depend
mainly on distance from the ocean ( D ) , latitude ( L) , and elevation (E) with
minor adjustments for the lengths of the slope ( V) and shading of the point
by surrounding mountains ( 0) ( the standardized coefficients in Table 7 indi­
cate the relative importance of the different indexing variables ) . The mapping
of M on a topographic slope would require mapping each mountain and valley
individually. To help in interpretation, trends in M, therefore, are presented
graphically for a transect that extends west to east at one latitude across the
sample region ( except for one example giving transects at three latitudes ) . In
each of several graphs, each internal line represents one trend of M with depar­
ture from the ocean. The top line, common to each graph, is for a set of index
values at one extreme of the range of values found in the sample region. The
top line predicts the closest approach to the species edge found in the region.
The other lines in a graph represent the other extreme and an intermediate
value for a particular environmental index. This permits an evaluation of the
relative influence on M of the values of the different environmental indices.
The species edge ( M 1 ) is approached only in the southeastern part of the
region at the low elevations. In eastern parts of the region at low elevations, M
values decrease rapidly ( Fig. 4a ) toward the north, indicating that demes in
=
24
1 .00
0.75
c
·a
0.50
"
0.25
f
•
c
:c
=
g
:o:;
•
•0
Q.
0.00
1 .00
d
/
0.75
0.50
-
0.2 5
-
/
/ /
I /
I I
.:;;" 1 I
• /
I
"" /
I
/
/
""
- o<'/ /
___ _ _ _ _ .,..,
/
/
....... ........
.. /
/
/
0.00 +------.---.---�
64
96
1 28
1 60
Distance from ocean (km)
1 92 64
96
1 28
1 60
192
Distance from ocean (km)
Fig. 4 . Influence of the site variables of a location on the position of the location within the spe cies
margin. Potential position ranges from ze ro (within the ce ntral population ) to one (at or beyond
the spe cies edge ) . The solid top line re presents the change with distance from the ocean of loca­
tions with the following initial conditions: E=elevation (460 m) , L=latitude (42 .0 ° north lati­
tude ) , O=minutes of sun exposure (750 ) , V=vertical height of the main slope (92 0 m) , and
T = slope in degrees divided by 45 (0. 7 7 ). Subfigures indicate the independent influence on the
posi tion of: (a) latitude, (b) elevation, (c) sun e xposure, and (d) slope he ight.
the north are farther from the species edge. In western parts, the "distance" of
demes from the edge does not change much from north to south. In western
parts, conditions for Douglas-fir are neither as severe as in the southeast nor
as mild as in the northeast. In all parts of the region, an increase in elevation
to 920 m means a steady retreat from the species edge ( Fig. 4b ) .
For environmental indices other than elevation and latitude, the largest
effects are shown in the western half of the region. In the west, demes are
nearer the species center if they are from areas with smaller amounts of sun
exposure ( Fig. 4c ) , or on mountains with shorter slopes ( Fig. 4d) , or on less
steep slopes ( not shown ) .
The closest approach to the species edge ( the top line, Fig. 4 ) represents a
prediction at the extreme end of the range of all environmental indices. Other
lines also reflect the extreme of all indices except the one being compared. Such
a combination of conditions will be rarely found in southwest Oregon. Changes
25
i n environment usually will occur along several environmental gradients
simultaneously, rather than along just one, and departure from the species
edge will be farther than shown in the separate graphs. Therefore, contrary to
the impression given by the transects in the figures, most of southwest Oregon
is predicted to be within the central population of Douglas-fir. Most of the part
outside the central population is in the inner half of the margin ( M < 0.5 ) .
Even in the southeast quarter of the region, the area near the species edge
probably is not large.
Douglas-fir at elevations < 915 m in southwest Oregon is apparently limited
because the majority of niches of individual trees require more moisture than
is available during parts of the growing season. Moisture is implicated because
the proximity of demes to the species edge mirrors precipitation gradients from
north to south, from west to east, and from high elevation to low elevation
within the region. Sun exposure magnifies the importance of moisture defi­
ciency. In the southwest quarter of the region, demes with less sun exposure
( lower 0) are farther from the species edge ( Fig. 4c ) . At low elevations in the
southeast quarter, moisture is apparently so critical that differences of sun
exposure have little effect on the place of the deme - all demes are near the
species edge.
Comparison of results of the cover-dominance and niche-habitat models
Neither of the models can be used to confirm a relationship between the
predicted and "actual" edge of the species range. Historically, it has been nec­
essary to rely on the presence or absence of individuals to indicate the edge. In
settled regions, however, human intervention can make presence or absence in
any specific area largely accidental. Also, in any region, the edge is likely to be
dynamic; changing climatic trends can alter conditions of the microhabitats
from year to year.
The relevance of the models is affirmed if they are consistent in their pre­
dictions with respect to the species margin; i.e., if they agree whether a stand
is within the central population or near the species edge. The models are based
on two unrelated sets of sampling points and data and consequently provide
independent evidence about the margin. Both models indicated that the closest
proximity to the species edge is found at low elevations in the southeastern
part of southwest Oregon. Unfortunately, the estimated limits of the species
cannot be compared directly because several of the significant indices of envi­
ronment were different in the two models.
As partial check of the agreement of models, predictions were made from
two sets of 21 stands. The sets were made up from stands that had been sam­
pled by the 251 low-elevation cover plots. In the first set, the stands were of
high basal area per hectare and consisted mainly of Douglas-fir. These stands
hypothetically sampled the central population of Douglas-fir as it is repre­
26
TABLE S
For central and edge stands, the mean and standard deviations of the observed fac tor sc ores (PC ­
1, PC-2 ), the predicted fac tors from the c ove r-dominance model, and the predic ted mismatc h
(M) from the niche- habitat model
Central stands ( n
Douglas-fir
predominant
=
2 1 ),
Edge stands ( n 2 1 ),
Douglas-fir absent or
subordinate
=
Predic ted
mismatch index
M
PC -1
PC -2
Predicted
fac tor scores
PC-1
3.47 ± 0. 39
0 . 1 7 ± 0.35
2 .17 ± 0.45
0.09 ± 0. 1 4
0.19 ± 0.26
0.42 ± 1 .28
1 .2 9 ± 0 .45
0.34 ± 0. 31
O bse rved fac tor sc ores
Cover plots
sented in southwest Oregon. In the second set, Douglas-fir was either absent,
or it contributed very little of the total basal area. These stands hypothetically
were at the distal edge of the species margin. Factor scores of PC-1 and PC-2
were calculated from plot data to describe the cover conditions in each stand.
Also, the plot-location data were used with the cover model to predict factor
scores of PC-1 for each stand, and with the niche-habitat model to compute
the mismatch index ( M) . If, as hypothesized, stands in the first set ( central
stands ) sampled the central population, then observed factor scores and factor
scores predicted from the cover-dominance model should be large and of about
the same magnitude, and the mismatch index should be almost zero. If stands
in the second set ( edge stands ) are near the species edge, factor scores should
be almost zero and the mismatch index should be almost one.
The observed factor scores of PC-1 reflected the cover-dominance of Doug­
las-fir in central populations. The mean of the factor scores was significantly
larger (P < 0.001 ) for central stands than for edge stands ( Table 8 ) . The amount
of basal area of Douglas-fir in central stands may be associated with a smaller
number of trees than for a similar amount in edge stands; factor scores of PC­
2 were smaller in the central stands ( Table 8) , although the difference was not
significant (P 0.40 ) .
As hypothesized, when predicted values were averaged from each of the
models, the central stands had higher (P < 0.002 ) mean factor scores of PC-1
and lower mean mismatch indices than did the edge stands ( Table 8) . The
separation between the predicted means for central and edge stands was about
the same for the two models; central and edge stands were different by 25% of
the range of mean factor scores ( i.e., ( 2. 1 7 - 1.29 ) /3.47 - 0 = 0.25 ) and by 25%
of the range of possible mismatch values ( ( 0.34 - 0.09 ) /1 - 0 0.25 ) . The
positioning of means within the range of values differed for the two models.
=
=
27
Mean factor scores for edge and central stands were equally spaced around the
center of the scale ( Table 8 ) . Mean mismatch indices for the two levels of
stands were both in the lower half ( < 0.5 ) of the scale. Consequently, of the
2 1 central stands, the number predicted to be nearer to the central population
than to the species edge was 20 by the niche-habitat model and 15 by the cover
model. Of the edge stands, the numbers predicted to be nearer to the species
edge by the niche-habitat and the cover models were, respectively, 6 and 17.
The niche-habitat model suggested that many of the stands that presently do
not support Douglas-fir may be well within the species margin.
DISCUSSIO N
There is no clear way to decide which model to use. The cover model sepa­
rated edge and central classes of stands more accurately than the niche-habitat
model. Variation within classes was small, confidence limits were small, and
classes were effectively discriminated. On the other hand, predictions at spe­
cific locations could be made with greater statistical confidence with the niche­
habitat model than with the cover-dominance model. The niche-habitat model
rather precisely described the relation of genotypes to environmental indices
and with no evidence of lack of fit. The niche-habitat model also needed fewer
variables than the cover model. This decreases the complexity and uncertainty
of the model - the more predicting variables used, the greater the probability
that some will have been included by chance. The niche-habitat model pre­
dicted the relation of stands to the central population with much more accu­
racy than did the cover model. It might be concluded that it also was more
accurate in predicting the species edge, but with no verifiable "edge" to check
predictions against, the conclusion is not warranted.
There were practical reasons for delimiting the species margin, and in this
respect, the niche-variation model has some advantages over the cover-domi­
nance model. The applications discussed below are therefore based only on the
niche-habitat model. Evidence ofspecies limits based on the presence or absence
of the species is preferred intuitively to evidence of other kinds. Cover and
frequency historically have been used to indicate species dominance and veg­
etation distribution. In southern Oregon, that preference is questionable. The
region has been intensely used by humans for several generations. This may
be one reason why areas presently without Douglas-fir were predicted to be
within the margin by the niche-habitat model.
The niche-habitat model indicates that most of the forest land at lower ele­
vation ( exclusive of areas with soils derived from ultramafic parent materials )
in southwest Oregon is near or within the central population of Douglas-fir.
Even in the southeast quarter of the region, the area near the species edge is
probably not large. And most of the area apparently beyond the edge is now
28
pasture or irrigated farmland. Still, there may be a significant part of remain­
ing forest land within the species margin of Douglas-fir.
The practical reason for estimating the species margin was to indicate areas
in which regeneration and growth problems may have a large adaptive com­
ponent. Natural regeneration may be slow and unpredictable for sites where
there are many poorly adapted seedlings even in the seedlot from the indige­
nous stand. Artificial regeneration in this case may be faster and more pre­
dictable than natural regeneration, but usually this advantage is obtained at
considerable cost.
The most successful short-term planting method in southwest Oregon has
stressed careful site preparation with brush removal. If seedling establishment
is the critical aspect of adaptation in the species margin, eliminating early
competition may be the only special procedure needed. The conditions an indi­
vidual can tolerate and grow in are broader when it is not competing for
resources ( Emlen, 1973; Ricklefs, 1979 ) . Without competition, a seedling can
survive stresses that would be otherwise lethal - some of the necessary condi­
tions of its niche have been relaxed to the fundamental state. By eliminating
competition with brush and grass species, the match of niche and microhabitat
is therefore made easier.
The benefits of site preparation may not carry to older stands. As a planted
stand begins to close, growing space begins to affect the niche of a tree. Because
a tree's competitors will vary in their ability to use scarce resources, the tree's
niche ( and the microhabitat ) is affected by the spatial arrangement of other
genotypes in the plantation. Competition reduces the dimensions of the niche
from its fundamental state. As competition increases and the niche approaches
the realized state, adaptation again becomes a larger factor in growth and sur­
vival of the tree. Under the assumption that adapted trees can best utilize the
scarce resources in the margin, a uniform spacing of adapted trees throughout
the plantation should increase productivity. In artificial regeneration, it is usu­
ally assumed that a large proportion of seedlings will grow into suitable types
and that the arrangement of genotypes in the plantation is not important. This
assumption is reasonable for the species center but less so for the species mar­
gin where a high proportion of seedlings may be poorly adapted. To guard
against patchy mortality, poorly stocked stands, and low productivity per acre
within the species margin, the best-adapted trees probably should be distrib­
uted throughout the plantation.
Site preparation makes no provision for the distribution of potential crop
trees. A satisfactory distribution of productive crop trees can be promoted: ( 1 )
by increasing the proportion of seedlings adapted to the margin, and ( 2 ) by
planting more seedlings per acre. Collecting wild seed from near the species
edge is the least expensive approach to ( 1 ) but it is also probably the least
effective. Breeding is an attractive alternative because a strain better adapted
than trees native to the margin is possible. In the native stand only individuals
29
that can grow under severe stress can survive near the outer edge of the margin.
These individuals would be expected to have beneficial genes or gene combi­
nations that could be passed on to offspring to make them better adapted to
conditions in the margin. Because of the limited number of individuals adapted
to margin conditions, the population at the edge cannot replace itself without
the flow of genes or propagules from more central populations ( Emlen, 1973 ) .
Improvement in adaptation ceases in this area. Advantageous genes are appar­
ently diluted by the net influx of genes from central populations. By controlled
breeding, beneficial gene combinations in edge trees can be combined and
preserved.
Planting more seedlings per hectare increases the probability that an adapted
seedling is planted within a spacing subunit ( e.g., 3 m X 3 m ) of the hectare.
For plantations in the margin, any seedling lot hypothetically is made up of
well-adapted and poorly adapted seedlings. The allocation of such seedlings to
planting spot is random because there is presently no way to distinguish between
the two types at planting time. The number of desired crop trees determines
the average spacing of crop trees and the size of the spacing subunit. Given the
number of crop trees and the proportion of well-adapted seedlings, the planting
density can be calculated. Planting at this density will help ensure that at least
one seedling in every subunit is adapted to microhabitats that exist within the
margin.
The number of seedlings to be planted will vary depending on the location
of the plantation within the margin. Calculation of this number is useful more
as a means of indicating possibilities than as a prescription. If it is important
that crop trees are adapted, then the number of seedlings to be planted per
hectare indicates the difficulty of achieving this within the margin. The cal­
culation is also useful for suggesting factors to be considered in regenerating
the species margin and in future research. The number itself should not be
taken as a recommendation for solving regeneration problems. Adaptation is
only one item affecting regeneration success.
Predicting planting density is affected most by the proportion of poorly
adapted seedlings, which changes from one edge of the margin to the other.
Assuming that this proportion ( M ) is estimated by the mismatch of niches
and microhabitats, M increases from 0 to 1 from the central population to the
species edge. Other factors affecting the number of seedlings to be planted ( N )
are: ( 1 ) the desired number of crop trees per hectare ( C ) ; ( 2 ) the planting
success ( S = proportion surviving ) - early mortality is assumed as being ran­
dom in respect to adaptation; (3 ) the proportion thinned early for spacing ( J)
- early thinning is also assumed random; and ( 4 ) the probability that a spacing
subunit will include at least one adapted crop tree ( Q) . The probability of this
occurring is less than 1 - a reasonable upper limit of expectations is Q = 0.98.
The probability of Q is calculated as:
Q = 1 ­ B NIC
30
1 X 1 05
5 X 1 04
;
...
CJ
1 X 1 04
d
5 X 1 03
.2'
1 X 1 03
!
5 X 1 02
...
Q)
Q.
Ill
i5
1 X 1 02 L-�L-�L-�L-�����J-�
0.7 0.8 0.9 1 .0
0.2 0.3 0.4 0.5 0.6
0.0 0. 1
Position in margin (M)
Fig. 5 . Effect of positi on in the margin on the number of seedlings required to provide for spacing
of " well- adapted" crop trees. The predicted values assume a probability of 0 .98 that a spacing
subunit will include at least one adapted crop tree, and th at regeneration is very successful. Plant­
ing survival ( S ) is 90% . The number of de sired crop trees (C) per 0 .4 ha ranges from 100 to 200.
where
and
X = S ( l -j ) ( l - M )
From this relationship, the number o f seedlings required per area ( N ) is:
The required number of seedlings increases exponentially with the decrease
in proportions of adapted seedlings ( increasing M ) across the margin. Also,
the higher the expectations for the plantation the more seedlings required. A
forester planning for many crop trees ( Fig. 5 ) , or for a higher proportion of
subunits that will include adapted crop trees ( Fig. 6 ) , will plant more seedlings
per hectare. High pre-establishment mortality (1- S ' affects the distribution of
adapted seedlings in the plantation exactly as does high M. Also, thinning
before the adaptational differences among seedlings have had time to be
expressed is equivalent to mortality. Poor survival in the plantation requires
that more seedlings be planted ( Fig. 7 ) . The added number is, moreover, much
larger near the species edge ( high M ) than near the species center ( low M) .
31
1 X 1 05
j
...
5 X 1 04
1 X 1 04
I
5 X 1 03
/ / 1.
/ /
!
Ill
f
1 X 1 03
a
gS
- -o . __
5 X 1 02
_
_
-
_...
-
./ /
_... .- ""'/ /
-- -
x 1 02���-L���--L-L-����-L��L_L_�
0.0 0 . 1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 .0
Position in margin (M)
Fig. 6. Effect of position in the margin on the number of seedlings required for uniform spacing of
150 crop trees (C 1 50 ). The predicted v alue assumes successful regeneration; planting survival
(S) is 90% . The probability that a spacing subunit will include at least one adapted crop tree (Q )
i s v aried from 0 .7 8 to 0.98.
=
1 X 1 Q5 �----,
5 X 1 04
- --- s ==0.5 - - --s :-g}_ - --
-
-
-
- -
x 1 02'��������L_��J-�-L��--L-L-�
0.0 0 . 1
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1 .0
Position in margin (M)
Fig. 7. Effect of position in the margin on the number of seedlings required for uniform spacing of
150 cro p trees ( C = 150). The predicted v alues assume a probability of0.78 that a spacing subunit
will include at least one adapted crop tree (Q ). The planting success (S) varies from 50 to 90% .
32
For example, the number added to compensate for a reduction in survival from
0.9 to 0. 7 is about 2.5 times larger for M = 0. 7 than for M = 0.2 ( Fig. 7 ) .
The calculations indicate that regeneration costs are likely to expand greatly
near the species edge. In the outer edge of the margin, large numbers of crop
trees may be needed to maintain productivity because growth will be slow and
the crop trees small. In this part of the margin, adapted trees are more rare,
and consequently, the establishment of more seedlings per hectare may be nec­
essary to offset mortality and poor growth as the stand matures. Also, in the
part of the margin where successful seedling establishment ( S ) is most impor­
tant, it is most difficult. Therefore, in the outer margin, site preparation is
likely to be more expensive than in the inner margin.
The predictions do illustrate some of the advantages of the niche-habitat
model. For one, the model provides a measure of distance along a biologically
relevant gradient. The gradient is closely associated with the genetic differ­
entiation of Douglas-fir populations and thus with adaptive fitness. Because
the dominance of Douglas-fir decreases along this gradient, conditions of
reproduction, seedling establishment, growth, and survival apparently deteri­
orate along the gradient. Amelioration of these conditions ( e.g., by site prep­
aration, shading, and production of special types of planting stock ) is likely to
be more or less difficult and uncertain depending on the plantation's position
on the gradient. Regeneration and growth-enhancing treatments that suffice
in the inner half of the margin may not be cost effective in the outer half. The
model supplies a quantitative framework for the research needed to develop
regeneration prescriptions appropriate to specific segments of the gradient. It
is within the margin that experimentally based regeneration prescriptions are
most needed and yet are most difficult to provide.
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