Biological Journal
OJ the Linncan Socicp (1984) 23: 303-322.
With 3 figures
The selection of cleistogamy and
heteromorphic diaspores
DANIEL J. SCHOEN* AND DAVID G. LLOYD
Department of Botany, University of Canterbury, Christchurch, N e w zealand
Accepted for publication June 1983
Models for the evolution of a mixture of cleistogamous (closed, autogamous) flowers and
chasmogamous (open) flowers are described. The ‘basic’ model takes into account features
associated with cleistogamous self-pollination, including the greater economy and certainty of
cleistogamous fertilization and the inability of cleistogamous flowers to contribute pollen to the
outcrossed pollen pool. Complete cleistogamous selfing is favoured when allocation to maternal
function, fertilization rate, and viability of progeny are sufficiently greater for the cleistogamous
component, and when the resources spent on ancillary structures in cleistogamous flowers,
cleistogamous seed costs, and inbreeding depression are low. The result is discussed with respect to
the cost of sex argument and relevant ecological data. Suggestions for the apparent rarity of
cleistogamy are presented. The ‘complex habitat’ model extends the basic model to situations in
which the success of reproduction by cleistogamy or chasmogamy varies according to the
environment of the parent. In this situation, reproduction by both cleistogamy and chasomogamy is
sometimes selected. A ‘near and far dispersal’ model addresses the question of the evolution of dual
modes of dispersal, which occur in some cleistogamous and non-cleistogamous plants. A dual mode
of dispersal may evolve if a narrowly dispersed seed type is more successful in establishing at the
sites located within its dispersal range compared with a second, more widely dispersed seed type
which experiences less sib competition. The prediction is discussed with respect to data from
amphicarpic plants.
KEY WORDS:-Cleistogamy
heterogeneity.
- self-pollination - mixed strategies - amphicarpy - environmental
CONTENTS
Introduction . . . . . . . . . . . . . . . . . . .
Basic model for the evolution of cleistogamy
. . . . . . . . . . .
Parameters and assumptions . . . . . . . . . . . . . .
The basic model . . . . . . . . . . . . . . . . .
Retrieval of the cost ofsex and indirect mating costs . . . . . . . .
Comparative fertilization rates . . . . . . . . . . . . . .
Seed size and viability.
. . . . . . . . . . . . . . .
Rarity of cleistogamy as a mode of self-pollination . . . . . . . . .
The evolution of cleistogamy in heterogenous parental environments-the complex habitat
. . . . . . . . . . . . . . . . . . . .
models
Coarse-grained environments . . . . . . . . . . . . . .
Spatially fine-grained environments
. . . . . . . . . . . .
The production of two seed or other type of dispersal structures by a single parent-the
near and far dispersal models . . . . . . . . . . . . . . .
Near and far dispersal of structures with the same genetic origin
. . . . .
Near and far dispersal models for cleistogamy . . . . . . . . . .
304
305
305
306
307
308
309
309
309
310
31 1
311
312
316
* Present address: Department of Biology, McGill University, 1205 Avenue Doctcur Penfield,
Montreal, Quebec H3A IBI, Canada.
+
0024-4066/84/120303 20 t03.00/0
303
0 1984 The Linnean Society of London
304
D. J. SCHOEN AND D. G . LLOYD
Conclusions . . . . . . . . . . . . . . . . . .
Acknowledgements
. . . . . . . . . . . . . . . .
References. . . . . . . . . . . . . . . . . . .
Appendix: ESS allocation to CL and CH seeds-the progeny model for cleistogamous
plants. . . . . . . . . . . . . . . . . . . . .
.
.
.
3 19
3 19
3 19
321
INTRODUCTION
Cleistogamous (CL) flowers remain closed and are structurally modified for
autogamy. Although a few species are reported to be obligately cleistogamous
(Uphof, 1938; Lord, 1981), nearly all species with CL flowers produce distinctly
different, open (chasmogamous, CH) flowers. Occasionally, the two flower types
occur as a polymorphism, with separate CH and CL individuals (Catling,
1983). In the great majority of cleistogamous species, however, both flower types
commonly occur on the same individuals during a single flowering season. They
constitute a multiple strategy, in which two types of structures perform the same
function at the same time (Lloyd, 1983).
Cleistogamous flowers are structurally modified for self-pollination by
developmental changes, particularly a reduction in the androecium and corolla
(Lord, 1981) which takes place before the time of pollination. Moreover, the
closed flowers preclude the participation of ovules and pollen grains in open
pollination. These two factors jointly distinguish cleistogamy from the modes of
self-pollination which allow open pollination (Lloyd, 1979) and from ‘induced
selfing’. In the latter condition, closed but structurally unmodified flowers selffertilize when they are totally or partially prevented from opening by
unfavourable conditions at anthesis. Such flowers, which are behaviourally but
not structurally modified for selfing when closed, have sometimes been described
as ‘pseudocleistogamous’ (e.g. Lord, 1981). This term has been used in several
senses, however, and induced selfing should be regarded as a separate mode of
selfing rather than an incomplete expression of cleistogamy.
Although apparently less common than selfing in open flowers, cleistogamy
has been reported in 56 families (Lord, 1981). The condition is often difficult to
detect and is conceivably more widespread than is currently believed. Many of
the associated features of cleistogamy are absent from other modes of selfing. For
instance, CL flowers are often greatly reduced in size and cost of production
(Darwin, 1877; Schemske, 1978). The development of CL flowers may be
associated with specific environmental conditions, or the proportion of CL
flowers on a plant may increase under certain conditions (Langer & Wilson,
1965; Lord, 1981, 1982). The position of the CL flowers on the plant often
differs from that of the C H flowers (Darwin, 1877; Uphof, 1938). The secondary
features add substantial complexity to the study of the evolution of cleistogamy.
They are, however, important determinants of the initial selection and
maintenance of mutations promoting cleistogamy, and will be considered here
in detail.
In the models for the selection of cleistogamy that are presented below, the
fitness of two phenotypes that differ in the frequency of CL flowers are
compared in terms of the gametes contributed to adults in the next generation.
Gamete contributions are expressed in a common currency of female gamete
contributions. Our justification for this procedure rests with the premises of
Fisher (1930) and Bateman (1948) who pointed out respectively that male and
female gamete contributions are equal in the total population, and that paternal
CLEISTOCAMY AND HETEROMORPHIC DIASPORES
305
fitness is characteristically limited by the ability of an individual’s mates to
produce eggs. The selected phenotype is the one that reproduces by a strategy
such that no other phenotype with a different strategy of reproduction can
invade the population; i.e. the selected phenotype represents an evolutionarily
stable strategy or ESS (Maynard Smith, 1976). The types of inheritance for
which phenotypic models are applicable have been discussed by Lloyd (1977)
and Maynard Smith (1981).
Conditions for the evolution of cleistogamy are presented first in a ‘basic’
model which assumes that the environment is spatially homogeneous. Genetical
and ecological implications of the basic model are then discussed, together with
suggestions for the comparative rarity of cleistogamy as a mode of selfpollination. In the ‘complex habitat’ model, the basic model is extended to
situations in which the parental environment is heterogenous in such a way that
the more successful of the two types of flowers varies according to the
environment of the parent. Next, in the ‘near and far dispersal’ model, the
evolution of a phenotype producing two types of progeny with the same genetic
origin but with different dispersal characteristics is considered. Seed or fruit
from CL flowers (CL seed or fruit) may differ from seed or fruit from C H
flowers (CH seed or fruit) in size, viability, and timing and range of dispersal
(amphicarpy) (Connor & Mathews, 1977; Schoen, 1984). In some
cleistogamous species, the CL fruit is buried (Weatherwax, 1934; Koller &
Roth, 1964; McNamara & Quinn, 1977; Cheplick & Quinn, 1982). The near
and far dispersal model is subsequently modified to include some of the special
features of cleistogamy.
BASIC MODEL FOR THE EVOLUTION OF CLEISTOCAMY
Parameters and assumptions
Two phenotypes (PI and P,) co-occur in the population, and differ only with
regard to the proportion of reproductive resources allocated to C H and CL
reproduction, P,.producing more CL flowers. The values of all parameters are
assumed to remain constant in a particular phenotype. All parameters can vary
independently. Parameters affecting the fitness of the phenotypes are as follows:
is the relative frequency of P I plants.
and o2 are the proportions of the total reproductive resources allocated to
the production of open, CH flowers and seeds in P I and P, (ol > 0 , ) .
is the proportion of CL reproductive resources directly allocated to
androecia and gynoecia (i.e. as opposed to the proportion spent on
ancillary structures such as nectar, peduncles, corolla, calyx, glumes,
lodicules, etc.). do is a similar quantity for the C H component. dc and do
will be referred to as the direct reproductive allocation.
and go are the proportions of the direct CL and CH reproductive
investment allocated to maternal (gynoecial) function.
CL seeds are produced if (1 -0) = r, = d, = g, = 1, i.e. with full fruit set
and all reproductive resources allocated to CL seeds. no is the number of
CH seeds produced if o = ro = do = go = 1. If each CL seed requires more
resources to produce, then n, < no, while the opposite relation holds if a
CH seed is more costly.
D. J. SCHOEN AND D. G. LLOYD
306
X is the number of mates that any one individual has in cross-pollination, as
a maternal parent and as a paternal parent.
and r, are the rates of fertilization of CL and CH ovules (i.e. proportions
of each that are fertilized). When Y = 1, there is complete seed set. Where
r < 1, seed set is incomplete.
S is the proportion of CH ovules that are self-fertilized through competing
self-fertilization (Lloyd, 1979). The amount of pollen utilized in selfing is
negligible compared to that utilized in outcrossing.
is the degree of inbreeding depression. Although 6 may take on any value
< 1, it will usually be > 0. The relative fitnesses of outcrossed and selfed
progeny are 1 and 1-6.
and u, are the viabilities of CL and CH progeny due to factors other than
VC
inbreeding depression (see below).
P is the number of pollen grains produced per CH flower when all direct
reproductive resources are allocated to paternal function. do (1 -go) p
pollen grains are produced when proportion 1-go of the direct
reproductive resources are allocated to paternal function.
w ,and w, are the fitnesses of the two phenotypes.
rC
a
The basic model
Initially the population consists of any frequencies of P, and P, plants. The
fitness of an individual is equal to twice the gamete contributions of its progeny
derived via cleistogamy, plus twice the gamete contributions of its progeny
derived via chasmogamous selfing, plus the gamete contributions of its
maternally-derived outcrossed chasmogamous progeny, plus the gamete
contributions gained as a pollen parent in chasmogamous outcrossing. The
latter component is the product of the fitness of the plants mates’ ovule
contributions and the individual’s relative share of the pollen pool in which it
competes for its mates’ ovules. Hence, for P I :
w1
= 2(1-0,)2,0J1-6)+0,2,0,[2s(1-6)+(1
-s)]
= 2[(1 -o,)Z,u,(l -6)+0,Z,u0(l -sS)]
c0
where 5 = ncddCrc,and Z, = n,d,,gor,; i.e. 5 and
combine the effects of the
parameters that influence allocation to seed production in the CL and CH
components. Similarly, for P,:
w2
.‘.
Wz-Wi
= 2[(1 -0,)ZcU,(l -6)+0,Z,u0(l -sS)].
= 2 ( 0 ~ - 0 ~ ) [ Z o ~ , ( 1 - ~ 6 ) - Z ,-@I.
~~1
The two phenotypes have equal fitness when w 2 - w , = 0, i.e. when:
Z,U,(1 -sS) = Z,UJl -6)
(1)
Conditions favour complete chasmogamy when the left-hand side of equation
(1) is less than the right, and complete cleistogamy is favoured when the
opposite holds.
CLEISTOGAMY AND HETEROMORPHIC DIASPORES
307
Retrieval of the cost of sex and indirect mating costs
When CL and CH fertilization rates are equal (r, = To), and when viabilities
and seed production costs for CL and C H progeny are equal (v, = v,,; n, = n o ) ,
conditions for the evolution of cleistogamy become d d , (1 - 6 ) > d d o (1 -s6). I n
the absence of inbreeding depression (6 = 0) and C H self-pollination (s = 0),
cleistogamy evolves when:
dcgc
’
dogo
(2)
i.e., when the product of direct and maternal resources is larger for the C L
component. The most basic features of CL flowers are their reduced corollas and
androecia (Lord, 1981). I n plants with insect-pollinated flowers, this may be
associated with reduced indirect costs. Attractants and rewards in insectpollinated plants can constitute between 8% and 58% of the total reproductive
costs (Schemske, 1978; Lovett Doust & Harper, 1980; Lovett Doust & Cavers,
1982; Schoen, 1982; Wilken, 1982). Much of these costs could be retrieved
immediately when CL flowers are first produced, making d, > do. Likewise, in
view of the reduced androecia characteristic of many CL flowers (Lord, 1981),
it is possible that a cleistogamous mutant would have a smaller investment in
paternal function from its inception. If reallocation of these resources to
maternal function occurs, gc > go. The maximum magnitude of this effect can be
calculated by assuming that go = 0.5 (Maynard Smith, 1971) and that gc = 1.
Then (2) reduces to:
2dc > do
(3)
Cleistogamy, in this situation, has a twofold advantage which derives from the
resources saved by not producing male gametes. The consequential reallocation
of resources to maternal function could be expressed as greater seed number per
plant, or larger seeds with greater viability.
In general, the saving of male gametes in cleistogamy is dependent on the
ratio gc/go (from equation 2). It is equivalent to the retrieval of the cost (in
resources) of producing male gametes in a comparison of asexual and sexual
reproduction (Lloyd, 1980). With competing self-fertilization in open flowers,
the advantage to selfing derives from greater gene contributions by the pollen of
self-fertilizing individuals, pollen that fertilizes both selfed and outcrossed ovules
(Maynard Smith, 1978; Lloyd, 1979). This is a twofold advantage, regardless of
the paternal costs, and is equivalent to the retrieval of the (genetical) cost of
sharing genes in a comparison of asexual and sexual reproduction (Lloyd, 1980).
The contrast in how the cost of sex is retrieved in cleistogamy and chasmogamy
serves to underscore the uniqueness of cleistogamy as a mode of self-pollination,
and it demonstrates again that the costs of sex attributable to producing male
gametes (Maynard Smith, 1978) and to sharing genes (Williams, 1975) are not
interchangeable. The second point has been discussed by Triesman & Dawkins
( 1976), Lloyd ( 1980), Charlesworth ( 1980), and Harper ( 1982).
Harding & Tucker (1969) and Nagylaki (1976) pointed out that selfpollination has no selective advantage if the selfing genotypes do not contribute
to fertilizations of other members of the population. I n this situation, neither the
cost of producing male gametes nor the cost of sharing genes is retrieved. Induced
self-pollination is of this nature.
308
D. J. SCHOEN AND D. G. LLOYD
Evidence suggesting inbreeding depression in cleistogamous plants has
recently been provided by Wilken (1982) and Waller (1984). Only when
indirect and androecial costs are reduced in CL flowers and the maternal
investment is high, is the ratio d g c / d d , likely to be large enough to overcome
inbreeding depression expressed during the evolution of cleistogamy. T h e
advantages obtained from reduced paternal costs and the greater direct
reproductive allocation in CL flowers, therefore, may help to explain why CL
flowers are generally quite distinct from C H flowers on the same individual, i.e.
why CL flowers typically have reduced androecia, corollas, and nectar expenses
(Schemske, 1978; Waller, 1979; Lord, 1981).
A central and largely unanswered question pertaining to the evolution of
cleistogamy concerns by how much seed production is increased in a newly
arisen cleistogamous mutant which saves on resources normally allocated to
male gametes, attractants, and rewards. The question is not unique to the
evolution of cleistogamy, and it reoccurs when considering the establishment of
a unisexual mutant in a population of hermaphrodites (Charlesworth &
Charlesworth, 1979). Data addressing this question would be valuable.
Comparative fertilization rates
The evolution of cleistogamy is influenced by several ecological factors. The
fertilization rate of CH ovules, To,. may be less than that of CL ovules, r,. This
will favour the selection and maintenance of cleistogamy (equation 1). Data
from Amphicarpum purshii suggest that CL seed set is higher than C H seed set
(McNamara & Quinn, 1977). In Microlaena polynoda, the frequency of CH seed
set was estimated to be 0.23 compared with 0.98 for CL seed set (Schoen, 1984).
Fertilization in CL flowers requires that pollen or pollen tubes encounter the
stigma without the mediation of a pollinating agent. Either anther dehiscence
must occur and the released pollen fall directly onto the stigma, or pollen tubes
must grow out of the undehisced anthers and into the stigma (Lee et al., 1979;
Campbell, 1982). If the precocious androecial maturation characteristic of
cleistogamy is not accompanied by a floral structure that ensures fertilization
(i.e. if r, << I ) , failures or inefficiencies in seed production will result. Equation
(1) then predicts that selection of cleistogamy will be difficult.
If self-fertilization is advantageous (e.g. because of adverse environmental
conditions for cross-pollination), cleistogamy may be selected especially in
species where the separation of anthers and stigmas in open flowers might
normally prevent autogamy. A developmental pathway leading to a new type of
flower, i.e. the CL flower, may facilitate the removal of floral adaptations that
normally prevent autogamy, thereby allowing for the required large r,/r,,.
Catling (1983) provides an example from the Orchidaceae of a species in
which the rostellum prevents selfing in the CH flower. In the simplified CL
flower, however, the rostellum has been lost as an obstruction to selffertilization. The prevalence of cleistogamy in certain groups characterized by
zygomorphic corollas (e.g. Impatiens, Viola, Lamium, Lespedeza, Antirrhinum) may
indicate a role of cleistogamy in restoring selfing ability in outcrossing flowers
with spatial segregation of anthers and stigmas.
CLEISTOGAMY AND HETEROMORPHIC DIASPORES
309
Seed size and viabilit),
Dimorphic seeds with different dispersal prospects are considered below.
Here, we are concerned only with how seed size and viability of C H and CL
offspring might influence the selection of cleistogamy when both types of seed
have similar dispersal patterns. Chasmogamous and CL seeds of roughly equal
size are probably the rule, but larger CL seeds are known in Gymnharrena
micrantha, Amphicarpum purshii, Microlaena polynoda, and Danthonia spicata, while
smaller CL seeds are found in Impatiens biJlra and Viola sororia (Koller & Roth,
1964; McNamara & Quinn, 1977; Connor & Matthews, 1977; Clay, 1982;
Schemske, 1978; Solbrig, 1981; Schoen, 1984). Seed size is likely to influence
both seed number and seed viability. Equation (1) predicts that when the ratio
n,v,/n,v, > 1, cleistogamy is more likely to be favoured. Factors besides seed size,
however, may play a role in determining offspring viability. Predation rate may
be greater for one type of seed, especially if one is more conspicuous (Campbell,
1982). This may often be the case with CH seeds. The maturation of one seed
type may be less susceptible to abortion caused by withdrawal of maternal
support or by environmental stresses, particularly if the two seed types mature
at different times (e.g. Slipa leucotricha, Dyksterhuis, 1945; Microlaena polynoda,
Schoen, 1984).
Rarity of cleistogamy as a mode of self-pollination
Cleistogamy is a relatively uncommon mode of self-pollination. Most plants
that self do so with flowers that can engage in some outcrossing as paternal and
maternal parents. Why then do a few species have special flowers for selfpollination? The model suggests that an advantage is required either from the
joint effects of increased seed production by diversion of resources from the
androecium and ancillary structures, and from the increased rate of fertilization in
CL flowers. C H selfing requires only the latter, and consequently is easier to
attain in many species. Cleistogamy is expected where much indirect or
androecial expenditure can be redirected to CL seeds. The relatively frequent
occurrence of cleistogamy in the grasses (Conner, 1979), where due to wind
pollination, paternal costs are likely to be high, supports this notion. T o further
test the supposition, however, more work on paternal and indirect costs is
needed, as well as on how fertilization is achieved in CH and CL flowers.
THE EVOLUTION OF CLEISTOGAMY IN HETEROGENOUS
PARENTAL ENVIRONMENTS-THE COMPLEX HABITAT MODELS
Cleistogamous plants may experience environmental variation which
differentially influences reproductive success via cleistogamy or chasmogamy.
During the time that environmental variation affects growth or reproduction,
entire plants may experience separate environments (coarse-grained variation)
or different parts of the same plants may experience separate environments
(spatially fine-grained variation) (Levins, 1968; Lloyd, 1983). Coarse-grained
variation for cleistogamous plants might lead to differences among plants in the
relative probability of successfully producing seed via CL or C H flowers, e.g.
because of spatially varying levels of pollinator activity. Fine-grained variation
would include situations in which flowers at different positions on the plant
D. J. SCHOEN AND D. G . LLOYD
310
receive different numbers of visits or have different probabilities of maturing or
dispersing seeds. Environments, therefore, may be defined in terms of the
patterns of variation in the level of pollination service, seed predation, etc. The
effect of variation in parental environment on conditions for the evolution of
cleistogamy is analysed here by extending the basic model.
Coarse-grained environments
Consider first one type of coarse-grained situation. During one portion of the
flowering season, period A, pollinator activity is at a ‘normal’ level, while during
a second portion, period B, there is a reduction in pollinator activity, and hence
in fertilization rate of CH ovules. Pollen contribution to other CH flowers is also
reduced during period B. Specifically, during period B, the fertilization rate and
pollen contribution of individuals are reduced by p (0 < p< 1) compared with
the fertilization rate and pollen contribution during A. The relative durations of
periods A and B are (1 -y) and y ,respectively. For simplicity, it is assumed that
parameters other than the CH fertilization rate and pollen contribution remain
unchanged, and that pollen dispersed in one temporal environment is not
present in the other. If the parental environment can be assessed and the
appropriate response made (i.e. the flower type that results in the greatest fitness
gain is produced), a modification of the basic model is possible. Assume that one
phenotype, P I , always chooses the more appropriate response. In environment
A, it allocates all resources to CH reproduction, and in environment B it
allocates all resources to CL reproduction. Contrast this with a second
phenotype, P,, a partial chooser. P, allocates proportions (1 - a ) and a of the
reproductive resources to CH and CL reproduction in environment A and
proportions b and (1-b) to CH and CL in environment B. The fitness
expressions for PI and P, become:
+
{yZ,u,( 1 - 6) (1 -y)Z,u,( 1 -s6)}, and
-Y)U
y(1 -b)]Z,~il- 6) [( 1 -y)(l-
w
=2
~2
= 2 * {[(I
+
+
U)
+yb( 1 - ~)]Z,O1,-(~6))
For all values of u > 0 and b > 0, w 1 > w 2 ; therefore P, will always be more fit
than P,. The selected phenotype is one that reproduces entirely by CL when
conditions are unfavourable for CH reproduction, and entirely by CH when
conditions are favourable for CH reproduction. This pattern of ‘choosing’ the
reproductive mode according to current conditions has been suggested to be an
important adaptive feature of cleistogamy (Heslop-Harrison, 1966) and is
suggested for many cleistogamous species (Uphof, 1938; Evans, 1956; Langer
& Wilson, 1965). A variety of unfavourable conditions are correlated with CL
flower production, e.g. disturbance of the habitat (Dyksterhuis, 1945) low
temperatures (Ponomarev, 1961), low soil moisture (Brown, 1952). Campbell
et u1. (1983) list additional references.
The production by a plant of the more appropriate flower type in a given
environment depends upon its ability to assess the environment and respond
accordingly (Lloyd, 1983). In seasonally coarse-grained environments, the
appropriate response could be accomplished if development of flower type is
linked to a seasonal cue such as day length or temperature which itself is
correlated with the relative success of CH and C1 reproduction. Many
CLEISTOGAMY AND HETEROMORPHIC DIASPORES
31 1
cleistogamous plants produce CL flowers only under certain day lengths (Evans,
1956; Heslop-Harrison, 1961; Langer & Wilson, 1965) and these day lengths
may correspond with periods of pollinator paucity, as in Lamium amplexicaule
(Lord, 1982).
If plants are unable to assess environmental variation, they must react to the
average environment. In this case, the expressions for the chasmogamous
components of w , and w 2 in the basic model must be modified by the term
[( 1 -y) +y( 1 - p)] = ( 1 -y&. Given the parental environment, cleistogamy will
be selected when:
Z,oX 1 - 6)> ZOU,(1 - s6)(1 -y p)
(4)
As the degree of reduction in the CH fertilization rate and pollen contribution,
p, and relative duration of the period unfavourable for CH reproduction, y,
approach 1, cleistogamy is increasingly favoured.
Spatially jine-grained environments
This type of variation can also be accommodated by a modification of the
basic model. Here, individual plants encounter environments A and B
simultaneously, with separate portions of a plant experiencing one or the other
environment. The rate of fertilization of CH ovules and rate of pollen removal
from CH flowers are reduced in environment B. For brevity, the fitness
expressions will not be presented here. They are similar to those above, except
that with fine-grained variation the pollen produced in either environment has
access to ovules in both environments. If no assessment of the conditions is
possible, the plant again reacts to the average environment, and equation (4) is
obtained. An appropriate assessment and response by different flowers may be
possible, however, if floral primordia at different nodes are developmentally
programmed to yield different flower types (Lord, 1980). As in the coarsegrained situation, it can be shown that the most fit phenotype is the one that
always chooses the appropriate flower type at each primordium, i.e. allocates all
resources to CH in environment A and all resources to CL in environment B.
Thus, the selected phenotype is one that produces CH and CL flowers
simultaneously. This pattern of flowering is most common in cleistogamous
plants that combine CL flower production with amphicarpy (Koller & Roth,
1964; McNamara & Quinn, 1977).
In general, heterogeneity in the parental environment when combined with
the ability of plants to assess and respond appropriately, may lead to the
selection of a phenotype which reproduces both by CH and CL flowers, either
sequentially or simultaneously, depending upon the pattern of the
environmental variation. Heterogeneity and assessment, therefore, appear to be
important factors leading to the evolution and expression of cleistogamy, as CH
and CL flowers do frequently occur on the same individuals.
THE PRODUCTION OF TWO SEED OR OTHER TYPES OF DISPERSAL
STRUCTURES BY A SINGLE PARENT-THE NEAR AND FAR DISPERSAL MODELS
A feature often associated with the dimorphic flowers of cleistogamous plants
is the production of two distinct types of seed or fruit that differ in their dispersal
312
D. J. SCHOEN AND D. G . LLOYD
range (amphicarpy or heterodiaspory). Typically, the CL seed is buried beneath
the parent while the CH seed is dispersed some distance away from the parent
(Koller & Roth, 1964; McNamara & Quinn, 1977; Cheplick & Quinn, 1982).
Here we examine the evolution of cleistogamy when C H and CL seeds have
different dispersal strategies. In an investigation of multiple srategies in plants,
Lloyd (1983) considered plants in which two types of structures are dispersed
into separate environments. When the two types of progeny are both seeds,
however, it is unrealistic to expect that they do not grow in the same
environment. T o analyse this situation, Lloyd’s (1983) progeny model for
multiple strategies is modified by considering two types of diaspores that are
dispersed to differing extents. For greater simplicity and generality, the model
initially considers two types of asexually produced seeds (or two seed types both
produced through self-pollination). This eliminates the need to consider
different paternal costs, pollen dispersal distances, and probabilities of
fertilization. Subsequently, a modification of the model is introduced to adapt it
to cases where one seed type is produced in CH flowers and the other in CL
flowers.
Near and far dispersal of structures with the same genetic origin
Two types of dispersal structures, referred to as types 1 and 2, are produced
by each plant. The unit cost of type 1 structures is less than that of type 2
structures. If a plant produces only type 1 structures, it produces n , of them,
whereas if it produces only type 2 structures, it produces n,. We assume in this
case that equal amounts ofdirect resources are available for components 1 and 2
of reproduction. When an individual allocates proportions q and (1 - q ) to type
1 and 2 structures, it produces n , q and n , (1 - q ) of each, respectively.
Type 1 structures are dispersed less distance than type 2 structures. Dispersal
of type 1 structures is assumed to occur evenly throughout a limited but
continuous area so that any seed competes with seed of N , parents, including its
own ( N , 2 1). Similarly, the type 2 structures of the parent are dispersed evenly
into an area containing the type 2 structures of N, parents, where N, again
includes the parent under consideration, and N , > N , . There are x sites per
parent in which either type 1 or 2 structures can become established and grow
to maturity. All type 1 structures of the parent in question fall within the N ,
region (the inner circle in Fig. l ) , together with a proportion N , / N , , of the type
2 structures of the parent. The remaining proportion of the type 2 structures,
( N , - N , ) / N , , fall outside the N , region. The latter area will be referred to as
the outer circle (Fig. 1). There are N , x sites in the inner circle and ( N , - N , ) x
sites in the outer circle. The type 1 and 2 structures compete jointly for sites in
which to grow to maturity. Following dispersal in each generation, all sites are
assumed to be filled. Because the two types of structures may encounter the sites
at different rates, it is necessary to specify encounter rates, e l and e,, for each
(0 < e < 1).
We seek allocations to type 1 and 2 structures at which a mutant with
allocation qm and 1 - qm to the two types of structures will have a fitness equal to
the remainder of the population of ordinary phenotypes having slightly different
These allocations are found by solving
allocations q and 1-q.
d(w,-w,,)/dq, = 0 when qm = q. If the turning point of the curve is a
CLEISTOGAMY AND HETEROMORPHIC DIASPORES
313
Figure 1. Dispersal ranges of type I and 2 structures for a single parent (symbolized by an ‘X’ inside
a square). The inner circle delimits the area in which the parent’s type 1 structures fall. Within this
area also fall the type 1 structures of N , parents (where N , includes the parent X). T h e outer circle
delimits the area in which the parent’s type 2 structures fall. Within this area fall the type 2
structures ofN, parents (where N, includes the parent X). A portion, (N, -N,)/N,, of the parent’s
type 2 structures fall in the outer circle and a portion, N,/N,, fall in the inner circle. Dots represent
other parents.
maximum, the solution represents a stable allocation or ESS (Hamilton, 1967;
Maynard Smith, 1974, 1979).
The fitness of a parent is defined as the number of its progeny which reach
maturity. This will depend upon the proportion of competing structures that are
produced by the parent (i.e. the parent’s proportional contribution to the
competition pool) and on the number of available sites for the progeny. The
total number of type 1 and 2 structures present in the competition pool in the
inner circle around an individual of the ordinary phenotype is:
n,e,qN,
+ ( N ,/N,)n,eA
1 -q ) N ,
The total number of structures in the inner circle around the mutant is:
1)qI+ ( N , / N z ) ~ ~ ~ -Zq mC) +( ~ “ 2 - 1)(1-4)1
nle1Cqrn
The number of type 1 and 2 structures that comprise the competition pool of the
outer circle for an individual of the ordinary phenotype is:
n,e,q(N, -NA+ C(N,-N,)IN2ln2e2(~
- m 2
and for the mutant
n le1q(N2 - N1) + C(N2 -N1 )IN2ln2e2C(l- qrn) + (N2 - 1)(1- q)l
The numbers of type 1 and 2 structures produced by an individual of the
ordinary phenotype that compete for sites in the inner circle around their seed
parent are n , e , q and (N,/N,)n,e, (1 - q ) , respectively. The number of type 2
D. J. SCHOEN AND D. G . LLOYD
314
structures produced by an individual of the ordinary phenotype that compete
for sites in the outer circle is [(N,-N,)/N,]n,e, (1-q). Similar terms
substituting qm for q give the production numbers of type 1 and 2 structures for
an individual of the mutant phenotype. Fitness is expressed as the sum of two
quantities, one representing the proportion of parent’s structures in the
competition pool of the inner circle multiplied by the number of sites available
there, and the second representing the proportion of the parent’s type 2
structures in the competition pool of the outer circle multiplied by the number
of sites available there. The fitness of the ordinary phenotype is:
=X
The fitness of the mutant is:
When
we obtain:
It can be shown by computation that equation (5)represents a maximum point,
and therefore the ratio of allocations of type 1 compared with type 2 structures
expressed in equation (6) is an ESS. Examination of equation (6) shows that a
necessary condition for the production of narrowly dispersed structures (i.e,
4 >0) is n , e , > n 2 e z . Whether there are available sites in the nearby area,
however, may depend on the post-reproductive success of the parent. The
prospects for near dispersed structures are likely to be higher if the parent dies,
i.e. is monocarpic. This may explain why multiple strategies involving near and
far dispersal strategies are largely confined to annual plants (Harper, 1977).
The more widely dispersed structures experience less sib competition. They
are produced at the ESS (i.e. 1-4 > 0) only if n e > n , e ,
{ [ 1 - ( l/N,)]/[l/N,)]}. If they are sufficiently successful at encounte:ing the
sites over which they are dispersed and are inexpensive to produce, then a
dispersal strategy involving them alone is selected. If the widely dispersed
structures are unsuccessful at encountering sites or are costly to produce, the
selected dispersal strategy involves only the narrowly dispersed structures.
CLEISTOGAMY AND HETEROMORPHIC DIASPORES
315
A stable multiple strategy producing both structures (i.e. 0 < 4 < 1, or
0 < 4/( 1 - 4) < CO) is selected under a restricted set of conditions. T h e first term
on the right side of equation (6) is always positive. Therefore, the conditions for
the production of both structures is determined by the term in square brackets.
This term is positive when
A stable multiple strategy of dispersal structures is brought about because the
two types of structures have distinct advantages (i.e. in lower costs or in more
often encountering the environment and experiencing less sib competition,
respectively) and, therefore, they have separately diminishing fitness returns.
When the two types of structures have sufficiently distinct opportunities, the
maximum fitness is obtained by producing both. The widest range of n , e l and
n2e2 values that leads to a multiple strategy is obtained when N , and N , are
maximally dissimilar (Fig. 2). As N , and N , approach each other, the zone of
multiple strategies shrinks and eventually disappears. Hence we expect multiple
strategies to evolve most often where the two dispersal structures have quite
different ranges of dispersal. The advantage that dispersing structures receive
from reduced sib-competition may be offset by a lower rate of establishment a t
more distant sites. The latter presupposes an environment that is either patchy
or is continuous but limited in space so that some propagules are dispersed
beyond the boundaries of the population. The narrow zone of conditions for
multiple strategies agrees with known .distributions of dispersal types. Multiple
strategies of dispersal are relatively uncommon. On the other hand, many plants
have effective means of dispersal, while others apparently do not. Presumably,
these correspond, in part, with either selection of far dispersed or near dispersed
structures depending on the relative opportunities at different distances from the
maternal parent (equation 6).
Hamilton & May (1977) considered two dispersal options which are the
extremes of those in our model. They found that allocation to dispersing
structures equals 1/(2- (n,e,)/(n,e,)},i.e. that there is always some allocation to
0.3
0:5
1.0
2.0
4.0
n m/ w 2
Figure 2. Allocation to type 1 structures ( q ) for various values o f N , , N,, n,c, and nzcz. The scale of
the abscissa is logarithmic.
316
D. J. SCHOEN AND D. G . LLOYD
the dispersing structures regardless of their success rate and unit cost. Equation
(6) reduces to this result when N , = 1 and N , = co. The result, however, is a
consequence of the special values chosen for N , and N 2 . Although it was not
developed as such, our model generalizes that of Hamilton & May (1977). In
general, the conclusion that dispersing structures should always be produced is
not warranted. Comins et al. (1980) also extended the model of Hamilton &
May (1977). Their analysis, unlike our own, is based on an island model, and is
primarily concerned with the interplay between the ESS migration rate, the site
extinction rate, mortality during dispersal, the number of adults in the
population, and the number of offspring produced. Differential resource costs of
dispersing and non-dispersing offspring were not considered by Comins et al.
( 1980).
Near and f a r dispersal model for cleistogamy
With cleistogamy the requirement of the simple near and far model, that the
two types of dispersed progeny both be the product of asexual reproduction or of
selfing, is not met. The CL seeds of the parent contain maternal and paternal
gamete contributions, while the CH seeds contain only the maternal gamete
contributions (assuming s = 0). We must also consider fitness gained through
the CH seeds of the parent’s mates via CH outcrossing as a pollen parent.
Furthermore, as we have seen, additional factors such as differential costs and
fertilization rates affect the success of cleistogamy and chasmogamy. These must
be incorporated into the model.
To simplify the analysis, we consider that CH seeds of a pollen parent’s mates
fall into a region that does not overlap with the maternal seed shadow of that
plant. The paternal shadow region contains the CH and CL seed of N3 parents
Figure 3. Dispersal ranges of CL and CH seed for parent X. The inner circle delimits the area in
which parent X s CL seed fall. Within this area also fall the seeds of N , parents (where N , includes
parent X). The outer circle delimits the area in which parent X’s CH seed fall. Within this area
also fall the CH seed of N, parents (where N, includes parent X). The circles outside the N, region
represent the CH seed shadows of parent X’s mates, to which X’s pollen is transported. Together
these areas comprise the seed shadow for N, parents.
CLEISTOGAMY AND HETEROMORPHIC DIASPORES
317
(Fig. 3). It is further assumed that the number of mates experienced by the CH
flowers of an individual is sufficiently large ( K > 10, roughly) that sib
competition among the paternally derived progeny is negligible. For brevity, we
combine the products n,d~,r,c,e, (1 -6) and n,d,,g,r,v,e, into variables A, and A,,
respectively. The two variables, A, and A,, represent the combined effects of the
factors that influence the success of the two modes of reproduction prior to
seedling competition. (We assume no selfing of CH flowers in order to simplify
the formulation.) For consistency with the general near and far dispersal model,
Q and 1-4 are used to denote allocation of resources to the less dispersed (CL)
seeds and more widely dispersed (CH) seeds, respectively. Fitness expressions
and the derivative of the fitness advantage (w,-w,) are given in the appendix.
When the derivative is set equal to 0, the ESS ratio of allocations to CL seeds
versus CH seeds is:
As in the general near and far dispersal model, a relatively narrow range of A,
and A, values, defined by A,> A,> A, ([l-(l/N,)]/[l-(l/N,)]}, g’ives a
multiple strategy. Numerical substitutions into equation 8 yield results similar to
those obtained with equation (6),although the curves are slightly steeper than
in Fig. 3. For cleistogamous plants, we predict a multiple strategy of dispersal
under conditions similar to those for progeny derived from genetically
equivalent parental sources. The CL seeds must be more successful at
establishing in the few sites located within their narrow dispersal range, while
the CH seeds must be more widely dispersed than CL seeds but less successful at
establishing. The environment need not be heterogeneous for either parents or
progeny. The prediction is upheld by the frequent occurrence of marked seed
heteromorphism in cleistogamous plants, and by the observation that narrowly
dispersed CL progeny are usually more vigorous compared with the widely
dispersed CH progeny (Dyksterhuis, 1945; Cheplick & Quinn, 1982).
Amphicarpy in Gymnarrhena micrantha and other plants is postulated by Zeide
(1978) to be due to the simultaneous operation by a plant of two distinct
reproduction strategies. Zeide refers to these as ‘pessimistic’ and ‘optimistic’
strategies, i.e. in an unpredictable environment there is an advantage to early
allocation to seeds (pessimistic strategy) and, if conditions permit, following a
period of vegetative growth there is continued allocation to seed production
(optimistic strategy). Zeide’s (1978) argument, unlike our own, predicts that
amphicarpy is found most often in unpredictable environments. Zeide based his
argument, in part, on the relationship between plant size and resources
allocation to near-dispersed, geocarpic (CL) seed versus far-dispersed, aerial
(CH) seed. He noted that allocation to near-dispersed seed is a curvilinear
function of plant weight with ay-intercept >> 0, and that beyond a certain plant
weight, allocation to the near-dispersed seed is constant. Allocation to the fardispersed, however, is a linear function of plant weight, with ay-intercept of 0.
The two contrasting allocation strategies noted by Zeide (1978) and others
(Campbell et al., 1983) can also be accounted for by our models. If it is
assumed that when reproductive effort is low there is a lack of sib competition
318
D. J. SCHOEN AND D. C . LLOYD
(i.e. sites are not saturated), and that A, > A,, the largest fitness returns can be
made with the more economically produced, and more successful CL seeds. But
as CL seed production increases, nearby sites become quickly saturated. As this
occurs, the multiple strategy is favoured and further increases in seed production
go into far-dispersed seeds.
The near and far dispersal model also helps to explain the relationship
between proportional allocation of resources to CH reproduction and plant size
in non-amphicarpic plants, which has been referred to as environmental
chasmogamy (Waller, 1980; Wilken, 1982). In one hypothesis, Waller (1980)
invoked sib competition as a factor that is intensified with increasing plant size.
He postulated that this sib competition might favour chasmogamy, since a
genetically diverse array of progeny increases the chances of survival among the
offspring. It can be demonstrated, however, that even when CH seed are not
genetically more diverse than CL seed that environmental chasmogamy may be
selected. A necessary condition is that an increase in plant size favours the
dispersal of one seed type more than the other, i.e. the effect of plant size is to
increase N, or N,, but not N,. The result may be dramatic, e.g. if
A,/A, = 1.0125 and N , and N, are initially 9 and 10 (N, may take on any
value), then a 50% increase in area of seed shadow (N, = 15) results in
proportional allocation to chasmogamy ( 1 - q) increasing from 0 to 0.74.
Additionally, if plant size is a good indicator that success of open-pollination, or
that number and quality of far sites is increasing, thereby extending the period
when CH reproduction is favoured in the heterogeneous parental habitat model,
increasing proportional allocation to chasmogamy with plant size may be
additionally favoured.
Venable & Lawlor (1980) consider plants which have two dispersal modes.
Their emphasis is on explaining why narrowly dispersed seeds often show
delayed germination, while widely dispersed seeds often show rapid
germination. Venable & Lawlor assume that the environment is patchy in both
space and time, i.e. composed of sites where seedling growth is good or bad
depending upon position and year. They propose that the observed patterns of
germination relate to selection for escape from poor growth conditions in time
(for the narrowly dispersed seed) versus space (for the widely dispersed seed).
These germination patterns for near- and far-dispersed seeds may also be
accounted for, in part, by the near and far dispersal model. For example, if the
near dispersed seeds are deposited subterraneously at the maternal site they will
have few opportunities because of spatial restrictions. The ability of progeny to
occupy the maternal parent’s site could be increased, however, by staggered
germination associated with dormancy. Sib competition is thereby reduced, and
the progeny jointly are more certain to take all opportunities that occur in time.
On the other hand, the widely dispersed progeny suffer little sib competition,
and so there is little advantage in delaying germination. Hence, the near and far
dispersal model predicts escape in time and space from sib competition. The
result is an addendum to that of Venable & Lawlor (1980).
I t should be noted that our models were not motivated initially by a concern
with germination heterogeneity. This is currently an area of active research (e.g.
L. Venable, pers. comm., J. Silvertown, pers. comm., K. Rice, pers. comm.). It
is a topic which we do not consider in detail; to do so would require a detailed
consideration of temporal heterogeneity.
CLEISTOGAMY AND HETEROMORPHIC DIASPORES
319
CONCLUSIONS
The models proposed here make a number of predictions that agree
reasonably well with the limited ecological data for cleistogamous species. That
self-pollination in obligately closed flowers occurs in small flowers having
reduced corollas and androecia (Lord, 1981) is in good agreement with the
predicted conditions for the selection of cleistogamy. The prediction stems from
the requirement that d, and g, be sufficiently large in obligately closed flowers so
as to compensate for the relative loss of opportunities to gain fitness through
pollen. A corollary to this central prediction is that cleistogamy is expected to
evolve in groups where ancillary and paternal costs are large, and where
substantial resources saved by producing small flowers with reduced androecia
can be redirected into maternal function. The latter condition further requires
that the CL fertilization rate be sufficiently high so as to allow increased fitness
through maternal function (large ye).
Other characteristics of cleistogamous plants also agree with the predictions of
the complex habitat and near and far dispersal models. These include
environmental or time-dependent reproduction by CL and CH flowers, the
occurrence of heteromorphic fruits and seeds with differential dispersal ranges
and viabilities, and the correlation between plant size and proportional
investment in CH reproduction and more widely dispersed diaspores. According
to the near and far dispersal model, the latter two observations are related to the
more economical production and limited opportunities for CL seeds. As the
opportunities for the CL seeds are exhausted, fitness returns become increasingly
greater with investment in CH reproduction.
Our models have exposed some of the complexities of cleistogamy,
particularly the number and variety of interacting factors that contribute to its
selection. Because of the complexity of the selection scheme, we do not expect
that the balance of selective forces will operate in the same manner in every
species. Cleistogamy may be favoured in one species because it increases the
fertilization rate by circumventing developmental obstacles to selfing. In other
species, however, cleistogamy may be favoured because increasing the allocation
to maternal function leads to a disproportionate gain in fitness. If we wish to
determine the relative importance of the selective factors included in the model,
much more information will be required on the allocation of reproductive
resources and the modes of fertilization in cleistogamous plants.
ACKNOWLEDGEMENTS
We wish to thank Elizabeth Lord, James Quinn, and Colin Webb for their
helpful comments on the manuscript. DJS was supported by the Fulbright
Program and the E. L. Hellaby Indigenous Grasslands Research Trust.
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APPENDIX: ESS ALLOCATION TO CL AND C H SEEDS-THE
CLEISTOGAMOUS PLANTS
PROGENY MODEL FOR
To adapt the general home and away dispersal model to cleistogamous
plants, it is necessary to account for the different gamete contributions to CL
and CH seeds. Parents gain two fitness contributions (the maternal and
paternal) through their CL seeds but only one (the maternal) through their own
CH seeds. They also gain an additional (paternal) fitness contribution through
the CH seeds of their mates by CH outcrossing. We assume for simplicity that
the CH seeds of the parent’s mates fall outside the N, region, in an area
containing the CL and CH seeds of N, parents. N, is assumed to be sufficiently
large so that sib competition among the paternally derived C H seeds can be
ignored. The CL seeds have a success rate of A,, and the C H seeds have a
success rate of A, (see text). The fitness of the ordinary and mutant phenotypes
are expressed in gamete contributions to the next adult generation.
wo = X{N1[
2Acq+(N,/N,)’40(1-4)
N1Acq + (N,/N,)N2A0(1- 4)
1
322
D. J . SCHOEN AND D. G.LLOYD
When,
a(w,
- wo)
%m
I
qn=qo
=o,
(All
we obtain equation (8). It can be demonstrated numerically that ( A l ) g'ives a
maximum point and, therefore, the ratio of allocations depicted in equation (8)
represent an ESS.