doi: 10.1111/j.1420-9101.2007.01475.x
SHORT COMMUNICATION
One big, and many small reasons that direct selection on offspring
number is still open for discussion
A. M. SIMONS
Department of Biology, Carleton University, Ottawa, ON, Canada
Keywords:
Abstract
bet hedging;
diversification strategy;
life-history evolution;
offspring size–number trade-off;
risk spreading;
stochastic environment.
In a recent paper, I proposed that natural selection should act to increase
offspring number when diversification bet hedging is favoured. The simple
underlying reasoning is that a target diversification strategy is more reliably
generated with increasing sample size. The intention of opening a discussion
has been realized; recent criticisms of the idea argue that selection does not act
to increase offspring number when population size is large or infinite. Here I
agree that criticisms have merit; indeed they are largely confined to the
caveats discussed in my original paper. The critique, however, implies a verdict
of outright rejection of the idea of selection on offspring number, which would
be erroneous. Contrary to the assertions of the criticism, then, the importance
of selection acting directly on offspring number remains an open question.
Introduction
A foundational concept of life-history theory is that of
the tradeoff:allocation of finite resources is partitioned
among competing life-history characters such that fitness
is maximized (Roff, 1992). Evolutionary tradeoffs result
when selection favours a simultaneous increase in two
(or more) characters in the presence of a negative genetic
correlation between them. Perhaps because of its relative
tractability, the tradeoff between offspring size and
number (Smith & Fretwell, 1974) has become the
standard theoretical and empirical example. The perception of this tradeoff has been limited to considerations of
the selective consequences of offspring size under particular ecological scenarios whereas offspring number has
been viewed exclusively as the fecundity resulting
directly from the tradeoff. However, in an earlier paper
(Simons, 2007), I proposed ecological situations in which
parental fitness may be directly affected by offspring
number.
The reasoning is as follows. Environmental unpredictability is expected to select for bet-hedging (Slatkin,
1974) strategies: traits that appear to be suboptimal over
short timescales, but maximize geometric mean fitness
Correspondence: A. M. Simons, Department of Biology, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, Canada K1S 5B6.
Tel.: (613) 520-2600 ext. 3869; fax: (613) 520-3539;
e-mail: asimons@connect.carleton.ca
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among generations (Seger & Brockmann, 1987). Diversification in the timing of seed germination (Cohen,
1966) is a classic example. An assumption not under
dispute here, and one for which we have some empirical
evidence (Simons & Johnston, 2006), is that individual
offspring phenotypes represent random draws from,
rather than individually programmed elements of a
putative diversification strategy. Given the existence of
an optimal diversification strategy – that is to say, one
that maximizes long-term fitness – the realization of this
diversification strategy improves with the number of
offspring produced. I showed that sample variance
approaches the ‘target’ variance with increasing sample
size (see Fig. 1 of Simons, 2007). The clear intent of my
original note was to propose the idea that, to the extent
that environmental unpredictably favours diversification
bet hedging, direct selection to increase allocation to
offspring number merits consideration (Simons, 2007).
I included a simulation model as a tentative illustration of
the concept. As is stated explicitly, ‘the simulation results
are meant only as a qualitative demonstration of the
effect of offspring number on geometric-mean fitness’
(Simons, 2007); quantitative assessments of the importance of the concept are thus neglected, and open for
future analysis.
As anticipated, the original paper prompted discussion
about the evolution of increased offspring number as a
bet-hedging mechanism: discussion includes an extensive critique (Kisdi, 2007) published in this journal.
ª 2007 THE AUTHOR. J. EVOL. BIOL. 21 (2008) 642–645
JOURNAL COMPILATION ª 2007 EUROPEAN SOCIETY FOR EVOLUTIONARY BIOLOGY
Selection on offspring number
Although it provides an excellent analysis of particular
limitations of the idea, it leaves the reader with the
mistaken impression that it has discarded the idea
outright. Here I show that despite an acknowledgement
that increased offspring number may evolve in small
populations, the critique focuses almost exclusively on
large populations, a condition I pronounced in my
original paper as less likely to result in selection for
increased number. Furthermore, I reveal errors of logic in
the criticism, including the unintended inference that a
hypothesis should be rejected because it has not been
tested. The most consequential problem is the hasty
conclusion drawn, which propagates the impression that
the proposal of selection on offspring number is ‘incorrect’, and that the issue is therefore closed. This is the one
big reason that, properly framed, the critique in fact
constitutes a valuable opening discussion.
Large populations
The critique (Kisdi, 2007) sets out to show that selection
does not act directly on offspring number when population size is large, not that it never acts. The ‘large
population’ qualification is expressly made in the
critique’s title, is clearly stated in the Abstract, specified
diligently again in the Introduction, and the main body
of the critique falls under the heading, ‘Large populations’. The critique shows that, in large populations, the
strength of selection on offspring number is weakened
because average fitness for a genotype should be
calculated not just for offspring of an individual parent,
but over offspring of all representatives of that genotype. The criticism is compelling, and is valuable in that
it shows that the potential for the evolution of offspring
number is restricted when populations are infinite or
large.
My original paper, however, makes no specific claim
about the applicability of direct selection for offspring
number when populations are large, although this is
what would be understood by reading Kisdi’s criticism.
The statement in the critique’s Abstract, ‘Contrary to a
recent article by A.M. Simons (2007; J. Evol. Biol.
20:813–817), I show that selection does not favour the
production of many offspring just to reduce sampling
variability when such mixed strategies are used in large
populations’ carries the unfortunate implication that
I restricted my discussion to large populations. Construed
this way, an outright rejection of my proposal seems
reasonable: ‘In this note, I set up a simple analytical
model to show that Simons’ (2007) claim is incorrect and
that in large populations there is no direct selection on
offspring number due to sampling stochasticity’ (Kisdi,
2007). Because its application is restricted to the arena of
infinite or large populations, Kisdi’s assertion – that my
general claim is incorrect – is unwarranted.
Furthermore, without going back to my original paper,
the reader would not be aware that I agree; I state quite
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specifically that selection on offspring number is more
likely to occur in small populations:
Diversification must be manifested at the individual
level to confer a bet-hedging advantage to a genotype, and this is most obvious for small populations,
or in cases where population size fluctuates widely
among generations. Under such situations, in which
a genotype is represented by only one or a few
individuals, the possibility that diversification can be
expressed collectively among individuals of the same
genotype is reduced (Simons, 2007).
The main point of the critique is thus weakened
considerably when understood to mean that direct
selection on offspring number is unlikely to apply under
the conditions that I have specifically outlined as those
under which it is less likely to apply.
Note that I not only specify that selection on offspring
number is expected to be stronger when population size
is small, but also raise the point that it is influenced by
demographic fluctuations. Real populations are not only
finite, but are subject to demographic fluctuation. This is
of paramount importance to the discussion most obviously because effective population size is smaller than
census size but, more importantly, because of the
negative covariance expected between population size
and selection for bet-hedging strategies: it is a defining
feature of bet-hedging traits that they confer nonzero
fitness through strong selective episodes. The monocarpic
plant I originally used to illustrate the concept, Lobelia
inflata (Campanulaceae), also provides a good example
here in that in 2005 an intense search turned up only five
reproductive individuals whereas one hundred to several
hundred were found in preceding (Simons & Johnston,
2003) and subsequent years. The model of infinite
population size unavoidably ignores this point of critical
importance to the evolution of offspring number in real
populations.
Finite populations
The critique has shown that selection for offspring
number is unlikely under assumptions of infinite or
permanently large populations. The arguments for large
populations, however, do not apply to populations in
which number of offspring ‘cannot be considered to be
infinite’ (Kisdi, 2007). In finite populations, the argument against selection on offspring number centres on
the applicability of the geometric-mean principle. The
contention that the geometric mean is ‘useless’ as a
measure of fitness when population size n is finite (Kisdi,
2007) rests on the fact that if n is finite, there is a
nonzero, positive probability of 100% mortality in any
generation, and thus all strategies go to extinction with
probability 1 given infinite time.
In my simulation (Simons, 2007) I used finite population size, and did not allow infinite time. It is correctly
pointed out that, as a result, at least some of the replicate
ª 2007 THE AUTHOR. J. EVOL. BIOL. 21 (2008) 642–645
JOURNAL COMPILATION ª 2007 EUROPEAN SOCIETY FOR EVOLUTIONARY BIOLOGY
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A. M. SIMONS
runs of my model must have resulted in zero geometricmean fitness, and that this was hidden by the fact that I
plotted only the average of 100 runs of the model to
provide the best estimate of geometric-mean fitness
associated with each value of offspring number. In
response, I provide here the proportions of simulation
runs that resulted in zero geometric-mean fitness
(Fig. 1). However, as expected based on foundational
bet-hedging theory (Lewontin & Cohen, 1969), these
trends in the proportion of runs resulting in extinction
corroborate the finding that increased offspring number
may be under direct selection in small populations.
Although true that all finite populations are destined for
extinction under the assumption of infinite time, crucial
information is overlooked: for all time less than infinity,
bet-hedging strategies reduce the likelihood of extinction. It is the assumption of infinite time rather than the
usefulness of the geometric-mean principle that causes
the failure of the analysis for finite populations. Furthermore, regardless of the resolution of the issue of the
usefulness of the geometric mean, a conclusion that my
proposal (Simons, 2007) is incorrect is based on unsound
logic. Specifically, it would be based on the notion that
the absence of an analysis for finite populations in some
way justifies a rejection of the idea of selection on
offspring number in toto.
% Replicate runs with zero GM fitness
100
80
60
40
20
0
0
5
10
15
20
25
Offspring number
30
100
Fig. 1 The effect of offspring number on the frequency of simulation runs for which geometric-mean fitness is zero for offspring
numbers ranging from two to 100. A diversification strategy of
SD = 12 days in the timing of seed germination or egg hatch is
assumed, and the quality of the environment within a season varies
randomly. The % runs of zero fitness is based on 100 estimates of
geometric-mean fitness over 30 growing seasons for each offspring
number. For a full explanation of the simulation model, which
illustrated the effect of offspring number on geometric-mean fitness,
see Simons (2007).
Still, an important issue has been raised: what is the
correct time scale over which to assess optimality of a
bet-hedging strategy? Consider these relevant facts: life
persists on this planet, life has evolved over a finite
period, all populations are finite, and all extant life is a
result of a process of reproduction that is inherently
multiplicative. A deduction that follows directly from
these facts is that extant life is a biased subsample that
represents only and all those forms that have proven to
have nonzero geometric-mean fitness. How do we
reconcile this fact with analytical results that show all
strategies are expected to have zero geometric-mean
fitness? The answer lies not only in recognizing the
difference between prior and post hoc probabilities and by
rejecting the notion of infinite time, but also in considering the evolutionary dynamics of real populations. It
becomes meaningless to calculate the fitness associated
with a particular heritable trait over greater and greater
periods of evolutionary time as mutation and recombination alter the identity of the ‘trait’ of interest (for a full
discussion of the geometric-mean principle in hierarchical selection, see Simons, 2002). However, because
biologically relevant environmental variance is thought
to be characterized by 1 ⁄ f noise, or ‘reddened’ temporal
spectra (Ariño & Pimm, 1995; Halley, 1996), use of too
short a time scale certainly incurs a risk of overlooking a
rare, severe event that might cause extinction. It is on the
balance between these considerations that I chose to
evaluate the geometric-mean fitness over 30 generations
in my illustration. Because diversification reduces the
probability of extinction (Fig. 1) in my model of finite
populations, increasing this time period would in fact
cause stronger selection for increased offspring number.
The explicit intent of my simulation was to demonstrate the plausibility of the idea: ‘This optimality
approach is a first step toward an understanding of the
selective advantage of increased offspring number, and
does not pretend to detail its evolutionary dynamics. For
example, the rate of evolution toward the optimal
balance between offspring number and size will depend
not only on the magnitude of fluctuating selection, but
also on the quantitative genetic basis of diversification
and demographic properties of the population’ (Simons,
2007). In fact the critique acknowledges that, in principle, selection for increased offspring number can occur in
finite populations, but that neither participant in the
discussion so far has employed appropriate techniques
(See references in Kisdi, 2007) to answer the question.
Conclusions
It would be premature to presume, from a demonstration
that my original model does not apply under particular
circumstances, that the discussion of direct selection on
offspring number is closed. Rather, Kisdi’s critique,
interpreted correctly, is encouraging in that it should be
taken to mark the beginning of this discussion. The
ª 2007 THE AUTHOR. J. EVOL. BIOL. 21 (2008) 642–645
JOURNAL COMPILATION ª 2007 EUROPEAN SOCIETY FOR EVOLUTIONARY BIOLOGY
Selection on offspring number
proposal that direct selection on offspring number alters
the optimal balance with offspring size (Simons, 2007) is
in essence qualitative; no quantitative claim of the
importance of this effect relative to other influences on
the tradeoff are made. Kisdi (2007) acknowledges the
potential for ‘weak’ selection on offspring number, ‘but
only in finite populations’. However, because this is
an indefinite quantitative claim, the strength of the
constraints on the general applicability of selection on
offspring number remains unknown. Evidence that it is
not universally applicable is not inconsistent with the
proposal, but does make a valid claim constraining its
applicability. If future research finds that diversification
bet hedging is selected for predominantly in consistently
large populations, we can conclude that the original
proposal is universally unimportant. On the other hand,
future analyses may show that selection for diversification accounts in part for the evolution of high propagule
number in small populations or in populations subject to
demographic fluctuations. The conclusion from my
original note bears repetition here: the degree to which
fluctuating selection influences the evolution of propagule number provides fertile ground for future study.
Acknowledgments
The author thanks M.O. Johnston and J.-G. Godin for
helpful comments. This research is supported by an
NSERC Discovery grant to A.M.S.
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Received 30 October 2007; accepted 8 November 2007
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JOURNAL COMPILATION ª 2007 EUROPEAN SOCIETY FOR EVOLUTIONARY BIOLOGY