The Relative Importance of Snow Avalanche Disturbance and Thinning on Canopy PlantPopulationsAuthor(s): E. A. JohnsonSource: Ecology, Vol. 68, No. 1 (Feb., 1987), pp. 43-53Published by: Ecological Society of AmericaStable URL: http://www.jstor.org/stable/1938803Accessed: 30/12/2008 13:53

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Ecology, 68(1), 1987, pp. 43-53 ? 1987 by the Ecological Society of America

THE RELATIVE IMPORTANCE OF SNOW AVALANCHE

DISTURBANCE AND THINNING ON CANOPY

PLANT POPULATIONS1

E. A. JOHNSON Department of Biology and Kananaskis Centre for Environmental Research, University of Calgary,

Calgary, Alberta T2N 1N4, Canada

Abstract. Snow avalanche return intervals on two avalanche paths in the southern Canadian Rockies were estimated from scarred trees and shrubs. The interval between avalanches increased exponentially down each path. The tree and shrub diameters at which avalanches could cause breakage were predicted using both the mechanics of large deflec- tions in tapered beams and the resulting stem bending stress, and these predictions were confirmed by comparison to actual diameters at breakage on avalanche paths. Lodgepole pine (Pinus contorta) and Engelmann spruce (Picea engelmannii) bend when small, but were broken by avalanches when larger than ~6 cm in diameter at the base. Glandular birch (Betula glandulosa) and willow (Salix glauca) never grew large enough to break. Breakage was influenced by size rather than wood elasticity or strength. Information on thinning mortality was reconstructed from live and dead stems in two Engelmann spruce populations and one lodgepole pine population. Dead trees were cross-dated, using ring widths, to determine time of death. Avalanche mortality of trees was more important than thinning mortality when the average interval between avalanches was < 150 yr. The shift from shrub- to tree-dominated growth habit down the avalanche path occurred when the average interval between avalanches was less than 15 to 20 yr.

Key words: avalanche frequency; bending stress; Betula glandulosa; disturbance; mechanical strength; mortality; Picea engelmannii; Pinus contorta; plant populations; Rocky Mountains; Salix glauca; snow avalanches; thinning.

Introduction

Natural disturbances are postulated to be one of the

important forces driving population and community dynamics (Wiens 1977, Paine 1979, White 1979, Oliv- er 1981). Evaluation of this assertion requires knowl-

edge of the frequency and magnitude of disturbance and how the force of disturbance affects the extent of

damage or mortality of organisms (Levin and Paine

1974, Runkle 1982). The objective of this paper is to address the questions: what is the chance that trees and shrubs will be broken when they are growing at a cer- tain place on a snow avalanche path, and how does the chance of mortality from avalanche compare to mor?

tality from thinning? The study was conducted in the Kananaskis Valley, a major north-south valley in the southern Canadian Rockies of Alberta (Johnson et al.

1985). Snow avalanches are driven by gravity acting on a

snow mass and are resisted by snow and air friction, ploughing, and drag (Voellmy 1955, Mellor 1968, Leaf and Martinelli 1977, Perla 1980). The number of times a section of slope is overrun by avalanches is best de- termined by the age of the scars left on the trees and shrubs growing in the avalanche's path (Burrows and Burrows 1976). Snow avalanches are believed to create

1 Manuscript received 4 June 1985; revised 22 January 1986; accepted 5 February 1986.

a continuum of average avalanche return times (return time = 1/avalanche frequency), with the bottoms of

avalanche-prone slopes being overrun by avalanches

only at long intervals (Perla 1980). In Alberta, the vege? tation in these extreme runout positions consists pre- dominantly of forests of lodgepole pine (Pinus contorta London var. latifolia Engelm.) and Engelmann spruce (Picea engelmannii Parry). The vegetation at the tops of avalanche-prone slopes, where avalanches occur very frequently, usually has a 1.5-m canopy of glandular birch (Betula glandulosa Michx.) and willow (Salix glauca L.). Saplings and broken small trees of Engel? mann spruce and lodgepole pine occur in this shrub

canopy, but never reach a height much greater than the shrub canopy before being broken, permanently bent, or uprooted. The shrubs are rarely if ever broken

by the avalanches. Subalpine fir (Abies lasiocarpa [Hook.] Nutt.) also occurs in the paths at higher ele? vations.

In this study, avalanche frequency for different slope positions was estimated from avalanche-scarred trees and shrubs. Next, a model for the mechanical basis of avalanche-induced stem bending and breakage pre- dicted the diameter at which breakage would start. This

prediction was validated using the observed breakage pattern. Finally, thinning mortality was estimated in two spruce populations and one pine population, and

comparisons to avalanche mortality were made.

44 E. A. JOHNSON Ecology, Vol. 68, No. 1

Fig. 1. Avalanche paths in Kananaskis Valley.

Previous studies of avalanche frequencies (Potter 1969, Butler 1979, Carrara 1979, Johnson et al. 1985) have not determined the decrease in frequency at dif? ferent slope positions, but have instead determined the

frequency only on the extreme runouts. Understanding the decrease in avalanche frequency down a path re-

quires that the slope position be related to avalanche

dynamics so that comparisons between avalanche paths can be made. My study compared two paths that were

reasonably similar in path form but differed in steep- ness.

In developing a mechanical model of tree breakage by snow avalanches, I incorporated the assumptions that tree boles are tapered and that both trees and shrubs are significantly bent before breakage. This ap- proach differs from that of Mears (1975), who used

large broken trees in extreme avalanche runouts to estimate the velocity and impact pressure of the ava? lanche.

Study Area

The upper Kananaskis River Watershed contains >250 recognizable snow avalanche paths (Gardner et al. 1983, Johnson et al. 1985). The two paths used in this study are located on the east slope of Mt. Lawson

adjacent to the Kananaskis River (115?10' N, 50?47'

W). Both paths are vegetated except for the steep scree back walls of the catchments (Fig. 1). The paths have

(1) monotonically decreasing slopes with single catch?

ments, where snow collects and from which it breaks

away when an avalanche begins; (2) unconfined tracks where the speed of the avalanche may increase, de?

crease, or stay constant but the snow mass remains

relatively constant; and (3) well-defined runout zones at the bottom of the path where the snow mass deceler- ates and stops (cf. Perla and Martinelli 1976). The

average slope angles were 24? and 26? (cf. definition of Johnson et al. 1985), and the path lengths from the middle of the catchments to the furthest identified run? out were 1140 and 2040 m, respectively.

Avalanches start to occur on these paths in Decem- ber and are possible through early June. Dry-snow av-

alanches predominate from approximately December to the end of February and early March, due to the cold continental polar air masses, which result in low-

density snow. Mixed and wet-snow avalanches are ex?

pected after early March, when Maritime Pacific air masses bring periods of large wet snowfalls (Janz 1976). Chinooks (Foehns) are frequent during the winter

(Longley 1967) and melt the surface snow which, after

re-freezing, creates planes in the snowpack along which

shearing may occur. Early and midwinter snow release is often along zones of granular snow or hoarfrost crys- tals near the snow pack base. Late winter and spring snow release usually occurs when the whole snowpack is near 0?C.

Avalanches are mostly surface slides, eroding the

ground only rarely. Stone lines (Rapp 1960) set out on the two paths in 1979 showed no disturbance after

being overrun by at least three avalanches. These paths are well vegetated throughout their length. High-ele- vation paths above tree line and on scree-covered slopes do show signs of erosion (Luckman 1978, Gardner

1983).

Methods

Dating avalanche events

The recognition of an avalanche event depends on not confusing it with other causes of the same kind of

damage (Burrows and Burrows 1976, Shoder 1977). Systematic observations were made of avalanche dam?

age on paths during summers following winters when avalanches occurred, and comparisons were made with

damage occurring from other causes, e.g., bears, por- cupines, falling trees, wind, ice storms, soil creep, fire, and frost cracks.

Not all avalanche injuries to trees and shrubs were

equally useful in identifying the annual ring corre-

sponding to the year in which the event occurred. Im-

pact scars on the avalanche-exposed trunk and branch- es were the most reliable evidence of avalanches. They were reasonably easy to differentiate from fire scars and animal damage although they could be confused with damage caused by falling trees. Avalanche impact scars were found everywhere within the flow height of the avalanches. Very old scars were often completely overgrown, leaving only a thin-line scar (which could be differentiated from a frost crack by its short length). Impact scars, except in very badly damaged specimens, also gave the best identification of events occurring in successive years.

Other evidence frequently gave unreliable dates of avalanche events. The ring responses caused by growth release of trees and shrubs from overstory shading and

by plagiotropic shoots or dormant buds released by broken terminal stems both often lag by a year or more behind the actual date of the avalanche event. Reaction wood was the most difficult to use in dating avalanches because tilted trees tend to return to vertical by redi-

recting the growth of the terminal leader; the formation

February 1987 AVALANCHES AND PLANT POPULATIONS 45

of reaction wood at the base then migrates around the stem as the tree straightens. This new reaction wood could be mistaken for evidence of another avalanche.

In identifying avalanches, impact scars were gener- ally so abundant that other less reliable indicators were not needed. If reaction wood, growth release, or broken terminals suggested an event, usually a careful search revealed scars.

No matter how accurately the evidence for avalanch? es is interpreted, the date of the event may still be in error if only ring counting is used, primarily because some growth rings may be missing on part of the stem.

Partially missing rings were particularly common in

injured and bent stems. To resolve this problem, stan? dard dendrochronological techniques (Stokes and Smi-

ley 1968, Fritts 1976) were used to establish the year of a particular annual ring as follows.

Cross sections of the whole tree or shrub were used when at all possible. Cores and wedges are very difncult to use for dating because they do not allow the whole

ring circuit to be examined and the exact start of scars, patterns of reaction wood, or growth release to be as- certained. The surface of each sample was first sanded with a mechanical sander and then finished with very fine sandpaper.

To date annual rings, we first visually noted if any rings could be seen to converge. Rings were rarely miss?

ing all the way around a disk. Next, we marked on the disk two radii, and on each radius marked decades with pin pricks. We then traced along each of the marked annual rings from one radius to the other to confirm that the decade marks corresponded. Finally, the ring widths were measured (taking into account missing rings) on both radii to the nearest 0.1 mm. These ring- width series were then compared to master ring-width indices, a process called cross-dating. Master ring-width indices for a species consisted of ring-width series of 10 to 20 trees that had been standardized by having their growth- and site-specific trends statistically re- moved (cf. Fritts 1976). Cross-dating then allowed rings to be accurately dated. It was then relatively easy to date the annual ring in which the event of interest occurred. Cross-dating was not used in all cases, but we found it useful for difncult specimens, old events, and events based on few confirming records.

Each avalanche slope was divided into segments of

relatively homogeneous slope angle. Slope angle in each

segment was measured as: 6 = arctan (VD/HD), where VD is the vertical drop in elevation and HD is the horizontal distance.

In order to produce a complete record of avalanches for a slope segment, an Event Record Plot was con- structed (modified from Shoder 1977). The record of avalanche events provided by each sampled tree or shrub was plotted: the horizontal axis showed the in- dividual trees on which scars were found and the ver? tical axis the calendar year in which each scar was formed. When all the trees or shrubs with records of scars had been plotted for a path segment, a visual

comparison of event timing was performed. Trees or shrubs whose event records were not duplicated by other plants were re-examined for errors in dating or

questionable identification. After these dating prob- lems were resolved, a master record of avalanches for a segment was compiled from the Event Record Plot.

The value of the event plot is not that it confirms the accuracy of the dates. Cross-dating presumably does that (Madany et al. 1982). The event plot is a means of evaluating the quality and quantity of evidence for an avalanche event.

Completeness and accuracy of the record for the two

paths was further checked using historical records of avalanches for the last 15 yr and maps of the extent of avalanches for the last 3 yr. In both of these paths, records of known avalanches were easily found in tree and shrub impact scars.

A valanche frequency

Frequency estimates for each path segment were cal- culated from the number of avalanche events divided

by the number of years over which avalanches could be recognized, and the frequencies were compared to the extreme-value distribution, which has been found to give the best fit to a 70-yr record of avalanches in

Roger's Pass, Alberta (Fitzharris 1981). The extreme- value distribution was also appealing because many other geophysical phenomena (e.g., flood levels, wind

gusts) fit this distribution. The data were plotted on extreme-value probability

paper, which gives a straight line when the fit to the distribution is good. Goodness of fit was tested visually using the median regression technique (Ferrill 1958). Visual testing is the only effective method for these

data, as for hydrological data (Kite 1976). Chi-square and Kolmogorov-Smirnov tests of goodness of fit are not sensitive with so few sample points.

Avalanche-induced bending and breakage

A woody plant responds to the impact of an ava? lanche by bending. If it is flexible enough, it is deflected out of the way and will be largely undamaged by the avalanche's passage. On the other hand, if the plant is

stiff, the stresses that build in the wood as it resists

bending by the avalanche may exceed the breaking strength and then the bole will break. Flexural stiffness is defined by Young's modulus of elasticity of the ma- terial (wood) and the moment of inertia. Bending stress is defined as force per unit area of the stem as it is bent;

breaking strength is the stress at which failure occurs. If the soil tensile stress on the roots is less than the

breaking strength of the bole, the plant may be up- rooted instead of broken.

A distinction is necessary between material and structural properties. Young's modulus and the mod? ulus of rupture are material properties, in this case of wood. Flexural stiffness, bending stress, and breaking stress are structural properties, which depend on a combination of material properties and the assembly

46 E. A. JOHNSON

avalanche

Ecology, Vol. 68, No. 1

deflection

moment arm

P(a) =

Fig. 2. Diagram showing a tapered tree bole (shaded area) being deflected by an avalanche. Variables are defined in Methods: Avalanche-induced Bending and Breakage.

and mass distribution of the material. The relevant structure in this case is the stem of the tree or shrub.

Breakage by bending was modeled for stems of smaller diameter. Shear is not considered to be signif? icant at these stem diameters but may be important in stems of larger diameter. The avalanche was assumed not to be armored with wood or other solid objects with impact characteristics significantly different from those of clean snow, and impact was assumed to act as a concentrated load at the center of gravity of the

plant. The center of gravity is the point at which a load will have the most effect on the vertical stability of the stem. Clearly, an avalanche does not concentrate its load at a single point but has a load distributed over the bole and canopy of a smaller plant. However, this

simplifying assumption was used because the actual

profile of avalanche loads on trees and shrubs is not understood at this time. Perla (1980) showed that even avalanche impact pressure profiles are controversial, with impact pressure peaks having been reported by different investigators to occur at the top, middle, and bottom of the flowing avalanche. As a final assumption, impact pressures in the range 10 to 300 kPa, the range of empirical measurements (Mellor 1968, Schaerer

1973, Perla 1980), were considered to always give loads

large enough to break the stems considered here.

Bending. ?The bending of a tree or shrub as it is hit

by an avalanche was treated as the large deflection of a tapered cantilever beam with load concentrated at the center of gravity (Fig. 2). The large deflection of a beam of uniform width can be written as:

dfl _ P(a - x) ds EIQ

' { }

which states that the rate of change in bending angle (6) with respect to position (s) on the beam is propor? tional to the bending moment P(a - x) and inversely proportional to the flexural stiffness (EI0). The symbol

a refers to the moment arm and x is height above

ground. The term (a - x) takes into account the short-

ening of the moment arm at large deflection. The de-

flection is the result of the avalanche load (P) pushing with a leverage of (a - x) on the beam and the beam

pushing back. The beam's ability to push back is given

by Young's modulus of elasticity (E) for the wood

multiplied by its moment of inertia I0 = 7rr4/4, where

r is the radius of a uniform circular beam.

Trees and shrubs are usually tapered towards the top rather than being beams of uniform diameter as as-

sumed in this formula for 70. This means that the top of the beam will bend more than the base. That is, the

beam does not bend with uniform curvature. To ac?

count for this behavior, the formula for I0 was modified

for a tapering diameter (cf. Kemper 1968) to calculate

I, the tapered moment of inertia:

I=I0[ks+ l]4,

k=-(rb- rt)/rhL, (2)

where I0 is now the moment of inertia at the base, rh is the radius at the base, rt is the radius at the center

of gravity, and L is the height of the beam at the center

of gravity. Following Kemper (1968), I was substituted for I0

in Eq. 1. Then, differentiating with respect to 5 and

letting dx/ds = cos 6 gives

d26_P_ cos 6_4k d6_ ~ds2~~W0 (ks + l)4 (ks+\)'ds'

Through the substitution ? = s/L, Eq. 3 becomes non- dimensional:

d26 PL2 cos e

d? EI0 [{kL)$ + l]4

_ 4(kL) d6_ (kL)? + 1

' d$

' (4)

February 1987 AVALANCHES AND PLANT POPULATIONS 47

o c

0) co

O C _co co > <

0.70|-

0.50

0.30

g 0.10

O.Oll 0.6

Average slope angle

26

-L 0.5 0.4

J. 0.3

1.67 2.0

3.33

10 20

100 0.2

c <D

"co >

O) co v- > <

CO

o c

co > co

tan 9 Fig. 3. Avalanche frequencies (average return times) as a function of slope position, plotted on extreme-value probability

paper. Slope position is defined as the tangent of the location's slope angle. Large tangents are at the top of the avalanche path and smaller tangents near the bottom. Error bars give ? 1 sem of average return times. Lines and parameters were fitted by the method of King (1971).

Eq. 4 is a nonlinear differential equation that has been solved analytically only for the nontapered case

(kL = 0) by Bisshopp and Drucker (1945). Kemper (1968) has obtained numerical solutions for the tapered cases (kL > 0) and gives graphs of these results. Kem?

per (1968) and Leiser and Kemper (1973) have vali- dated the solution using several species of trees and shrubs. The values from Eq. 4 are strictly valid only below the proportional limit where Hooke's law ap- plies. To use Kemper's graphs to determine the bend?

ing of a stem by avalanches of varying load (P), one

requires values of PL2/EI0, k, and L. The height L is defined as 39% the height of the tree (Adamovich 1975). Taper is assumed to occur uniformly from bottom to

top. Stem diameter and height are related in trees and shrubs as diameter = height^, where j3 is between 1.5 and 2.0 (McMahon 1973, McMahon and Kronauer

1976). Young's modulus was determined on a static bend?

ing machine using procedures specified by the Amer? ican Society for Testing and Materials (1984). The only modification of these methods was that the wood was collected during January and February and was kept and tested at ? 5?C to approximate the wood's con? dition at avalanche impact. Young's modulus is re? duced by low temperatures (Panshin and Zeeuw 1980).

The samples of lodgepole pine and Engelmann spruce wood used to determine Young's modulus and the modulus of rupture (see Stem Breakage, below) were collected from forests adjacent to the avalanche paths. The samples of glandular birch and willow were col? lected on the avalanche paths. The mean ? standard error for Young's modulus for lodgepole pine was 29427.8 ? 1541.3 MPa (n = 17 samples), for Engel? mann spruce 35930.3 ? 2983.9 MPa (n = 9 samples), for willow 41968.1 ? 2183.4 MPa (n = 12 samples), and for glandular birch 25048.8 ? 3223.9 MPa (n =

22 samples). Bending stress. ? The bending moment in a tree or

shrub as it is hit by an avalanche is assumed to be

greatest at the base. A stem is assumed to be free to bend to its base even though it may be imbedded in a snow layer near the base that is not involved in the avalanche. A tree or shrub counters the bending mo- ment by tension and compression forces in its stem

separated by a distance equal to or less than its di? ameter (see, e.g., Wainwright et al. 1976):

FI P(a) = ? , (5) r

where P is the applied load, F is the bending stress, / is the moment of inertia for a tapered beam defined in

Eq. 2, and r is the radius of the bole measured at the base. The bending stress at the base of the bole can be determined by solving Eq. 5 for F using the value of the moment arm (a) already obtained when estimating bending from Kemper's graphs.

Since the avalanche impact on a tree or shrub is rapid (dynamic), the actual stress and bending is twice that of static loading (Love 1906).

Stem breakage. ?The modulus of rupture gives strength in tension, since wood is weaker in tension than in compression when broken against the grain (Panshin and Zeeuw 1980), and was determined for wood at ? 5? on the static bending machine using the standard testing method (American Society for Testing and Materials 1984). If stress (F) is replaced by the modulus of rupture, Eq. 5 gives the bending moment at which the tree or shrub will break.

The mean ? standard error of the modulus of rup? ture was: for lodgepole pine, 39961.7 ? 1110.1 kPa; for Engelmann spruce, 50696.0 ? 6506.5 kPa; forwil-

low, 61884.5 ? 2815.1 kPa; and for glandular birch, 33479 ? 6139 kPa.

Age-specific avalanche mortality

The age-specific chance of being hit by at least one

avalanche, qA(x ? b), is:

qA(x~ b)= 1 - (1 - l/7)<-*-*>, (6)

48 E. A. JOHNSON Ecology, Vol. 68, No. 1

where x is the tree age, b is the age at which the tree can first break, and T is the average return time for

path location.

Age-specific thinning mortality

The mortality for trees not subject to avalanches was determined in three 100-m2 stands: two stands of En?

gelmann spruce (high and moderate density, respec- tively) and one moderate-density lodgepole pine stand. The spruce stands had developed after avalanches 60 and 80 yr BP (before present) and the pine stand had

regenerated on an avalanche path, but after a forest fire 57 yr BP.

Mortality was determined using the following field methods. All live trees were aged by ring counts, and their diameters measured. The time-since-death of dead

standing and downed stems was determined by cross-

dating the ring-width series of the dead tree to the ring- width series of the master chronologies (see Dating Avalanche Events). Careful examination was made of the duff layer to discover buried stems. Due to decom-

position, no record was available for seedlings and smaller stems dead for more than ~40 yr.

Results

A valanche frequency

Visual inspection of Fig. 3 shows that an extreme- value distribution gives a good but not excellent fit to the data. The avalanche frequencies of the upper parts of the avalanche path (higher values of tan 6) had small standard errors, while for the avalanche frequencies of the furthest runout path positions (lowest values of tan

6) no standard error could be calculated because only two avalanche events were recorded.

At the top of each of the two paths, average return interval was ~2.5 yr, but the return intervals of the two paths diverged with distance downslope. The

steeper (average 26?) path's return interval increased more slowly over a longer path length.

Avalanche-induced bending and breakage

Fig. 4 shows that small-diameter stems deflect com-

pletely at very small loads and experience smaller stress in bending. Larger diameter stems require larger loads to produce equivalent deflection, and larger stresses occur in bending at smaller deflections. The trees and shrubs have similar wood elasticity, but differ in the effect that the larger diameters (in trees) have on the flexural stiffness and moment arm (Fig. 4A). The birch never grew much bigger than 2.5 cm diameter and willow never grew much bigger than 5 cm diameter. If the shrubs were capable of getting larger, they would become subject to bending stresses similar to those on trees at that size.

By plotting the modulus of rupture and the elastic limit on the stress axes of Fig. 4A, one can predict the diameter at which breakage and non-elastic responses

should occur. It is important to remember that al-

though the modulus of rupture is the same for different diameters within a species, the loads required to bend stems of different diameter to reach this rupture stress are different (Fig. 4B). For example, the modulus of

rupture of pine at both 10 cm and 14 cm diameter is 39962 kPa, but the loads required to reach that level of bending stress are, respectively, 610 N and 1350 N, and the deflections are, respectively, 0.65 and 0.60.

Stems were considered to be completely bent when the relative deflection was >80%. Therefore, breakage was considered not to occur at deflections >80%. The

predicted diameter of breakage of both pine and spruce was ~6 cm. Birch and willow were always too small to break because they were completely bent before

reaching their breaking stress. Birch could break at ~4 cm and willow could break at ~6 cm. The accuracy of the predicted diameters at breakage in Fig. 4 was tested

by comparison to the actual breaking diameters ob- served in 78 lodgepole pine and 115 Engelmann spruce; the difference between predicted and observed was not

greater than would be expected by chance at a = .05

(chi-square test).

Age-specific avalanche mortality

The age-specific avalanche mortality (Fig. 5) in- creases at a rate dependent on the average return time or slope position (see Fig. 3). For example, for an av?

erage return time of 2.0 yr or a slope position near the

top of the path, there is a 0.50 probability of avalanche in the 1st yr after breakage can start. For an average return time of 50 yr or a slope position in the extreme runout there is a 0.50 probability of avalanche by the 34th yr after breakage can occur.

Age-specific non-avalanche mortality

Thinning mortality was found to begin in the high- density Engelmann spruce stand at ~25 to 30 yr and in the moderate-density stand at ~50 yr (Fig. 6). In the lodgepole pine stand, thinning was found to begin at ~25 yr, increase until 50 yr, and then, apparently, to decrease (Fig. 6).

Discussion

Avalanche frequency continuum

Fig. 3 shows the continuum of avalanche frequencies along two paths. Frequency does not change propor- tionally with slope position (tan 0), but as a double

exponential (the extreme-value distribution is de- scribed by a double exponential function; Gumbel

1958). The result is a very rapid change in the chance of an avalanche occurring as one moves down the path. This is particularly important in the runout zone, where small changes in slope position translate into large in- creases in the average time interval between avalanches

(Fig. 3). The actual rate of change on these paths ap- pears to be related to the average slope angle.

February 1987 AVALANCHES AND PLANT POPULATIONS

Lodgepole Pine Engelmann Spruce

49

MOR

Glandular Birch Willow

MOR

MOR

Fig. 4. (A) The predicted bending stress measured at the base of a stem as a result of being deflected (5/L; deflection 5 was measured relative to the stem's height L). The two lines for each basal diameter show one standard error above and below the mean due to the variation in Young's modulus. For glandular birch and willow, lines for all three diameters overlap. MOR = modulus of rupture; PL = proportional or elastic limit. Inset (B) shows the load required to produce a given bending stress.

50 E. A. JOHNSON Ecology, Vol. 68, No. 1

<D .c o c i? CO > CO <D c o

co CO 0)

o c CO

o 5 10 15 20 25

(Tree age) - (age at which breakage begins) [yr] Fig. 5. Age-specific mortality from an avalanche, qA(x ? b), for 11 different average return times T, which can be related

to slope position using Fig. 3. Age of the tree (x), age at which breakage becomes possible (b), and return time (T), are all in years. Any avalanche is assumed to be capable of breaking the stems considered here.

Impact pressures are not related uniquely to path position. Each path position can be expected to be crossed by avalanches with large variation in impact pressures. As this variation is due to differences in snow

density and to the avalanche's mass and drag (Perla

1980, Johnson et al. 1985), slope position is not be- lieved to contain enough information to predict the loads to be experienced.

The significance of this frequency continuum for

vegetation is that avalanches are predictable for path

Engelmann Spruce Lodgepole Pine

E CD

CD E

24

16

0 0

20 40 60 80

Age (years)

r o.i2 o E

? 0.08 "o a>

? 0.04

0.00

Density = 125 stems/] 100 m2

o k_ CD -O E

20 40 60 80

Age (years)

5 10

Diameter (cm)

0.16

? 0.12 O E .y 0.08

CD & 0.041

< 0.00

20 40 60 80

Age (years)

E CD

24

m- 16

JQ E

0 oi

5 10 15 ^0 5 10 15

Diameter (cm) Diameter (cm)

Fig. 6. The age-specific mortality from non-avalanche causes, q(x), and the current diameter distribution of Engelmann spruce (at two densities) and lodgepole pine >3 cm dbh. The empirical mortality curves (-) are supplemented by hy- pothesized seedling mortality (-).

February 1987 AVALANCHES AND PLANT POPULATIONS 51

positions. The alternative view, often implicitly held, is that avalanches are accidents, i.e., completely un-

expected. This view gives no consideration to the fact that the vegetation has experienced avalanches several times before and that its composition is shaped by, and therefore can reveal, the length of time between re- currences.

Threshold of breakage

The diameter at which breakage can occur marks an

important boundary condition for plant populations on avalanche paths. Below this diameter an individual is not at risk of death from an avalanche. Above this diameter (Fig. 5) the path position (7) determines how

long a plant can be expected to live before avalanche

breakage. The threshold for each species will also have an effect

on the growth habit of the canopy species. The thresh- olds of the paths studied here seem to be determined not by major differences in species wood strength or

elasticity (modulus of rupture or Young's modulus) but

by plant size. Pine and spruce are capable of growing to larger heights and diameters than the birch and wil?

low, which gives them a competitive advantage over the shrubs at non-avalanche locations. However, shrubs have a competitive advantage when avalanches recur more often than every 15 to 20 yr.

From Eq. 6, the probability of at least one avalanche in a year (qA) can be plotted against the path position (T) so that the curves describe the distribution of prob- abilities at which the trees can overtop the shrubs. Fig. 7 gives the distribution of qA for 15 to 20 yr, when pine and spruce would be first overtopping the shrubs. As can be seen in this graph, trees near the top of the path, where the average time interval between avalanches is

short, will always have very high probabilities of av? alanche and little chance to gain dominance over the shrubs before breakage. Trees lower on the path, where there are longer intervals between avalanches, will have lower probabilities of avalanche; this means that the trees have a better chance of overtopping and shading out the shrubs. The breakage threshold directly influ- ences the probability of overtopping, since breakage threshold is mainly dependent on plant size and not on wood properties.

Comparison of avalanche and thinning mortality

Whereas avalanches are catastrophic, affecting all individuals above the height threshold, thinning selects individuals by position in the canopy (Harper 1977). Furthermore, while avalanche probability increases with time since the last avalanche (Fig. 5), thinning is associated with a certain period in stand development (Fig. 6). The most significant difference between ava? lanche and thinning effects, however, is in the mortality probabilities. Thinning probabilities rarely get above 0.10 (Fig. 6); avalanche probabilities are >0.10 for

0 10 20 30 40

Average interval between avalanches (yr)

Fig. 7. The distribution of probabilities of at least one avalanche (qA) at the age when trees could be overtopping the shrubs; x and b as in Fig. 5.

trees 5 yr past the breakage threshold, at all slope po? sitions with average return time <35 yr, and >0.10 for trees 10 yr past the breakage threshold, at positions with average return time < 150 yr (Eq. 7). Thinning is

approximately as important as the probability of av? alanche mortality when the average avalanche return interval is 150 yr (compare Fig. 6 to Fig. 5). As shown

by Johnson et al. (1985) and confirmed in this study, average avalanche return intervals > 130 yr were never found. Therefore, path positions with a hypothetical 150-yr average avalanche return interval can be as? sumed never to experience avalanches.

We are now in a position to consider the question "What is the relative role of avalanche disturbance and

thinning competition in determining the canopy on

avalanche-prone slopes?" This is a problem of the scale of the two processes. By scale, I mean the specific eco?

logical consequences of changing the time and spatial dimensions of the disturbance and competition pro- cess. The breakage threshold and the thinning thresh? old establish the domain in time and space in which avalanche disturbance can affect the canopy for ava?

lanche-prone slopes. The breakage threshold is defined by plant size and

the mechanics of breakage in tapered beams, while the

thinning threshold is defined by plant size and density. In this study the breakage threshold gave a critical avalanche slope position of tan 0.48 (for average slope 24?) and tan 0.35 (for average slope 26?), and a return interval of 15 to 20 yr. On slope positions steeper than this critical position, or with time intervals shorter than the critical avalanche return interval, avalanche mor?

tality is always more important to trees than thinning mortality. In this study the thinning threshold occurred at slope positions of about tan 0.4 (for average slope 24?) and tan 0.26 (for average slope 26?), and a return interval of 150 yr. On slope positions not as steep as

52 E. A. JOHNSON Ecology, Vol. 68, No. 1

this critical position, or with time intervals longer than the critical avalanche return interval, avalanches do not occur. That is, these critical values give the time and space scale at which avalanches cease to be a dis? turbance factor.

For plants between the breakage and thinning thresh-

olds, there are slope positions and avalanche return times where neither avalanche nor thinning mortality has a clear ascendancy in determining the canopy growth habit. An avalanche that destroys the forest enlarges the length of the path influenced by disturbance at the

expense of thinning. In the years that follow an ava?

lanche, the trees will regrow and slowly begin the thin?

ning process, thus increasing the length of the path over which the vegetation is influenced by thinning.

ACKNOWLEDGMENTS

Several people helped in the field work: L. Hogg, M. J. Hood, T. Leonard, K. Nordin, and C. Carlson. Critical and useful comments were ofFered on the research and drafts of the paper by R. Perla, D. H. Knight, and two anonymous referees. The research was supported by the Natural Sciences and Engi- neering Research Council of Canada. The personnel of Kan? anaskis Provincial Park?J. Murphy, R. Chamney, and G. More?were always helpful.

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