Aust. J. Bot., 1991, 39, 283-93
Floral Biology and Reproductive Phenology of
A vicennia marina in South-eastern Australia
Peter J. ClarkeAa and Peter J. MyerscoughA
gSchool of Biological Sciences, The University of Sydney, N.S.W. 2006, Australia.
BDivision of Fisheries, CSIRO, P.O. Box 94, Vincentia, N.S.W. 2540, Australia.
Abstract
Flowering, pollination and reproductive phenology of the tree, Avicennia marina (Grey mangrove),
were examined on the south-east coast of Australia in New South Wales. Individual flowers are
protandrous and open for 2-5 days, while a flower cluster has open flowers for 24 weeks. About
16000 pollen grains and four ovules are produced per flower. Self-pollination of an individual flower
is unlikely because of protandry, but the sequence and synchrony of flowering, together with pollinator
behaviour, favour geitonogamy. Some fruit is set when cross-pollination is restricted by bagging flowers,
which indicates partial self-compatibility. Subsequently, fruit abortion is higher in the bagged treatment
than in those open-pollinated; this may reflect some pre-dispersal inbreeding depression. Between 4
and 41% of open-pollinated flower buds set fruit, most of which had one or rarely two seeds.
Phenologically, each reproductive stage is unimodal and the whole process from bud initiation to
abscission of mature fruit is completed within a year. Initiation of floral buds, flowering, growth and
abscission of fruits are almost synchronous among fecund trees at a particular latitude each year.
Latitudinal differences occur consistently among populations that are separated by less than 2° of latitude;
those at lower latitudes flower earlier. Flowering of individual trees varies greatly between years and
many trees fail to reproduce each year, although the populations remain fecund from year to year.
A flexible breeding system and regular population fecundity ensure annual propagule supply in the
populations studied.
Introduction
The grey mangrove, Avicennia marina (Forsk.) Vierh., is widespread and common
on the coasts of Australia and Asia. Despite this, its floral biology has only been
briefly described by Tomlinson (1986). The floral biology of mangroves in general has
received little attention, and Tomlinson (1986) highlights the need for quantitative and
experimental information for understanding the ecology and genetics of a group of
species that are of considerable environmental importance. This paper examines aspects
of the floral biology of A. marina var. australasica (Duke 1990a, 1991) from the central
and south coast of New South Wales. Flowering, pollen : ovule ratios and pollination
were quantitatively examined over a range of spatial and temporal scales; furthermore,
field experiments were undertaken to investigate the breeding system.
The floral phenology of Australian mangroves has been reported in general terms
by Jones (1971), Hutchings and Saenger (1987) and more comprehensively by Duke
et al. (1984), and of A. marina specifically by Duke (1990b). In this paper we describe
variation in reproductive phenology and the yearly pattern of reproduction by following
tagged reproductive shoots.
0067-1921/91/030283505.00
284
P.J. Clarke and P, J, Myerscough
Materials and Methods
Flowering
Flowering was observed at two estuaries in Jervis Bay (Cararma Creek, 35°00’S, 150°47’E and
Moona Moona Creek, 35°02’S, 149°40’E) during January 1989 and January 1990. Two trees were
randomly selected from each estuary and on each tree two flower clusters (sensu Tomlinson 1986,
see Fig. lb) were haphazardly chosen. Flower clusters were tagged and their development followed
at weekly intervals until the basal flower buds were ready to open. Thereafter, observations were made
at daily intervals. Sequential drawings of each cluster were made and the following noted: corolla
opening, anthesis, style condition, corolla abscission, calyx and bract enlargement around ovary. Any
insects visiting the flowers during our inspection were noted, and their behaviour observed.
We examined the influence of pollinators on persistence of open corollas by bagging flower buds
to exclude pollinators. The results were analysed by a 2-factor nested ANOVA; bagged and unbagged
flowers were fixed treatments, while trees were a random nested factor.
The numbers of reproductive units (flower clusters, flower buds, flowers, and fruits) were recorded
from populations in the Sydney region and at Jervis Bay, sampled as described for reproductive phenology
(see below).
Pollen and Ovule Numbers
Pollen was sampled from three populations in the Sydney region (Hawkesbury River, 33°32’S,
151°14’E; Lane Cove, 33°48’S, 151°09’E; Towra Point, 33°59’S, 151°12’E). At each population two
trees were randomly chosen and within each tree four flowers were randomly selected. The ovaries
were also dissected and ovules counted. Pollen from one anther of each flower was spread on a slide,
stained with lactophenol-cotton blue and counted under a microscope at 540× magnification.
Pollination
Pollination success was assessed by examining stigmas under a dissecting microscope at 50× magnification and counting the number of pollen grains on the stigma. Five flowers with divergent stigmatic
lobes were examined from each of two trees at three locations in the Sydney region. The results were
analysed by a 2-factor ANOV,X; locations were treated as a random factor with three levels, while trees
were nested and also treated as a random factor.
Observations of isolated trees flowering and setting fruit in the field suggest that A. marina is selfcompatible. To test this an experiment was devised to encourage self-pollination. Flowers cannot easily
be hand-pollinated to see if selfing is successful because of the naturally low fruit set and the large
number of pollinations needed. It is also not possible to emasculate flowers to test for agamospermy
because removal of anthers induces spontaneous abscission. Nylon mesh bags were used to enclose
branches with flowers and their insect life while in bud, thus minimising crossing. Bags with holes
cut in them were used as controls, and branches without bags were also marked as an open-pollination
treatment. It was thought that there would be enough insect life in the bag treatments to act as selfing
vectors, although pollination levels might be lower without the presence of honey bees. The numbers
of flower buds, flowers and fruits were recorded at approximately 3-monthly intervals. The experiment
was performed in 1989 in the Sydney region and repeated in 1990 at Jervis Bay without a bag control
but with the number of buds in each treatment increased five-fold. At each location, two populations
were selected within which two random trees were sampled; on each tree, four replicate branches were
used for each of the treatments. The results were analysed by a 3-factor hNOVA with treatments fixed,
random populations nested and random trees nested.
Reproductive Phenology
The occurrence of flower buds, flowers and stages of fruit development was observed at three locations
in the Sydney region in 1987, 1988 and 1989. Observations were also made at two locations at Jervis
Bay during 1989 and 1990. At each site, two trees were randomly chosen from two patches. On each
tree in the Sydney region 10 reproductive shoots were tagged, whereas five shoots were tagged on
each tree at Jervis Bay. On each reproductive shoot the numbers of flower buds, flowers and fruits
were recorded at regular intervals. Each year a different set of randomly chosen reproductive trees
was tagged.
This type of census differs from littertrap collections (cf. Duke 1990b) because it more directly
Floral Biology of Avicennia marina
285
estimates the dates of first and last occurrence of a given reproductive stage, and the date when each
stage peaks in abundance (Primack 1985). Provided that the census is taken at regular intervals the
date of peak abundance of a stage can be estimated for each population and year observed. This
allows the synchrony of reproductive stages to be compared between and within populations. Such
censuses also reveal the fate of reproductive units, although this will not be reported here.
Yearly Reproductive Status
The reproductive status of permanently marked trees was assessed in the Sydney region during
1987, 1988, 1989 and 1990. At each of the three populations, four reproductive trees were haphazardly
chosen from two patches 500m apart in 1987. The presence of flower buds and the relative size of
the fruit crops were noted on the same trees each year.
Fig. 1. Flower, inflorescence and infructescence morphology of .4. marina in New South Wales.
(a) Floral shoot, (b) flower cluster, (c) flower bud, (d) ’male’ stage, (e) ’female’ stage, (/3 young
fruit, (g) mature fruits. Flower sections, scale = 5 mm; flower cluster, scale = 8 mm; habit
and fruit, scale = 40 mm.
286
P.J. Clarke and P. J. Myerscough
40
Fig. 2. Frequency histogram for
the number of flower clusters
found in reproductive leaf axils
over all years and locations.
1
2
3
4
5
Number of flower clusters / leaf axil
Results
Flowering
Tomlinson (1986) describes the characteristic inflorescence of Avicennia as a panicle
that ends in a basic unit he described as a flower cluster (Fig. la). Some authors have
referred to the basic unit as a ’cymose inflorescence’ but in this study it is called a
flower cluster because the terminal flower does not open first (Fig. lb). In A. marina
there are usually three terminal or axillary flower clusters, although the number can
range from 1 to 6 (Fig. 2). Each cluster consists of 1-14 decussately arranged flower
buds in a capitate unit (Figs lb and 3a), the mean number of buds found on a cluster
was four for all populations and years sampled. Flower buds were often eaten by larvae
of a moth; these larvae hollow the stem of the flower cluster and enter the buds via
the pedicel. After taking into account the losses due to the activity of these larvae
and bud abortions, the numbers of buds formed always exceeds the numbers that develop
fully and flower (of. Fig. 3a, b).
Table 1. Flowering statistics ~or A vicennia marina in Jervis Bay
Flower buds/cluster
Flowers/cluster
Period (days) with open and attached
corollas in:
Individual flowers unbagged
Individual flowers bagged
A flower cluster
Mean
Standard error
7.7
6.0
0.6
0.6
8
8
6-10
3-8
3’7
3"8
27
0’2
0.2
5’2
24
24
8
2-5
27
10-31
No. of samples
Range
In the flower cluster the basal pair of buds is the first to open, followed acropetally
by the next pair, but only after the corolla has abscised from the pair below. The
flowers are sweetly scented and the yellow-orange corolla tube produces a nectar-like
secretion toward the base. The number of flowers opening in a flower cluster ranged
from 0 to 10 with a mean of two for all years and populations sampled (Fig. 3b).
It takes 10-30 days for a cluster to complete flowering, whereas an individual flower
retains an open corolla for 2-5 days (Table 1). The period did not differ between the
samples or change when pollinators were excluded (ANOVA, F~,40 = 0"2, P > 0" 1).
Floral Biology of Avicennia marina
287
(a)
40-
o
o
1
23
4 5 6 7 8 9 10
11 12
13 14
Number of flower buds / flower cluster
(b)
50-
40,
.> 20 ¯
10"
0
01
2345678
9 10
Number of flowers opening / flower cluster
Fig. 3. Frequency histogram for (a) the number of flower buds found on
a flower cluster pooled for all years and locations and (b) the number of
flowers opening on a flower cluster pooled for all years and locations.
The flowers of A. marina are protandrous (Fig. ld, e). The anthers dehisce within
a day of opening, and the pollen remains on the anther or on the corolla as a sticky
unit. The following day, the stigmatic lobes diverge (Fig. le) and appear receptive for
a further day or so. When the stigma shrivels, the corolla tube abscises and the sepals
and bracts enlarge to surround the ovary; the bracts persist at the base of the fruit
until it drops (Fig. l f). Fruits usually consist of a single embryo surrounded by a thin
pericarp, but occasionally two or even three embryos form. Fruits that mature to a
viable stage are invariably restricted to the base of the cluster where often only one
fruit is held; as the fruit increases in weight the infructescence becomes somewhat
pendulous (Fig. lg).
288
P.J. Clarke and P. J. Myerscough
Pollen and Ovule Numbers
Pollen numbers did not vary significantly among samples from trees or populations
(ANOVA, F2,27 = 2"8, P > 0"05). We estimate that each flower produces 16000 pollen
grains, of which about 3% were deformed or lacked cytoplasm and appeared inviable.
All flowers examined had four ovules and they all appeared to be healthy and viable.
Pollination
Numerous potential pollinators were observed visiting flowers of A. marina: they
include ants, wasps, bugs (Lygaeidae, Miridae), flies (Cecidomyiidae), bee flies, cantherid
beetles and moths (Pyralidae). However, the most common visitor was the honey bee,
Apis mellifera, which is apparently attracted to the nectar-like secretion found toward
the base of the corolla tube. The pollen is displayed on the anther and occasionally
falls as a sticky mass onto the corolla lobe; the sticky cluster appears to be transported
intact by insects. Pollination is apparently highly successful, as over 95% of receptive
stigmas exhibited pollen. However, the mean number of pollen grains found on each
stigma (9) is less than 1% of anther output. The mean number did not differ among
trees (ANOVA, Fl,26 = 0"7, P > 0"5) or among the populations sampled (ANOVA, F2,26 =
2.0, P ~ 0"1).
Table 2. The proportion (as %) of fruits set for bagged, control and open treatments
Location
Bagged
Mean
s.e.
Treatment
Control
Mean
s.e.
Open
Mean
Sydney region
Site 1
Young fruit
Mature fruit
Site 2
Young fruit
Mature fruit
Site 1
Young fruit
Mature fruit
Site 2
Young fruit
Mature fruit
38.0
2.0
6.3
1,0
2.0
0.4
1-3
0.4
7.7
0’ 1
2.1
0’ 1
3.7
0
0’9
0
31.0
1.2
9.5
I. 1
41.2
4.3
10.0
2-1
1.2
1-3
3.7
1.7
1.2
0’8
---
---
6.1
1.0
1.6
0.4
---
---
6.3
1.9
1.8
0.8
3,4
2.1
Jervis Bay region
No significant differences were detected in the numbers of fruit set among the nested
factors for the pollination experiment, so these factors were pooled and the treatment
factor was tested over pooled mean square. No significant differences were detected
among the bagged, control and unbagged treatments in the number of immature fruits
set in either of the repeated experiments (ANOVA a, F2,44 = 0.6, P > 0"1; ANOVA b,
F1,29 = 2"5, P ~ 0"1) (Table2). Open-pollination resulted in 4-41% of open flowers
setting fruit, although this was further reduced by the time fruits were mature. In both
experiments there appear to be fewer mature fruits produced from the bagged treatments
(Table 2), although significant differences in the number of fruits maturing were only
detected at Jervis Bay (F1,29 = 6" 1, P < 0.05). In all cases the number of ovules producing
embryos was one, although as previously mentioned, two embryos occasionally form
and in one case three were observed.
Floral Biology of Avicennia marina
289
Buds
S 1987
S 1988 I~
S 1989
J 1989
Flowering
$1987
1988
$1989
1989
Mature fruitfall
Young fruits
1987
1988
1989
1989
o
8
4
12
16 20
24 28
32 36 40 44 48 52
Weeks of calendar year
Fig. 4. Reproductive phenology for pooled trees and populations in the Sydney region
(S) over 3 years of observation and Jervis Bay (J) for 1989, The modal date in the occurrence
of each reproductive event is shown as a heavy vertical bar, 50% confidence limits shown
as a box and the range as a horizontal line.
TabLe 3. Summary statistics for the timing of flower bud, flower and immature fruit presence
Values are the number of weeks from the beginning of the calendar year for the appearance of a reproductive unit.
HR, Hawkesbury River; LC, Lane Cove; TP, Towra Point; MM, Moona Moona Creek; CC, Cararma Creek
Year and
location
1987
1988
1989
1989
1990
HR
LC
TP
HR
LC
TP
HR
LC
TP
MM
CC
MM
CC
Mean
5.6
7.1
6.2
5.3
5.7
5.3
4.4
5.4
5.0
6-2
6.6
9.2
8.5
Developed buds
Mode
Range
3
6
6
3
3
3
3
3
3
6
6
6
6
3-16
3-24
3-16
3-12
3-12
3-12
3-16
3-16
3-16
6-14
6-14
6-30
6-18
Mean
9.5
11-7
11.0
8.3
9.1
8.5
7.8
8.7
9.6
10.9
9.6
16.2
15.5
Open flowers
Mode
Range
12
12
12
9
9
9
6
6
9
14
14
14
14
6-28
6-24
6 16
6-12
6-12
6-16
3-24
6-24
3-16
10 14
10-14
10-26
10-26
Mean
15.6
15.6
17.4
16.0
16.7
19.9
11.3
13.3
13.9
16.6
16.6
17.0
18.5
Immature fruit
Mode
Range
12
16
16
12
12
16
12
12
12
12
12
14
16
9-50
9-52
9-52
948
9-50
9-52
6~18
6-50
6-50
6-52
6-52
6-52
6-52
P.J. Clarke and P. J. Myerscough
290
Reproductive Phenology
Macroscopic flower buds can be observed on trees in the Sydney and Jervis Bay
regions during December. By January the stalks to the flower cluster have fully elongated
and the buds are sufficiently developed to be counted. Developed flower buds are present
on trees for up to 6 months, but are only abundant during January and February
(Fig. 4). Flowering begins in January and can extend until June, although most flowers
are open during February and March (Fig. 4). Immature fruits are present on trees
from the end of March, reach a peak in April and thereafter decline in numbers due
to abortion and predation (Clarke, unpublished data). Fruits grow at different rates
but the embryo is not large enough to be viable until about October. Most fully grown
fruits fall during November and abscission rarely extends beyond December (Fig. 4).
Thus, the cycle from bud initiation to fruit fall is completed in a year.
Following the abscission of fruits and stalks, a primary vegetative shoot forms in
the old cluster axis. Shoots take at least 2 years to become reproductive again. The
modal date in the seasonal occurrence of each reproductive stage differs among years,
populations and regions but not among trees within populations. The modal date for
the presence of flower buds varies between regions, populations and years by no more
than a few weeks in the Sydney region (Table 3), with the most northerly site at the
Hawkesbury River consistently developing buds and opening flowers sooner than other
populations (Table 3). Flowering in all populations of trees extends over several months
and is synchronous among trees within populations. The number of flowers opening
each day is initially small, but increases rapidly, with a peak mass flowering for a
few weeks, followed by a prolonged decline (Fig. 5). Differences in the starting dates
and modal dates of flowering follow the same latitudinal pattern as bud initiation (Table 3,
Fig. 5).
60
~ 40
~
LL
Fig. 5. Mean number of flowers
open on shoots in 1989:
Iq, Hawkesbury River trees;
Q), Lane Cover River trees;
A, Towra Point trees.
20 I~
100
,
0
4
8
12
16
20
24
28
Calendar week
The length of time before mature fruits abscise differs among populations and years.
Most fruits in the Sydney region are not fully developed until November, although
in some years this can be delayed until December. Trees at the Hawkesbury River
site (the most northern) consistently drop fruit in late October, before those at Lane
Cove River and Towra Point. They are followed by trees in the Jervis Bay region,
which produce ripe fruit in late November and during December.
Yearly Reproductive Status
A census of trees over 4 years showed considerable variation in the reproductive
status of trees (Fig. 6). Of the 24 trees followed, only six flowered every year. Some
Floral Biology of Avicennia marina
291
trees flower and fruit each year, but those with complete canopy crops did not produce
another large crop the following year. A similar pattern was observed within a tree
where fruit is produced on one branch and in the following year heavy flowering shifts
to another branch. These observations suggest that the ability to produce flower buds
is limited by the number of shoot axes taken up by flowers the previous year. Observations
of tree populations in each location indicate that there is some stand synchrony, i.e.
localised masting in flowering and fruiting from year to year. This rarely extends to
the whole population as stands on different sides of a bay or a river can flower abundantly
in alternate years.
100 -
90 []
[]
[]
80 ~
70’
Hawkesbun/River
Lane Cove River
Botany Bay
40’
20.
10’
o
1987
1988
1989
1990
Fig. 6. Variation in reproductive status of trees repeatedly observed over 4 years;
n = 8 for each site.
Discussion
Protandry and the short duration of individual flowers in A. marina are characters
shared by other species of mangrove. Primack (1985) found that 3.3 days was the
mean period over which individual mangrove flowers are open in tropical Australia,
which is intermediate between tropical forest species (1-3 days) and temperate forests
(1-14 days). Primack et al. (1981) suggest that protandry promotes outcrossing in
mangroves, and that insect pollination facilitates it. Pollen: ovule ratios found in
A. marina are more typical of the wind-pollinated mangrove species of Rhizophora
(Tomlinson et al. 1979), although Sonneratia alba, a moth-pollinated mangrove, has
similar pollen: ovule ratio (Primack et al. 1981). According to Cruden (1977), such
high pollen : ovule ratios indicate a relatively inefficient pollination system and an outbreeding strategy more commonly found in low-disturbance communities. While
A. marina is protandrous and pollen : ovule ratios are high, the timing of anthesis, massflowering, and the visiting behaviour of pollinators would make pollen transfer within
a plant likely. Apparently some of these geitonogamous pollinations would succeed
because the results of the bagging experiment suggest that this species is self-compatible.
However, without emasculation to test for agamospermy and artificial self-pollinations,
the results are not conclusive.
An interesting trend in the results of the bagging experiment is that more fruit matured
on inflorescences open to cross-pollination. This possibly indicates some inbreeding
depression resulting in the premature loss of fruit. Primack et al. (1981) suggested
that geitonogamy in coastal colonising plants would allow some fruit set in isolated
colonising plants, and thereafter the proportion of such pollinations would decline as
pollen is transferred between plants. Pollen transfer between plants in such situations
would still result in sibling mating. However, this is counteracted in A. marina by dispersal
292
P.J. Clarke and P. J. Myerscough
of propagules, canopy suppression of seedlings and irregular yearly flowering among
trees in close proximity.
Duke’s (1990b) study of latitudinal variation in flowering and fruiting of A. marina
from litterfall data over 15 months in 1982-83 gave broadly similar results to ours
for the same latitudinal station at Botany Bay. A latitudinal trend along the NSW
coast is evident in our results: the northernmost population flowered 2-3 weeks earlier
than the population some 200 km further south. Duke (1990b) correlated such differences
with various climatic variables, and found that mean daily temperature correlated with
development time to flowering and to fruiting. The differences in temperature factors
between the sites in the present study are very small, which suggests that either A. marina
is very sensitive to some temperature variable or there is some other latitudinal factor
influencing flowering. Latitudinal variation in the period from anthesis to the fall of
propagules is present in the Rhizophoraceae (Duke et al. 1984) and in A. marina (Duke
et al. 1984; Duke 1990b). Above 19°S this developmental period is about 2 months,
whereas in the Sydney region it is 7-8 months. Duke et al. (1984) suggest that propagules
maturing in the tropics are released at a time most favourable for their development.
On the south-eastern coast of Australia, propagules of A. marina fall at a time when
temperatures are optimal for growth and development of seedlings.
Although reproductive events are relatively synchronous among trees at a particular
latitude, and this is consistent among years, the reproductive status of individual trees
is highly variable between years. Stands will switch synchronously from a reproductive
¯ to a non-reproductive state but this does not extend to whole populations in an estuary.
Such a patchy flowering pattern may promote outbreeding or simply reflect changes
in sediment resource availability. Finally, the proximal outcome of a flexible breeding
mechanism and regular reproduction in the population is that there is an annual supply
of propagules that forms the basis for expanding or maintaining populations.
Acknowledgments
We thank John Clarke for field assistance in the Sydney region and Lani Retter "
for assistance at Jervis Bay. Michael Cole kindly allowed us access to his unpublished
work on the growth of Avicennia. Tony Martin and Murray Henwood provided valuable
comments on a draft of the manuscript. David Mackay transformed rough sketches
into fine illustrations. The New South Wales National Parks and Wildlife Service gave
us access to the Towra Point Nature Reserve. The Department of Defence supported
studies at Jervis Bay as a part of the CSIRO Baseline Studies of Jervis Bay.
References
Cruden, R. W. (1977). Pbllen-ovule ratios: a conservative indicator of breeding systems in flowering
plants. Evolution 31, 32-46.
Duke, N. C. (1990a). Morphological variation in the mangrove genus Avicennia in Australasia: systematic
and ecological considerations. Australian Journal of Systematic Botany 3, 221-39.
Duke, N. C. (1990b). Phenological trends with latitude in the mangrove tree Avicennia marina. Journal
of Ecology 78, 113-33.
Duke, N. C. (1991). A systematic revision of the mangrove genus Avicennia (Avicenniaceae) in Australasia.
Australian Journal of Systematic Botany 4, 299-324.
Duke, N. C., Bunt, J. S., and Williams, W. T. (1984). Observations on the floral and vegetative phenologies
of north-eastern Australian mangroves. Australian Journal of Botany 32, 87-99.
Hutchings, P., and Saenger, P. (1987). ’Ecology of Mangroves.’ (University of Queensland Press: St
Lucia.)
Jones, W. T. (1971). The field identification and distribution of mangroves in eastern Australia.
Queensland Naturalist 20, 35-51.
Floral Biology of Avicennia marina
293
Primack, R. B. (1985). Patterns of flowering phenology in communities, populations, individuals, and
single flowers. In ’The Population Structure of Vegetation’. (Ed. J. White.) pp. 571-94. (Dr W.
Junk: Dordrecht.)
Primack, R. B., Duke, N. C., and Tomlinson, P. B. (1981). Floral morphology in relation to pollination
ecology in five Queensland coastal plants. Austrobaileya 1, 346-55.
Tomlinson, P. B. (1986). ’The Botany of Mangroves.’ (Cambridge University Press: Cambridge.)
Tomlinson, P. B., Primack, R. B., and Bunt, J. S. (1979). Preliminary observations on floral biology
in the mangrove Rhizophoraceae. Biotropica 11, 256-77.
Manuscript received 4 March 1991, accepted 30 April 1991