When genes go to sleep: the population genetic consequences of seed dormancy and monocarpic perenniality.

Abstract

In many annual plant populations, seeds may be dormant for several seasons before they germinate. Here, we investigate the consequences of both conditional (dispersed seeds cannot enter a dormant stage) and unconditional seed dormancy on the amount and the distribution of neutral genetic diversity within and among populations. We present joint demographic and population genetics models for single and subdivided populations and derive the effective size and population differentiation at both local and metapopulation scales. We suggest that a Wahlund effect is unlikely to result from age structure alone. Furthermore, the differentiation among populations is decreased by the presence of seed banks. We also extend these models to describe monocarpic (semelparous) perennial life cycle, where the nonreproductive stages are vegetative rosettes instead of dormant seeds. The main difference between the models relies in the way the density-dependent regulation is acting. The effective size of monocarpic perennial species may be less than the census number of individuals, and among-population differentiation is always larger than in annual species. We discuss our results in the light of recent population genetics surveys of annual plants with seed banks.

Full text

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vol. 163, no. 2the american naturalistfebruary 2004
?
When Genes Go to Sleep: The Population Genetic
Consequences of Seed Dormancy and
Monocarpic Perenniality
Renaud Vitalis,1,2,*Sylvain Gle ´min,1,3,†and Isabelle Olivieri1,‡
1. Laboratoire Ge ´ne ´tique et Environnement, C.C. 065, Institut des
Sciences de l’E´volution de Montpellier, Universite ´ Montpellier II,
34095 Montpellier Cedex 05, France;
2. Station Biologique de la Tour du Valat, Le Sambuc, 13200 Arles,
France;
3. Station de Ge ´ne ´tique et Ame ´lioration des Plantes, Institut
National de la Recherche Agronomique de Montpellier, Domaine
de Melgueil, 34130 Mauguio, France
Submitted January 27, 2003; Accepted August 20, 2003;
Electronically published February 13, 2004
Online enhancements: appendixes.
abstract: In many annual plant populations, seeds may be dor-
mant for several seasons before they germinate. Here, we investigate
the consequences of both conditional (dispersed seeds cannot enter
a dormant stage) and unconditional seed dormancy on the amount
and the distribution of neutral genetic diversity within and among
populations. We present joint demographic and population genetics
models for single and subdivided populations and derivetheeffective
size and population differentiation at both local and metapopulation
scales. We suggest that a Wahlund effect is unlikely to result from
age structure alone. Furthermore, the differentiation among popu-
lations is decreased by the presence of seed banks. We also extend
these models to describe monocarpic (semelparous) perennial life
cycle, where the nonreproductivestagesarevegetativerosettesinstead
of dormant seeds. The main difference between the models relies in
the way the density-dependent regulation is acting. The effective size
* Corresponding author. Present address: School of Biological Sciences,Royal
Holloway, University of London, Egham, Surrey TW200EX, UnitedKingdom;
e-mail: renaud.vitalis@rhul.ac.uk.
†Present address: Laboratoire Ge ´nome, Populations, Interactions, Adapta-
tion, Universite ´ Montpellier II—Institut Franc ¸ais de Recherche pour
l’Exploitation de la Mer—Centre National de la Recherche Scientifique, Unite ´
Mixte de Recherche 5000, Universite ´ Montpellier II, 34095 MontpellierCedex
05, France; e-mail: glemin@univ-montp2.fr.
‡E-mail: olivieri@isem.univ-montp2.fr.
Am. Nat. 2004. Vol. 163, pp. 295–311. ? 2004 by The University of Chicago.
0003-0147/2004/16302-30023$15.00. All rights reserved.
of monocarpic perennial species may be less than the census number
of individuals, and among-population differentiation is always larger
than in annual species. We discuss our results in the light of recent
population genetics surveys of annual plants with seed banks.
Keywords: age structure, effective size, F statistics, IBD probabilities,
monocarpy, seed banks.
Seed dormancy is defined by the transitory inability of
mature seeds to germinate. Yet this simple statement en-
compasses different processes (Leopold 1996), and this
inactive phase may be the result of at least three phenom-
ena called innate, secondary, and enforced dormancy
(Harper 1977). Innate dormancy prevents seeds from ger-
minating onto the maternal plant; secondary (induced)
dormancy refers to the alteration of seed germination abil-
ity, induced by some environmental factor (e.g., burial,
chilling) experienced by seeds after maturation; and en-
forced dormancy characterizes the incapacity of seeds to
germinate when one or several essential requirements for
germination (e.g., light, water resource, oxygen) are lack-
ing (Rees 1997). In plant populations, prolonged seed dor-
mancy (beyond 1 yr) builds up the so-called seed banks
(Harper 1977), that is, pools of seeds that remain dormant
in the soil. Commonly found among plant species, dor-
mancy also exists in some insects, where diapausing eggs
may play the same role as dormant seeds (De Stasio 1989;
Weider et al. 1997).
Whatever the exact physiological processes involved,
seed dormancy is an important life-history trait that pro-
foundly influences plant population dynamics. In plant
communities living in habitats where many sites are avail-
able for recruitment each year, high germination rateshave
evolved, and seeds rarely dorm beyond 1 yr (Watkinson
1990; Rees 1996). In those communities, species exist as
seeds for only a short period of the year, and the resulting
seed bank does not last more than a single year. But in
other plant communities such as those consisting of, for
example, annuals in deserts (Venable et al. 1993) oraquatic

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296The American Naturalist
plants in temporary marshes (van der Valk and Davis
1978), prolonged seed dormancy has evolved so that seed
banks may persist for more than 1 yr. Many models have
been devoted to the evolution of seed dormancy (see Oli-
vieri 2001 for a review). Those models rely on the rationale
that dormancy, like dispersal, prevents the risk of extinc-
tion (Pacala 1986) and enables seedlings to escape from
competition with both relatives and nonrelatives (Venable
and Brown 1988, 1993; Rees 1996). Seed dormancy also
dampens oscillatory dynamics in variable environments
(Caswell and Hastings 1980; Thrall et al. 1989; Crawley
and Rees 1996), as partially evidenced in the field (Kalisz
1991; Kalisz and McPeek 1992; Jarry et al. 1995). More
strikingly, it has been shown that during a 35-yr survey
in grassland remnants of the Swiss Jura mountains, species
with longer-lived seeds in the soil had lower rates of local
extinction than did species with shorter-livedseeds(Sto ¨ck-
lin and Fischer 1999).
What are the consequence of seed dormancy for pop-
ulation genetics? Adaptive genetic polymorphism is ex-
pected to be more easily maintained in temporally varying
environments if the emergence of seedlings is delayed
through time (Hedrick 1995). Yet the presence of seed or
egg banks generally slows down the rate of evolutionary
change (Templeton and Levin 1979; Brown and Venable
1986; Hairston and De Stasio 1988). Seed dormancy may
also greatly influence the level and the distribution of neu-
tral genetic variation in natural populations. This has been
recognized recently in several articles where the authors
compared the levels of allozyme variation among seeds
collected in the soil and flowering plants (Tonsor et al.
1993; Alvarez-Buylla et al. 1996; Cabin 1996; Cabin et al.
1998; McCue and Holtsford 1998; Mahy et al. 1999). Be-
sides this empirical evidence, there have been a few at-
tempts to formalize the idea that seed banks may influence
the rate of loss of neutral polymorphism. Kaj et al. (2001)
developed a coalescent theory for single populations of
annual organisms with seed or egg banks and showed that
age structure causes a decrease in the coalescent rate; Nun-
ney (2002) derived the effective size of single populations
of annual plants with seed dormancy as the product of
the number of adult plants and the average time to ger-
mination. Here, we provide a full framework to derive not
only the asymptotic effective population size (for both
single and subdivided populations) but also the expected
values of F statistics in order to determine the extent of
genetic differentiation within and among populations. In
particular, we link an explicit demographic model to the
transition equations between probabilities of identity by
descent for any pair of genes sampled in the population,
as suggestedbyRousset(1999a). Wealsodistinguishpollen
from seed dispersal and highlight some consequences of
conditional dormancy strategies (i.e., when dormancy is
conditioned on seed philopatry).
The life cycle of an annual species with a seed bank is
very similar to that of a monocarpic perennial plant that
lacks seed dormancy (and, more generally, to that of a
semelparous species with discrete breeding seasons; see,
e.g., Nunney 2002; Waples 2002). Vegetative rosettes play
the same role as the seed bank in the establishment of
overlapping generations (Templeton and Levin 1979).
Therefore, we also examine equivalent models for mono-
carpic perennial plants and derive the expected level and
distribution of genetic variation in such species. We show
that the way the density-dependent regulation is acting has
important consequences for effective population size and
differentiation.
Life Cycle in Single Populations
Annual Plants with Seed Banks
Here, we present an age-classified model for a single pop-
ulation of an annual plant species with seed dormancy.
We assume that the flowering plants represent the first
stage of the life cycle and that the life cycle is further
classified into n more stages that represent dormant seeds
of increasing age (n is the maximum age a seed can attain,
after which it dies). Considering a finite maximum life
span for dormant seeds is an addition to Nunney’s (2002)
model. We use a time interval of 1yrtodescribethechange
in class abundances. For the sake of clarity, the notation
used throughout this paper is given in table 1.
Each year, flowering plants produce r seeds per capita.
Among those seeds, a fraction g germinates the following
year, while a fraction(1 ? g)
state. The dormant seeds incur acost cd, and onlyafraction
of them survive. Also, the following year, seeds(1 ? c )
d
in the bank may either germinate at rate g or stay in a
dormant state and incur further costs with probability
. Note that Nunney (2002) considered the (1 ? g)(1 ? c )
d
probability of seed persistence in the bank from year to
year to be, that is, assuming no cost of seed
n { (1 ? g)
dormancy. The complete life cycle graph is shown in figure
1A. We assume that density acts on the survival of seed-
lings. Among all the seedlings produced at the beginning
of the season, only a fixed number of them survive to
adulthood. Let r be the total number of competing seed-
lings that are produced each time step per capita; that is,
?
ip1
of seeds reaches a dormant
n
i
r { rg 1 ?
[(1 ? g)(1 ? c )] . (1)
d
{}
Let
Tbe the column
N(t) p (N (t), …, N(t), …, N (t))
0in

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Age-Structured Population Genetics297
Table 1: Summary of main parameter notations
NotationParameter definition
as
bs
ap
bp
a
b
cd
cz
g
mp
ms
m
n
nd
N
NT
pi
p
r
s
z
Qh
Qh
Rh
Rh
(i, j)
Sh
T
Probability that two seeds sampled in a deme come from a single deme
Probability that two seeds sampled in different demes come from a single deme
Probability that two pollen grains sampled in a deme come from a single deme
Probability that two pollen grains sampled in different demes come from a single deme
Probability that two genes sampled in a deme after pollen dispersal come from a single deme
Probability that two genes sampled in different demes after pollen dispersal come from a single deme
Mortality rate of seeds (or rosettes)
Cost of dispersal
Germination rate (or flowering rate in the monocarpic perennial model)
Pollen backward immigration rate
Seed backward immigration rate
Mutation rate
Maximum longevity of seeds (i.e., number of age classes in the seed bank)
Number of demes in the island model
Number of flowering plants
Total number of individuals (adults plus rosettes) in the monocarpic perennial model
Probability that a seed germinating from the seed bank is i years old
Proportion of individuals born from seeds produced in the previous generation
Net fecundity
Selfing rate
Forward seed dispersal rate
IBD probability of pairs of genes in adults after pollen dispersal
IBD probability for pairs of genes in adults after seed dispersal
IBD probability between a gene in an adult and a gene in a seed after pollen dispersal
IBD probability between a gene in an adult and a gene in a seed after seed dispersal
IBD probability for pairs of genes in seeds
Generation time
?
?(i)
(i)
vector of age-class abundances at time t (here, the super-
script T denotes the transpose of a vector). The change in
abundance during the time step
recurrence of the form
N(t ? 1) p FN(t)
population projection matrix (see Caswell 2001). This
matrix reads(n ? 1) # (n ? 1)
is given by a
, where
(t, t ? 1)
is the
F
…
…
…
5
…
rg/r
g/r
0
g/r
0
0
_
g/r
0
0 v .
_
0






r(1 ? g)(1 ? c )
0
_
0
d
F p
(1 ? g)(1 ? c )
d
0 (1 ? g)(1 ? c )
d
(2)
In our particular case,
referred to as a Leslie matrix (Leslie 1945). All the elements
in the first row of the matrix have been divided by r to
account for the density-dependent regulation acting on
seedling survival. With the density dependent regulation
considered here, the population is stationary, that is, the
leading eigenvalue of
F p 1
vector
˜
˜˜
N p (N , …, N , …, N )
0i
, gives the stationary distribution of class abun-
˜˜
N p FN
dances (Caswell 2001). In the following, we use the no-
is an age-classified matrix, also
F
. The dominant right eigen-
Tof, which satisfies
˜
F
n
tation
Tedious but straightforward algebra shows that
for the stationary number of adult plants.
˜
N { N0
i
˜N p rN[(1 ? g)(1 ? c )],
i
(3)
d
for
F
ability from age class j to age class i. To derive the recur-
rence equations that describe the change in the probabil-
ities of identity between pairs of genes, we need to know
the probabilities of common origin for random pairs of
genes and therefore the probabilities of origin of individ-
uals. Let us define B as the matrix of backwardequilibrium
transition probabilities. The
, gives the probability that an individual in age classb(jFi)
i atwas in age class j at t; that is,t ? 1
. Then, B may then be written as
˜˜
jk
k
to n. Letdenote the
gives the forward transition prob-
th element ofi p 1
. By definition,
f(iFj)(i, j)
f(iFj)
th element of B, noted(i, j)
b(jFi) p
f(iFj)N /? f(iFk)N
…
…
…
5
…






p (1 ? p)p
1
(1 ? p)p (1 ? p)p
0
0
_
0
1n?1n
0
1
0
0
_
1
B p 0,(4)
_
00

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298The American Naturalist
Figure 1: A, Life cycle graph for single populations of an annual plant
species with a seed bank or a monocarpic perennial species. Each circle
represents an age class, and the Ni’s represent the age class abundances.
The transitions between classes are represented as arrows, and the tran-
sition probabilities are given. B, Life cycle graph for a subdivided pop-
ulation of an annual plant species with a seed bank and conditional
dormancy. For the sake of clarity, only two demes are represented. C,
Life cycle graph for a subdivided population of an annual plant species
with a seed bank and unconditional dormancy or a monocarpic (sem-
elparous) perennial species. See table 1 for the main parameternotations.
where
1 ? (1 ? g)(1 ? c )
1 ? [(1 ? g)(1 ? c )]
d
p p
(5)
n?1
d
gives the fraction of flowering plantsthatcomesfromseeds
produced in the previous time step (and thus
the fraction of flowering plants born from seeds that come
from the seed bank) and
gives[1 ? p]
1 ? (1 ? g)(1 ? c )
1 ? [(1 ? g)(1 ? c )]
d
i?1
p p
i
[(1 ? g)(1 ? c )](6)
d
n
d
gives the conditional probability that among the pool of
seeds that germinate from the seed bank, a seed is i years
old.
The flowering plants that are issued from seeds pro-
duced in the previous generation are 1 yr old. Those that
are issued from i-year-old seeds have an age of
Therefore, the mean time to seed germination (generation
time) is
ip1
.i ? 1
; that is,
n
T p p ? (1 ? p)?
(i ? 1)pi
1
T p 1 ? n ?1 ? (1 ? g)(1 ? c )
d
1 ? n
?
.(7)
n?1
1 ? [(1 ? g)(1 ? c )]
d
With infinitely long seed longevity, lim
, which reduces to (1 ? g)(1 ? c )]
d
absence of any cost to seed dormancy, as in the model
proposed by Nunney (2002).
(T) p 1/[1 ?
(T) p 1/g
nr?
in thelim
nr?
Monocarpic Perennial Plants
As it has already been suggested (see, e.g., Nunney 2002;
Waples 2002), the life cycle of annual plants with a seed
bank is closely related to the life cycle of monocarpic pe-
rennial plants or semelparous animal species (i.e., long-
lived species that reproduce only once in their lifetime).
In the following, we therefore reinterpret the model pre-
sented above as an age-classified model for a single pop-
ulation of a monocarpic perennial plant species. We still
assume that the flowering plants represent the first stage
of the life cycle and that the life cycle is further classified
into n more stages that now represent vegetative rosettes
of increasing age. Again, we use a time interval of 1 yr to
describe the change in class abundances. Each year, the
flowering plants produce r seeds per capita and then die.
All seeds germinate at the beginning of the next year and
start growing. A fraction g of them produces flowering
plants, while a fraction(1 ? g)
settes. The rosettes survive with probability
rosettes from previous years may either produce flowering
plants at rategorstayinavegetativestateandincurfurther
costs with probability(1 ? g)(1 ? c )
sistent with the graph shown in figure 1A, with
the number of flowering plants and
of i-year-old rosettes.
In this model, however, we assume that the density de-
pendence acts on the survival of newborn individuals. All
the seedlings produced at the beginning of the season are
in competition, and only a fraction of them survive to
produces vegetative ro-
(1 ? c ) . Also,
d
. This life cycle is con-
N (t)
being thenumberN(t)
i
d
being
0

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Age-Structured Population Genetics299
either the flowering stage or to the 1-yr-old vegetative
rosette stage. The projection matrix reads
…
…
…
5
…
rg/r
g
0
g
0
0
_
g
0
0 .






r(1 ? g)(1 ? c )/r
0
_
0
d
F p
(1 ? g)(1 ? c )
d
_
0 (1 ? g)(1 ? c ) 0
d
(8)
In this model, r gives the number of newly produced
individuals each year per capita and has the same form as
in equation (1). Here, the fertility terms of the matrix F
(i.e., the first elements of the first two rows) have been
divided by r. It is worth noting that both models (annual
and perennial) assume that competition occurs only
among the seedlings. However, the annual model has
density-dependent regulation in all the germination terms
(all the elements of the first row in
rennial model has density-dependent regulation only in
the fertility terms of.
F
With the form of density-dependent regulation consid-
ered here, the population is stationary. We note N is the
first element of the dominant right eigenvector
we assume that the total number of plants (flowering
adults plus rosettes) that can possibly grow is fixed and
equals , thenNT
), whereas the pe-
F
of. If
˜N
F
˜
N { N p
0
n?1n?1
g 1 ? (1 ? g)
[
(1 ? c )
]
d
N ,
T
n?1n?1
1 ? (1 ? g)c ? (1 ? g)(1 ? g)
d
(1 ? c )
d
(9)
which reduces toas andN p gN /[1 ? (1 ? g)c ]
T
n r ?
d
i
˜N p rN[(1 ? g)(1 ? c )]/r.
i
(10)
d
The matrix B of backward transition probabilities has the
same form as in the previous model and is given by equa-
tion (4). In the monocarpic model, however, p must be
interpreted as the fraction of flowering plants born from
seeds produced in the previous time step and
the fraction of flowering plants that come from vegetative
rosette stages.
as (1 ? p)
Genetic Variation in Single Populations
Identity by Descent
In this section, we formulate a population genetics model
on the basis of the age-classified models. The purpose is
twofold. First, we want to derive from this model the
effective population size of an annual species with a seed
bank and a monocarpic perennial species. Second, wewant
to predict the expected genetic differentiation within pop-
ulation of such species. To do so, we describe the change
in the probabilities of identity by descent between pairs
of genes.
A fraction s of the offspring is produced by selfing. We
define the selfing rate s as the probability that two ho-
mologous gene copies of one individual come from the
same parent. With, individuals reproduce at ran-s p 1/N
dom (panmixia). After reproduction, individuals produce
seeds. Seeds germinate, seedlings grow, and genes are sam-
pled among flowering plants. Among those, a fraction
comes from the seed bank (or from vegetative(1 ? p)
rosettes in the monocarpic model), and a fraction p has
been produced in the previous generation (see eq. [5]).
The number of offspring produced each time step is as-
sumed to be very large (infinite), and the random number
of offspring that descend from a single parent is binomially
distributed (Nagylaki 1995). Therefore, an offspring is
equally likely to descend from any of the N individuals
reproducing in the population.
We note Q0is the probability that the two copies of a
gene sampled within an individual are identical by descent
(IBD); Q1is the IBD probability between two gene copies
sampled from two seedlings in the population;
probability that a gene sampled among the seedlings after
seed dispersal is IBD to a gene sampled in an i-aged seed;
is the probability that two homologous gene copies
S0
within a i-aged seed are IBD; and
ability between two gene copies sampled among one i-
aged seed and one j-aged seed. We assume an infinite allele
model (IAM) for mutation. The recurrence equations that
describe the changes in IBD probabilities over one time
step are detailed in appendix A in the online edition of
the American Naturalist. Note that the same set of equa-
tions stands for both the annual model with seed banks
and the monocarpic perennial model.
is the
(i)
R1
(i)
is the IBD prob-
(i,j)
S1
Effective Population Size
Gene identity probabilities are tightly related to coales-
cence times (Male ´cot 1975; Slatkin 1991; Rousset 1996),
and the largest eigenvalue l of the transition matrix that
gives the gain in IBD probabilities is related to the as-
ymptotic rate of coalescence between gene lineages, as
, where Nedenotes the effective popula-
l p 1 ? (2N )
e
tion size (e.g., Ewens 1979, 1982; Whitlock and Barton
1997). In class-structured models, effective populationsize
has been defined as
e
eq. [48]), where n is the number of classes, Niis the size
of class i, andis the sum over all possible (kl) pairs of
kii
?1
(Rousset 1999a,
n
ip1
?1
N { (?
k /N)
iii