Lecture 9 - Allocation to Reproduction: When & How Much

      The story of clutch size and tradeoffs between size and
number worked their way around the basic question of life history.
That question is usually phrased in some way to ask how to schedule
allocation to reproduction through the lifespan of the organism.
How much should be allocated at each age? We've already seen one
general model of the question in the form of graphs for iteroparous
and semelparous species, in which current reproduction and residual
reproductive value were plotted against age for semelparous and
iteroparous species. But why should a species evolve to be
iteroparous versus semelparous? If being iteroparous is
advantageous, how is lifetime reproductive effort scheduled? This,
then, brings us neatly to consider reproductive effort in relation
to reproductive strategies. My take on the subject differs a bit
from text treatments. To consider reproductive effort, I begin by
comparing semelparity, with a maximum reproductive effort expended
at an optimized age and/or parental size, with iteroparity, with
time and age dependent optima in the expenditure of energy on
reproduction `designed' to maximize lifetime fitness.

Semelparity versus Iteroparity
     The first part of the question of when to reproduce, having
looked at effects of a and clutch size, is whether to reproduce only
once, i.e. semelparity or big-bang reproduction, or whether to
reproduce more moderately but repeatedly, i.e. iteroparity.  From
different points of view it might seem apparent that advantage
accrues to either one strategy or the other. Reproducing early, and
according to the big- bang approach (so that the organism needn't
worry about possible effects on adult survivorship) caution can be
'thrown to the winds', and G considerably shortened.  This should
clearly increase 'r'. However, consider the opposite approach. Even
if every litter were somewhat smaller, the iteroparous species can
have many such litters, and a much larger number of offspring (R0)
over a life cycle. It seems as if, over that lifespan, over the long
run, numbers should pile up. How are we to quantitatively assess the
relative merits of these two alternatives?  The comparison is part of
Cole's (1954) classic paper, and comes to what, at the outset, seems
to be a shocking conclusion.
     Cole assumed that the semelparous species has perfect
survivorship to age 1 year, then reproduces, producing a litter of
size b.  The iteroparous species has perfect survivorship, not only
until it begins reproducing at age 1, but also thereafter; it
produces a litter of size b annually.  The population growth can then
be compared. The advantage of the iteroparous species, with an
indefinite lx of 1 is surprisingly small. Looking first at the
semelparous species, and beginning with exponential growth as a
                            Nt = N0 ert

if t = 1 year, and each female has a litter of size b, then the
growth equation can be re-written:

                           Nt/N0 = er = b
                            rs = ln (b)

The calculations for the iteroparous species involve another infinite
sum, with the approximate result that:
                           ri = ln (b+1)

Cole's way of stating this comparative result is clear and concise:
     'for an annual species, the absolute gain in intrinsic
      population growth which could be achieved by changing to the
      perennial reproductive habit would be exactly equivalent to adding
      one individual to the average litter size.'

Not only that, but the gain, logically, is a function of litter size
and the age of first reproduction, which aren't considered in this
basic comparison. The gain from changing to iteroparity (when the
litter size of the semelparous species is equal) increases both with
delay in first reproduction (i.e. increasing a) and with decreasing
litter size. These effects should follow logically. Consider litter
size first. If it takes one extra in the litter for a semelparous
species to keep up, that represents a bigger proportional increase in
reproductive effort when litter size is small than when it's large
(e.g. a 50% increase if b = 2, but only a 1% increase if litter size
is 100). It's a little harder to think in terms of alpha, but recognize
that the semelparous species has bouts of reproduction only every
alpha years, while, once started, the iteroparous species reproduces
every year. If alpha increased from 1 to 5 for both the iteroparous and
semelparous species being compared, then by the time grandchildren
are born in the semelparous species, the iteroparous parent will have
produced offspring at ages 6,7,8 and 9, each time with a litter of
size b. That's clearly a bigger advantage than accrued when alpha was 1.
Cole produced a graph showing the combined effects of alpha and b on the
percent gain from becoming iteroparous, and it shows clearly that
iteroparous life histories are most advantageous for species limited
to small litter sizes and delayed reproduction.  This general pattern
fits with observations.
     Most semelparous species tend to have short pre-reproductive
periods. That minimizes the advantage that might be gained by
becoming iteroparous. A few examples make the basic point.  Annual
plants (many weeds) and almost all insects complete their life cycles
in a single year, and most which do not complete life cycles in 2
years instead (e.g. most salmonids, biennial plants such as weedy
thistles, teasel, onions, garlic). There are extreme exceptions, such
as the 'century' agave and some bamboos, but they will be the subject
later. Semelparous species also typically have very large litter
sizes.  Many produce 106 eggs or more, e.g. Musca domestica, the
common housefly, oysters, or the salmon.

     These observations, and many others which could be presented,
suggest that in most cases semelparous species fit the life history
patterns which would minimize the gain from becoming iteroparous.
The problem can also be approached from the opposite point of view.
It is clearly advantageous, from an evolutionary view, to increase
the intrinsic rate of increase 'r', 'all else being equal'. A change
in 'r' could result from becoming iteroparous while maintaining
litter size, or from an increase in the semelparous litter size.
Since either change could be equally effective, we can look at the
change in semelparous litter size required to achieve the same 'r' as
would be reached by switching to iteroparity while just maintaining
litter size. Once more, Cole produced the figure which demonstrates
the requirements for equivalence. The change in litter size required
can be dramatic. Take the lowly tapeworm as an example:

   The approximate daily litter size of the mature tapeworm is
   100,000 eggs.
   Including larval development time, the maturation time, or
   alpha, is approximately 100 days.

If this species were to become indefinitely iteroparous, we find from
Cole's graph that the equivalent semelparous litter size to achieve
the same growth rate would be about 800,000. The species is not, of
course, indefinitely iteroparous, and the required semelparous litter
size is not quite so large. This comparison, and particularly this
figure, make it clear that the apparent 'advantage' of semelparity,
i.e. the ability to catch up by adding only 1 to the litter size,
strongly depends on the length of pre-reproductive life and on litter
sizes involved. Thus, although this began by making it seem that
there was little advantage in bet-hedging to permit repeated
reproduction, there are real situations which suggest a considerable
advantage (in an evolutionary sense) to iteroparity.
     At ths point Cole introduced a figure you've already seen, the
one which demonstrates the proportional gain in 'r' from increasing
the number of reproductive cycles. The only thing to add to what's
already been said is to recognize that the advantage gained by
additional reproduction declines for all cases, but particularly for
those with low alpha. In an evolutionary sense, that means that the
selective pressure to increase the period alpha to omega decreases, and
beyond the first few reproductions, the slight advantage that might accrue
from further reproduction may easily be balanced by other pressures.
     Cole's results have, since their publication, been a thorn in
the side of life history theory.  Nobody claims Cole was wrong, Cole
was correct, rather a large number of theoreticians have tried to
show that the unreality in Cole's assumed life history is responsible
for the smallness of the difference between iteroparity and
semelparity. The key assumption in Cole's treatment was the
assumption that all lx in both strategies were = 1.  Adding mortality
schedules have clarified some of the results.
     The outcome of making survivorship more realistic was initially
possibly even more controversial.  Bryant (1971) showed that under
assumptions of 1) constant litter size and 2) a monotonically
decreasing lx = e-mx, or, for that matter, any monotonically
decreasing lx, the value of 'r' for an iteroparous species is not
even increased as much as by adding 1 to the semelparous litter size.
That's logical, if you stop and think about it. If Cole showed
equality by adding one to the litter size when the iteroparous
species was immortal, less is contributed by a mortal species, since
the contribution to the sum lxmx is decreased by declining
survivorship. For the case of a perfect type II curve, as evaluated
by Bryant, equality occurs with a growth (or litter size for the
semelparous species):
                          r = ln (b+1) - m

where, remember, m is the constant describing the death rate. If the same
mortality occurs also in the first year of life, then the growth rate of
the iteroparous species is:
                           r = ln (b) - m

The valuable indication from Bryant's attempt to move closer to
reality is probably not the exact mathematical formulae, but the
recognition that for type II species, semelparity becomes more likely
as the mortality rate m increases. This, too, fits with natural
history observations.
     At this point you might wonder why there is such a thing as a
long-lived iteroparous species.  A more recent attempt to add reality
to Cole's model will show us when and why.  Charnov and Schaffer
(1973) used a more general approach to correct for Cole's generous
assumption about survivorship. Their model includes, but separates,
pre- and post alpha mortality. As a result, you will see that they
can suggest where iteroparity should evolve. The comparison begins
again between an annual and a perennial species. Assume that the
litter sizes for the two types of species are Ba for the annual
species and Bp for the perennial species.  The survivorship pattern
in the first year is l1 = C for both types. Following reproduction in
the first year, the semelparous species dies, and the perennial
species continues with an annual proportional survivorship px = P.
The comparison is easiest if we compare finite rates of increase, 
 = er, and t = 1 time unit, usually a year, so that:

                         N(t+1) = l

For an annual species the number alive to breed is C x N(t), and each
of these has a litter of size Ba, or:
			N(t+1) = C x N(t) x Ba
a = Ba x C

For the perennial species there is adult survivorship and repeated
reproduction as well. Counting noses just before reproduction, so
that surviving adults haven't yet added the additional litters, we
                N(t+1) = Bp x C x N(t) + P x N(t)
p = Bp x C + P

For an annual species to make up the advantage of iteroparity, the
growth rates must be equal, therefore:
                       Ba x C = Bp x C  +  P

                          Ba = Bp  +  P/C

Now, let's go back and consider previous cases. Cole suggested that
we disregard survivorship to develop an initial model. With
immortality both P and C are taken as 1, their ratio is 1, and the
result here is identical to that Cole obtained. Bryant suggested that
if we impose type II survivorship after alpha, then an advantage less
than 1 in litter size accrues. His survivorship pattern is equivalent
to saying P is fixed, and less than C; the advantage here is again
less than 1.  Then, when is iteroparity favored?

     To determine that we need to look at the relationship between P
and C, i.e. between proportional survivorship through the
reproductive period and pre-reproductive survivorship.  Consider the
Deevey survivorship curves. For type III its obvious that P is far
larger than C, the early part of the curve is very steep, and the
curve is relatively flat through reproduction.  For type II (and
remember, for comparisons of real numbers we need to convert back
from the usual log scale to a linear one) P and C are more similar,
but the curvature makes it 'flatter' during than before reproduction.
For the mammalian type I curve, you might think that P and C are
equal, but remember Caughley's basic pattern; it showed an initially
moderately high qx, or equivalently an initial decline in lx, before
an extended, flat, low set of values through reproduction, i.e. C is
less than P.  Using a simple graphical treatment, early survivorship
is compared to the reproductive period in slopes of the curves.  If
early survivorship is steeper than the later period, then the
perennial habit is favored to that degree.
     We can extend this analysis by using somewhat more realistic
models for semelparity and iteroparity, one in which reproduction
does not necessaarily occur in the first year, but rather at age K
(and in each subsequent year if the species is iteroparous).  The
comparison now uses Euler's equation. In this system of equations, for
purposes of simplicity and clarity, l stands for lambda, the finite rate 
of increase. For the iteroparous species:

             1 = Bi x C [1/lK + P/lK+1 + P2/lK+2 + ...]
                    1 = Bi x C/lK [ 1/(1 - P/l)]

for the semelparous species:
                           1 = Bs x C/lK
                            lK = Bs x C

setting the growth rates to equivalence, by substitution we obtain:

                          Bi/Bs = 1 - P/l

That is, life history equilibrium leans in favor of iteroparity when
the iteroparous litter can be much smaller than the semelparous
litter which produces the same population growth rate. That occurs
when either:
     a) the adult survivorship px or P, is very high, or
     b) the finite rate of increase (or annual population growth) is
        very low.
That, of course, is exactly what intuition suggests. The higher the
adult proportional survivorship the more the advantage to be gained
from iteroparity, since that means many more litters will be produced
over the lifespan.

An Energetics View of Iteroparity vs. Semelparity
     The various approaches used by Cole and his followers to test
the advantage of iteroparity are all based on comparison of
population growth rates; they do not consider the position of the
individual committed to a strategy.  A final view of the contrast
between iteroparity and semelparity, and when each should be
expected, considers instead the energetics of the reproducing animal.
It is, therefore, a little less abstract in approach.  An animal
reproducing iteroparously must save energy for future reproduction;
that energy is required for maintenance and possibly growth.  An
animal reproducing semelparously, to maximize success, should
energetically commit all available (divertable) energy to
reproduction at the expense of all other structures in the body,
since it will not survive to reproduce again.  This suggests the
possibility of using cost/benefit comparisons related to economics to
decide what conditions should lead to different strategies.
     That approach, in the form of a set of graphs, was used by
Gadgil and Bossert (1970) to suggest patterns which lead to
iteroparity.  At any age the amount of reproductive effort which
should be expended is determined by balancing the profit to be gained
by reproduction (measured by the reproductive value at that age, i.e.
offspring plus future expectations) against the costs inevitably
incurred.  To compare all possibilities, Gadgil and Bossert defined 3
shapes of profit and cost functions to be plotted against
reproductive effort.  Reproductive effort is defined, for the
purposes of these graphs, as the proportion of total energy devoted
to reproduction.  The graphs are in arbitrary units, i.e. we won't
assign real numbers, but indicate the shapes of patterns. The 3 kinds
of curves are concave, linear and convex. So that the patterns have
an underpinning of reality let's consider a few examples:

    Consider the cost and profit functions for migrating salmonid
    (e.g. Atlantic and Pacific salmon) reproduction.  The initial effort
    required to spawn even one egg is the enormous cost of migration from
    deep ocean to upstream fresh water.  Thus the curve rises very
    sharply at low reproductive effort. However, the additional cost to
    spawn more eggs is basically the metabolic cost of egg tissue
    production, which is much more modest and basically flat (i.e. each
    egg costs about the same amount, independent of how many have been
    already formed). That combination produces a cost curve which is
    'extremely' convex.  For simplicity, the curve can be drawn with a
    less extreme rise, and a not quite flat top (things aren't usually
    that dramatic) to reflect the more general pattern.
      Meanwhile, the profit from increases in reproductive effort,
    i.e. the number of offspring, increases at least in direct proportion
    to the number of eggs. If there are advantages to schooling of fish
    fry, then the profit curve might not be linear, but a bit concave,
    reflecting the improved survivorship (lx, i.e. not just numbers but
    the expectation of survivorship for each individual) when offspring
    numbers increase and schools are formed. The combination of a convex
    cost curve and a linear or concave profit curve predicts maximum gain
    at maximum reproductive effort - be semelparous (see below for the
    complete consideration of curve combinations.

      Which curves might fit the mammalian situation? Avoid thinking
    of man. With that caveat, I suggest that the cost function could
    range from linear (if we consider the direct costs, including
    parental care, there is no obvious reason to suggest either declining
    or increasing costs per offspring as litter size changes) to concave
    (if we also consider indirect costs, e.g. homeothermic stress,
    increasing risk of predator tracking with increased litter size). It
    probably isn't strongly concave, but at least slightly non-linear in
    that direction. The profit function is probably convex, in parallel
    with what we've seen for the provisioning of birds, from the
    decreasing individual size of individual offspring with increasing
    brood size. Again, the curvature is probably not dramatic, since
    homeothermy leads to some sharing of warmth among members of a brood,
    which helps, but also sharing of teats, which limits food intake no
    matter how hard the mother works.
      Where is the benefit/cost ratio maximized for mammals.  For the
    salmon costs to reproduce at all are high, but once reproduction begins
    benefits rise much faster than costs as effort increases.  The maximum
    ratio occurs at maximum reproductive effort, suggesting the animal
    spend everything it can on reproduction, i.e. be semelparous.  For the
    mammal costs rise slightly faster than linear as litter size increases,
    but profits rise at a rate at least slightly below linear.  The maximum
    ratio occurs at some intermediate level, the exact effort determined by
    the curvatures of benefit and cost curves, i.e. save a considerable
    fraction of total energy, and reproduce iteroparously.

     There are, based on 3 curve shapes for each of benefit and cost, 9
combinations.  Most make a clear prediction of semelparity or
iteroparity, a few depend for their predictions on recognition of
survivorship and cost per unit.  In those cases the ratio remains
constant, but long-term total profit changes.
     To see how each graph is taken to indicate semelparity or
iteroparity, scale the x axis (reproductive effort) from 0 to 1.  A
big-bang reproducer should achieve the best benefit-cost ratio at an
effort of 1, an iteroparous species at some intermediate level,
retaining energy for maintenance and growth.  When is it advantageous
to withhold energy from reproduction?

     a) If the profit function is convex.  In this case, above some
intermediate reproductive effort the profits cannot keep pace with the
proportional increase we might expect for metabolic costs per
offspring.  With costs increasing faster than profits, energy should
not be spent inefficiently, but retained for use in the next bout of
reproduction, when they can be spent with greater efficiency, at
moderate reproductive effort, where gains increase most rapidly with
effort.  This is just the 'law of diminishing returns' applied to
reproductive ecology.  The efficiency argument even applies when the
ratio remains constant.  For that, the middle case, the total number of
offspring produced from a given amount of energy can be maximized by
reducing reproductive effort, even if benefit-cost ratio has no

     b) If the cost function is concave.  In this case the cost per
unit gain in fitness becomes too high at high reproductive effort.
Retaining a portion of the energy available, the animal can produce
offspring (or increments in fitness) at a lower cost per unit in later
bouts of reproduction.

     c) In all other circumstances animals should wait until the
maximum benefit-cost ratio has been reached, then put all available
energy into reproduction.  Under these circumstances the semelparous
reproductive habit is optimum.  That incudes the case where profit and
cost are both linear.  There is no change in cost per unit with effort,
and we now know the advantage of early reproduction.  There is no
advantage to restraint, especially given survivorship factors, so
semelparity should result.

     d) If more complex functions for benefit and/or cost are
considered, e.g. sigmoid shapes, there will almost always be some
intermediate level of effort at which the curve goes through an
inflection point, i.e. a change from concave to convex.  In most cases
that inflection will be the critical point at which benefit-cost ratio
will be maximized, and an iteroparous strategy will result.

     Almost all views of the balance between iteroparity and
semelparity have now been considered.  Their assembly leads to one last
evaluation, how long should the period alpha to omega be?  This clearly also
relates to the intensity of reproductive effort in iteroparous species.
Obviously, that depends on the security of survivorship (px), and on
the variability in reproductive success (one possible indicator being
initial survivorship l1).  If survival is relatively assured, then no
single bout of reproduction is under severe pressure to produce
success.  On the other hand, if survivorship is low or variable, then
the pressure for success from any single bout (or a few) is much
higher, and more effort (and a shorter alpha-omega is likely.  This is a
hypothesis developed by Murphy (1968).  His data comes from marine
fisheries, and show a tight relationship between the reproductive
period and variability in success (measured as a ratio of
highest/lowest success).
     Unpredictability in annual success rate is exactly what we might
expect of species in mature communities. A good example might be a
climax forest. The only places young are successful is where openings
develop due to death or chance destruction of mature individuals. Such
clearings are rare, chance events. So each year a tree puts out a crop
of seeds, but it may be many years of suppressed growth before even one
is successful in such a chance clearing. The profit function is
therefore convex, i.e. the chance of a clearing happening cannot be
missed, so its necessary to put out a seed crop each year, but there's
no use overdoing it, there's little advantage in putting out a huge
crop. Energy is retained to improve survivorship, so that the
individual is likely to survive to a time when an opening develops, and
be capable of producing offspring to colonize that opening.  Whether we
call evaluation of this strategy as resulting from unpredictability in
reproductive success, a convex benefit function, or a relationship in
which C << P, the result is the same.
     If some reasonable level of success is relatively assured, i.e.
variance in success is low, then the reproductive span is shortened,
ultimately to semelparity. Again any of the models can be invoked.
Rather than pursue that, let's look at a summary view produced by
Murphy (1968), but clearly fitting, with appropriate changes in
terminology, any of the models.  Its a 2 x 2 table in which lifespans
(really reproductive spans for Murphy) and variability in reproductive
success (or P/C comparisons, or benefit functions) are combined:

                         long-lived               short-lived

reproductive success    see below (?)             semelparous
steady (assured)                                  strategies

reproductive success    iteroparous               not possible

     Two of these boxes have already been discussed as (or more)
thoroughly as necessary. The upper right hand box, semelparous
strategies, is a necessary association of lx and mx. If a species is
short-lived, quantifiable as a small e0, then the only pattern to
reproduction which will permit persistance is steady, assured success.
Else, as the next paragraph describes, extinction will follow.
     The lower, right hand box is also simply explained. This is what
happens to a short-lived species does not have assured success.
Extinction is the inevitable result when a species attempts
reproduction only once (or possibly a few times) while the variability
in reproductive success is high. That variability ensures that at some
time a few bad years will follow in succession, and prevent an entire
mature population from producing any surviving offspring, i.e. local
extinction.  These are species that have adopted a short-lived,i.e. a
low P, but also a low C strategy.  In its simplest form this just won't
work. The closest real species come to this is to have facultative
(that is have the potential for) dormancy in offspring. In this way the
low survivorship of parents and low annual success in offspring can be
mitigated through appearance of offspring (release from dormancy) when
chances of offspring success are high. Looked at in terms of the end
success of offspring, rather than annual success rates, this strategy
becomes a special case of the upper right hand box, short adult life
but predictable offspring success. This strategy is fairly common in
weeds, whose seeds may remain dormant for more than 100 years, and in
some desert plants. The desert plants produce seeds that, at the time
of dispersal, contain inhibitors which must be washed out before
germination will occur. The limiting factor on the desert is sufficient
water. Heavy desert rains will wash out those inhibitors, and also
guarantee a sufficient supply of water to complete a growth cycle. This
is a biochemical form of buffering against environmental variability.
     The box in the upper left has a ?. There are a number of
approaches to indicate why that box should not be occupied by observed
reproductive strategies. The most intuitive of them considers the
effect of such a strategy on species interactions. This is a species
which is long-lived and has predictable reproductive success. That
should make this population very successful. If the species in question
is a prey item, its predator will evolve to more extensively utilize a
species which is predictable, either through numerical or functional
responses. An optimally evolved predator should probably adopt a type 3
strategy, i.e. specialize on this prey through formation of a search
image if the predator is capable of that kind of behavioural response.
The result of increased predation on this prey, whose life history we
are following, will be either a reduced lifespan or greater variability
in reproductive success (or adaptations to make their accessibility to
predators less predictable). That moves the strategy for the species
out of the ? box and into either of the more usual strategies.  In fish
species the tendency is toward shortened life and steady reproductive
success. In a number of plant species (particularly long-lived trees)
the opposite adaptation has appeared. These trees (apple trees are an
example of one kind of response) have variable reproductive success;
some years a heavy seed crop is produced (so-called mast years) and
other years the crop is much smaller. In nature this can be considered
an adaptation to restrict insect (or other) herbivores by starvation,
though it can also be a necessary reponse to energetic demands of
reproduction. In this latter sense, it is a cost of reproduction.
Having reproduced heavily in one year, the 'cost' is a very restricted
reproduction in the following year. The pattern stands, whether the
mechanism is energetics or predator avoidance.
     If these strategies are well established, do all species fit one
of the possible strategies?

Exceptions - There Are Always Exceptions!
     There are always exceptions.  If it seems like the possibilities
have  been  neatly pidgeon-holed, but it's time to see  what  can  be
learned from the oddballs.  The most common form of exception to  the
strategy  table developed by Murphy is the presence of a  variety  of
long-lived  semelparous species. 13 and 17 year cicadas  are  obvious
examples, but in terms of lifespans, they're small change compared to
the  plant  examples.  We'll  look at 2  different  rationales  which
produce  long-lived semelparity in plants, using semelparous  bamboos
and the agave ('century plant') as examples.

The Bamboos
      Not  all bamboos are exceptions to the established life history
patterns. Many species are iteroparous perennials; these grasses have
more or less extended pre-reproductive periods, then flower and  set
seed annually until senescence. There are, however, a number of
perennial, monocarpic bamboos, and included among them seem to be all
of the economically important bambo species. An aside: this fact is a
problem, as well as an incitement to scientific interest.
Populations of these bamboos are, therefore, managed, and natural
cohorts are inevitably mixed with agriculturally selected strains.
Long-term genetic implications of the apparent strategy may not, as a
result, be testable. The studies of bamboos are largely the result of
the work of Janzen, summarized in a review paper (1976), and, for a
different  group of bamboos with a differing explanation, by Gadgil
and his collaborators (1984).
      What evidence is there that something unique is going on in
semelparous bamboo life histories? Janzen uses history to pique our
curiosity.  Historical records indicate that a major Chinese bamboo
species, Phyllostachys  bambusoides, flowered en masse (that  is
simultaneously  over hundreds of square miles) in 919 and again in
1114, but not at any point in between. Cuttings of the rhizomes of
this species were brought to Japan and established there. Those
cuttings flowered during the period between 1716 and 1735, then again
in 1844-1847, but not during any intervening year (if there are
records of flowering between 1114 and 1716, Janzen did not find
them). Transplants from Japan, as well as the parental stock,
flowered next in the 1950's. Those transplants were scattered in
England, Russia, and Alabama among other places. All flowered  within
3-4 years of each other. It was this widespread mass flowering that
aroused Janzen's curiosity. The flowering appears to be somehow
genetically programmed and fixed. That program is essentially
unaffected in its Swiss clock-like precision by the enormous
variation in environmental conditions represented at its flowering
sites (Japan, England, European Russia, Alabama, etc.).
     Many other bamboo species also flower in relative synchrony, and
with  quite long intermast intervals. Among bamboos this life history
contrasts  with  another pattern which is also common; many species
produce seed crops annually after a maturation period of varying
length.  A  partial list of the species which reproduce synchronously
and have long intermast intervals is shown in the table below.
      The flowering in species like P. bambusoides is 'unique' in 2
ways. One is its freedom from environmental perturbation. Unlike
most other mast reproducing species like oaks, beeches, and many
fruit tree species (all of which have far shorter inter-mast periods)
there is no apparent environmental cue to initiate mast year
reproduction; unlike the others few (almost certainly none) of the
potential seed predators are likely to survive the inter-mast period.
Yet seed predation is hypothesized by Janzen to be the selective
force behind this, as well as other masting phenomena.  How can seed
predation be so important?
      To  understand that we need to recognize 1) how large the  seed
crop  can  be  and  2)  how large the response and  variety  of  seed
predators can be. It seems almost everybody (including man) likes  to
eat  bamboo seed. It is (surprisingly, to me at least) slightly  more
nutritious  than  either  rice (brown,  of  course)  or  wheat  among
commonly  consumed  grains  in the human diet.  Among  the  'natural'
consumers  are  small rodents, wild pigs, and the  jungle  fowl  (the
progenitor   of  the  domestic  chicken).  Janzen  claims,   possibly
controversially, that domestication of the chicken and pig  may  have
been  possible because of their dependence on bamboo seed crops,  and
the  ability  of  man  to substitute managed annual  seed  crops  for
natural  and mast seed crops. The response of natural seed  predators
to  this  mast crop is dramatic. The functional response includes  an
increase  of 50-100% in the number of eggs/clutch in the jungle  fowl
(remember that this species is an indeterminate egg layer, but has  a
fixed brood size, normally 2). Numerical responses through migrations
of  enormous  proportion are anecdotally reported in that  historical
literature. Rat 'plagues' follow mast years as a result of  migration
plus  reproduction; in Africa movements of flocks of  weaver  finches
numbering in the millions follow geographic 'migration' of  the  mast

                               Table 1

      The range of intermast intervals in bamboos which flower
                   synchronously over large areas.            
Genera                    Locations             Intermast Interval

Arundinaria spp.          Kenya, Himalayas    	    11 - >50
Bambusa spp.              India, Burma,Brazil	    31 - 150+
Chusquea spp.             Jamaica, Chile,Brazil        15 - 34
Dendrocalamus spp.        India, Burma       	    15 - 117
Phyllostachys spp.        China, Japan        	    13 - 120      

      The  responses observed in P. bambusoides follow logically when
you know the size of the crop. Though the reports may be extreme
(remember, Janzen's trying to make a case) seed crops 5-6 inches deep
(a solid layer of seeds) below parental stalks are observed. Larger
seeded species prevented accurate surveys by endangering the workers;
seeds fell in such profusion that equipment was damaged and workers
      This level of mast crop production is a partial explanation for
the observed life history. A crop of this proportion can satiate seed
predators, and therefore permit some of the seeds to escape predation
to establish the next generation. But why is the masting cycle 1)so
long and 2) so tight in timing? The explanation for length and tight
timing, both under genetic control, comes, in part, from the effect
of the seed predators. There will be relative synchrony in flowering
in bamboos because they are wind-pollinated and apparently obligate
outcrossers. That alone would impose local synchrony; it would cause
high levels of local pollen flow, but severly limit genetic exchange
between demes. Seed predators sharpen that synchrony, and impose it
over larger geographical areas. Janzen argues that plants which
anticipate the mast year (say by one year) are unlikely to produce
sufficient seed to satiate seed predators. However, predator
populations are likely to be of moderate size, since there has been
no recent mast crop, and it's possible that a few seeds might escape.
those that delay until after the mast year will face insurmountable
problems. They face predation from a fully expanded predator
population (from both functional and numerical responses), and are
very unlikely to escape seed predation. Seed crops of these plants
will be wiped out. Only man, by lazily harvesting only when its easy,
i.e. during the mast year, may select against synchrony. The loss of
genotypes which flower slightly out of synchrony explains why the
masting cycle is so tight. (Note again the potential effect of
artificial  selection, working against this pattern). It should be
mentioned that mast year crops don't, in nature, wait around for slow-
witted predators.  They germinate quite rapidly, and seedlings are
not heavily predated.
      The question of long inter-mast periods remains. How does an interval
of approximately 120 years evolve?  Janzen hypothesizes a scenario
that begins with an annually iteroparous bamboo, representing the
most common life history among bamboo species. Since seed predators
are common, and escape of seed rare (unpredictable reproductive
success), an individual that switched to semelparity (a chance
mutation within the population) and was able to produce a much larger
seed crop might satiate the local, numerically adapted population  of
seed predators and increase the number of seeds escaping  predation.
Its larger seed crop means that among escapees, offspring of the
semelparous mutant will slowly increase their proportion in the
population.  This, of course, occurring at the expense of parental
death.  Janzen believed this switch would likely have been successful
only in the tropics. Predictable rainy seasons would bring escape
through germination, and the commonness of territoriality among seed
predator species would limit local numerical responses. Once
semelparous,  mutations  which produce delay  will be selected for
against the 'wild-type'(iteroparous) parental stock. The  longer
these new mutants wait, the larger their  energy reserves, seed
output, and success compared to whatever increases in predation they
draw to the seed crop of the parental+mutant population. When the
iteroparous parental stock has been completely replaced, slight
further shifts in alpha are strongly selected against. This follows
from the explanation for why timing is so tight. Tails of the
distribution of seed production are more completely devoured than the
peak, since seed predator adaptations are designed for mast
reproduction.  We now have a semelparous population with a moderate
(??) inter-mast period. How are extremely long inter-mast intervals 
achieved?  By doubling  the previous period. Such a mutation permits 
the bearer to produce larger numbers of seeds than those who lack it, 
yet achieves the  buffering (protection) of producing seed simultaneous  
with the parental populations. The same kind of advantage that led to the
switch to semelparity now leads to replacement by a doubled-population.  
Toward the end of the replacement process, selection against the parental 
stock may be quite strong.
      Although details may differ, predator satiation is also  argued
to  be  the  mechanism by which periodical cicadas evolved (Lloyd  and
Dybas  1966).  Thus  the  basic  ideas  of  evolution  of  long-lived
perennial semelparity are not unique to bamboos, after all.
      To fully consider the possible reasons for delayed reproduction
in bamboos, it's important to recognize there may be reasons  other
than  seed  predator satiation. Most 'tree-like' plants  increase  in
biomass logistically. The relative growth rate (the realized  'r'  or
growth rate per head) declines with size and age, since height growth
and structural tissue is supported by a 'crown' of photosynthetic
leaves  which reach a 'relatively' constant biomass. That's not  true
of  bamboos.  They are grasses, reproducing vegetatively  to  produce
large  clumps (genets) in which each culm (ramet) grows to full adult
height, producing a full adult compliment of leaves and maintaining a
green  stem.  Thus  photosynthetic and support  tissues  increase  in
parallel,  and  genet  growth remains exponential  over  an  extended
period.  That  means  that  the  biomass  potentially  available  for
allocation  to  reproduction  also  continues  to  increase   rapidly
(exponentially) until mast seeding.
      How much reproduction are we talking about? You already have an
image  of  the  total seed crop beneath synchronized, mast  flowering
bamboos.  To indicate how common such species are Gadgil  and  Prasad
(1984)  found  that  70  of 72 Indian bamboo species  were  perennial
monocarps,  but  that only 8 were synchronized over  wide  geographic
areas.  The  basic life history is, therefore, common,  but  Janzen's
arguments of the importance of mobile seed predators in producing and
synchronizing  it possibly less common. Can the idea  of  exponential
growth increasing seed production without reference to predators also
explain a massive mast reproduction.  Let's consider it on the  basis
of  flowering  per  adult stem. Flowers on grasses are  organized  on
spikes,  with  a spike of flowers at each node (the slightly  thicker
rings  on  a  piece  of dried bamboo). Gadgil found  in  one  of  the
synchronized,   mast  flowering  species,  Bambusa  arundinacea   the
following flowering rates:

                    65 flower bearing nodes/ramet
                         x 133 spikes per node
                         x 156 flowers per spike
             = 1.3 x 106 flowers/culm at mast flowering
                         x 50-200 culms/genet

Even  with  the  limitations of wind pollination, 24%  of  seeds  had
developed endosperm, resulting in 150-800 Kg of seeds/genet,  and  an
allocation of biomass to reproduction of between 20-30%. Not only  is
the  total impressive, but the allocation to reproduction in  bamboos
is  far higher than in trees (usually at most a few percent). This is
without  reference to predators. Both 'stories', taken together  make
the advantage of delayed, mast flowering clear.

Cactus flower re-visited - but not the movie
Optimization  of  fitness  as maximization  of  the  sum  of  current
reproduction  and  residual  reproductive  value.  Curves  predicting
semelparity are concave; those predicting iteroparity are convex.
      Are predator satiation and/or clonal growth the only mechanisms
which  can  produce  perennial monocarpy?  Not if interpretations  of
life history forces in Agaves are correct.  Schaffer, in a series  of
papers  with many coauthors, came to the conclusion that, in  theory,
any  species should maximize the sum of current fecundity (or mx) and
expected  future  reproductive value (which can  be  determined  from
proprtional  survivorship and reproductive  value  of  the  next  age
class,  i.e. px and Vi+1). Graphing these two components on  separate
axes,  a  maximum is achieved by greatest distance from  the  origin.
Maximization  of the sum is, of course, the way to maximize  fitness.
If  the curve is concave, maximum distance from the origin is at  one
of  the  end  points,  i.e.  either  retain  all  energy  for  future
reproduction,  or use all available energy.  Concave  curves  produce
semelparity,  with  delay  if,  early  on,  expectation   of   future
reproduction  exceed possible present offspring  production.   Convex
curves  produce  iteroparity,  with  partial  allocation  to  present
      How  can  this fit with Janzen's (or Gadgil's) explanation  for
bamboos. An intermediate reproductive effort (and iteroparity)  might
be  swallowed up, literally and figuratively, by seed predators,  but
the  percentage  seed  set  increases with bi  through  satiation  in
Janzen's  view. Gadgil notes that until genet 'senescence', at  least
in  growth  rate, the expectation of future reproduction with  clonal
growth   markedly  exceeds  present  reproductive  output  potential.
Neither of these is what the Schaffer's see in Agaves. Instead,  they
argue that optimal foraging by pollinators will maximize the seed set
of  individuals  making the largest reproductive effort.  This,  too,
selects for semelparity in isolated, individual Agave plants.  If  it
costs a pollinator considerable energetic output to get from isolated
plant to isolated plant, he should logically choose those which offer
the most food for the least flight cost, i.e. those with more flowers
(or  greater  reproductive effort from the plant's  point  of  view).
That's  just  optimal  foraging in a  very  simple  form.  Now,  what
evidence  is there that Agaves are pollinated by foragers functioning
optimally, and that optimal foraging leads to delayed semelparity?

     a)  At  least for the group of semelparous Agaves, but  not  for
     congeneric iteroparous species, there is a significant  positive
     correlation  between the percent of flowers  which  successfully
     produce fruit and the size of the inflorescence. Note that  this
     is  not  a  correlation with total flower number. The number  of
     fruits  would logically increase with number. This is a  tougher
     challenge.  The  positive  correlation  is  with  percentage  of
     flowers  developing fruit. This corresponds to  the  curvilinear
     profit function associated with semelparity.

     b) The same conclusion can be reached from the opposite point of
     view,  i.e. from the point of view of pollinator behaviour.  The
     number  of  pollinators observed on a plant  per  centimeter  of
     inflorescence   was  positively  correlated  with  inflorescence
     length  (which  is proportional to the number of flowers).  More
     pollinators  were  attracted to each  flower  in  larger  floral
     displays. This correlation was larger in semelparous species  of
     agave than in iteroparous ones, even though the same pollinator,
     Bombus  sonoris,  works both semelparous  and  iterparous  agave
     species.  An  interesting,  but  unanswered  question,  is   why
     pollinator  selectivity  should  be  different  in  agaves  with
     differing   life  histories  when  the  flowers  look  virtually

Are There Semelparous Mammals?
      Thus  far  two  long-lived semelparous  plants  have  been  the
examples  of  life histories representing exceptions to the  patterns
expected  a  priori. We expect semelparous species to be short-lived.
At  the  same time, we expect mammals, relative to other land animals
usually  considered K-types, to be long-lived and  iteroparous,  with
typically  Deevey type I survivorship curves. Thus equally exotic  is
the  idea of a short-lived, semelparous mammal. There is at least one
exception  of  this type, a marsupial mouse genus,  Antechinus,  from
Australia. Species within the genus vary in life history. Females  of
all  species  are iteroparous; at least moderate numbers  survive  to
reproduce  in  a  second year. Males differ among species.  Some  are
similarly  iteroparous.  Those species  live  in  the  tropical  rain
forests of New Guinea, where resources are predictably available,  or
in  arid  central  Australia, where resource availability  is  highly
unpredictable. In the former conditions, much like the  situation  in
mature forests, adult survivorship is relatively predictable as well.
However,   with  populations  consistently  near  carrying  capacity,
juvenile  success is not well assured. Whether you want  to  consider
Murphy's model of the predictability of success or compare the P  and
C  for  these  populations, the predicted and  observed  strategy  is
iteroparity.  With extremely unpredictable resources, as  in  central
Australia,   the  argument  can  be  made  that  adults   are   'more
experienced'  and  'better  buffered'  from  stored  energy   against
unpredictability.  Lump this together as a hypothesis  of  tolerance.
Once more, therefore, P is much larger than C and iteroparity appears
to  be  the  predicted strategy. More evidence about the survivorship
patterns in these populations would help to overcome hand-waving, but
it hasn't, to my knowledge, been collected.
      Other  species, however, have semelparous males. They occur  in
highly   predictable,  but  highly  seasonal  environments;  forests,
woodlands and heaths of coastal forest regions along much of  eastern
and  southern  Australia  support these species.  Their  reproductive
cycles are strongly adapted to the seasonal pattern. The period  from
gestation through lactation takes about 4 months, and weaning  occurs
between  November  and February, i.e. during the southern  hemisphere
summer. If an additional cycle of reproduction were to occur during a
single  year,  as  it does in other, ecologically similar,  placental
(eutherian)  mammals  in similar temperate environments,  the  longer
cycle  in  the marsupial would place maximum resource demands  at  an
inappropriate  time (winter) with respect to resource  abundance.  At
the time of lactation and weaning for the second brood there would be
little insect (the key food) abundance to support it.
      Given  limited survivorship of males to reproduce in  a  second
year  in  a seasonal environment, it's possible that selection  could
(and/or  should) maximize reproductive effort in the first  year  for
these marsupials. If there is to be but one chance to reproduce,  the
behavioural  responses of Antechinus males, and the  consequences  of
the behaviour pattern, become logical. At the time of breeding, males
become  highly aggressive and disperse widely. Dominant males sire  a
great preponderance of the offspring, and others are driven off.  The
effort  required to achieve dominance is very high. The  relationship
between  effort and reproductive success is, therefore, very  shallow
(approximately  0 success at low to medium effort)  then  rises  very
steeply  at the right hand (high effort) side of a graph.  This  cost
curve  is  one  which  predicts  semelparity.  Associated  with   the
increased  aggressiveness is increqased adrenocortical  activity.  By
the  end  of the mating season males suffer from a form of the  Selye
stress  syndrome.  As was hypothesized to explain microtine  cycling,
the  stress  syndrome  means that there  is  a  lack  of  appropriate
response to normal levels of stress - the protective kind of response
-  as  well  as immune suppressive responses associated with  adrenal
hormone titre changes, and complete regression of the testes.  While,
in theory, males could survive to a second year, in practice no males
survive the post-reproductive period.
     There is also an interesting corollary to this in the energetics
and resource availability which result from male semelparity. Females
raise  their litters in the absence of an adult male population,  and
thus  in  the  absence of food requirements to support  those  males.
Litter  sizes  can therefore be larger, as well as the  size  of  the
littermates,  in species with semelparous males. Does  the  shift  in
size fit with the basic hypotheses formulated by Cole in constructing
the  paradox, or with the modifications made to improve  reality?  Is
there  a  sufficient increase in litter size for these  'semelparous'
males  to  match  the population growth of an iterparous  Antechinus?
Larger litter sizes are consistently observed in the male-semelparous
Antechinus  species, with average litter size in the range  of  10-12
young,  than in iteroparous congeners, with litter sizes from  <8-10.
Now  compare  with  the paradox.   for Antechinus  is  1  year.  Pre-reproductive  survivorship is considerably less  than  1,  but  in  a
highly seasonal environment the adult survivorship is also much  less
than  1  if  the  species were iteroparous. Thus, there  is  a  rough
simiilarity to the scheme Cole used to construct the paradox, and  an
appropriately  larger  litter size,  i.e.  1  or  2  larger,  in  the
semelparous species to achieve approximately equal population growth.
So  we  finish this section hjaving found that Cole's paradox is  not
only  correct in theory, but may have a parallel 'proof' in the  real


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