Mario Pineda-Krch Department of Theoretical Ecology, Ecology Building, S-223 62 Lund, Sweden. Tel.: +46 46 222 4142; fax: +46 46 222 3766; e-mail: Mario.Pineda@teorekol.lu.se
In the absence of sexual recombination somatic mutations represent the only source of genetic variation in clonally propagating plants. We analyse the probability of such somatic mutations in the shoot apical meristem being fixed in descendant generations of meristems. A model of meristem cell dynamics is presented for the unstratified shoot apical meristem. The fate of one mutant initial is studied for a two- and three-celled shoot apical meristem. The main parameters of the model are the number of apical initials, the time between selection cycles, number of selection cycles and cell viability of the mutant genotype. As the number of mitotic divisions per selection cycle and number of selection cycles increases the chimeric state dissipates and the probability of mutation fixation approaches an asymptote. The value of this fixation asymptote depends primarily on cell viability, while the time to reach it is mainly influenced by the total number of mitotic divisions as well as the number of initials.
In contrast to the presumed operation of Muller’s Ratchet in plants the chimeric state may represent an opportunity for deleterious mutations to be eliminated through intraorganismal selection or random drift. We conclude that intraorganismal selection not only can be a substantial force for the elimination of deleterious mutations, but also can have the potential to confer an evolutionary change through a meristematic cell lineage alone.
Meristems are mitotically derived undifferentiated cell lineages that are unique to vascular plants. The activity in these cell lineages results in primary growth which gives rise to all differentiated plant structures as well as to the basic plant form. In plant species with facultative or obligate clonal reproduction, meristems also give rise to vegetatively produced offspring – ramets – i.e. they link lineages of mitotically derived descendant individuals.
We build on a stochastic model for meristem growth previously employed by Klekowski & Kazarinova-Fukshansky (1984a, b). They simulated the long-term retention of different categories of somatic mutations for various types of shoot-apical meristems and showed that intraorganismal selection could have a large influence on the fate of somatic mutations. One of their conclusions was that many apical meristem organizations in higher plants are not very adept at losing deleterious somatic mutations, some, namely stratified meristems, even promote the long-term accumulation of mutations due to the operation of Muller’s Ratchet ( Klekowski et al., 1985 ). We adapt their model of an unstratified shoot apical meristem to the case of ramet production in vegetatively propagating plants.
Outline of meristem ontogeny
Shoot-apical meristems sensu stricto (cf. Romberger et al., 1993 , p.225) can generally be divided into two main types, structured and stochastic meristems, both of which are based on one or several initial cells that are the ultimate source of all cells in the shoot. Structured meristems are characterized by a deterministic perpetuation of the initial function of an initial cell, i.e. after mitosis of the initial cell one daughter cell always remains undifferentiated and functions as the subsesquent initial ( Steward, 1978; Klekowski, 1988). This type of meristem is mostly found in certain vascular cryptogams (Pteridophytes) ( Klekowski et al., 1985 ). In contrast, stochastic meristems have a population of initial cells within which the initial function perpetuates to some of the cells ( Antolin & Strobeck, 1985). This process is stochastic or probabilistic rather than deterministic ( Romberger et al., 1993 ). This type of meristem is predominant among seed plants (Spermatophyta) (cf. Klekowski et al., 1985 ; Otto & Orive, 1995).
We define cell fitness as the mean cell generation time, i.e. the average time required for all of the cells in the lineage to divide once. Thus if τ is the number of time units between subsequent selection cycles (τ= 1,2,3,…) and μw and μm are the mean generation time for the wildtype and the mutant, then the number of wildtype cells at time of selection is 2τ/μw and the number of mutant cells is 2τ/μm. μw can be expressed as a function of μm as μw=μmγ where γ is the difference between the wildtype’s and the mutant’s generation time (0≤γ). If 0<γ<1 the mutant has a longer generation time than the wildtype, and thus a lowered fitness relative to the wildtype while if γ>1 the mutant has a shorter generation time than the wildtype and an increased relative fitness. If we norm μw to 1 we obtain 2τγ mutant cells and 2τ wildtype cells.
Let α be the number of initials and i the number of mutant cells, where α>1 and i≤α. Then i2τγ is the number of mutant cells and (α−i)2τ is the number of wild type cells at time of selection. The total number of cells in the cell pool is then i2τγ+(α−i)2τ.
The number of potentially realizable states attainable by the system after the first selection cycle is α+1. However, for α>2 certain states may not be attainable due to there being too few cells of a given genotype to enable transition to all conceivable states j, i.e. i2τγ<j or (α−i)2τ<(α−j) (cf. the case when α=3). The states are segregated into two homogeneous states, one wild type (mutation loss) and one mutant (mutation fixation), and α−1 heterogeneous states (chimeric). Since the meristem behaves according to a set of constant transition probabilities among the possibles states (α+1), the sequence of successive states can be described as a stationary or time homogeneous Markov chain (cf. Mailette, 1990).
Let Pij be the probability of transition of the system from state i to state j. Then P=[Pij] where 0<i,j<α. Pij can also be interpreted as the transition probability from a state with i mutant cells to a state with j mutant cells. State 0 and α are absorbing since they are genetically homogeneous and cannot contribute to any other state, thus P00 and Pαα always equal 1.
The elements Pij are given by the hypergeometric distribution
The denominator is the total number of different possibilities to choose α new apical initials from a pool of i2τγ+(α−i)2τ cells where 0<α≤(α−i)2τ+i2τγ. The first factor of the numerator is the number of possibilities to choose α−j wildtypes from (α−i)2τ wildtype cells where 0<(α−j)≤(α−i)2τ and the second factor is the number of possibilities to choose j mutants from a pool of i2τγ mutants where 0<j≤i2τγ.
The general transition matrix for an α-state system is
Since empirical observations suggest that each component meristem holds between two and four initial cells ( Steeves & Sussex, 1989; Uhrig et al., 1997 ) we will here limit our analysis to α=2, α=3, and only briefly mention the trends for α>3.
Shoot apical meristem with α = 2
Assuming α=2 the transition matrix P (eqn 2) for this three-state system (Fig. 2) is
The states (0, 1 and 2) are defined as state 0 being wildtype, state 1 chimerical and state 2 mutation fixation (Fig. 2). By substituting i and j in eqn 1 the following transition probabilities are obtained (P22 and P11 are excluded since states 0 and 2 are absorbing)
Equations 4–6 can be simplified to
The limiting properties of the above elements in P when the number of selection cycles, n, grows are
For simplicity P10, P11 and P12 are denoted Pw, Pc and Pm. The corresponding limiting properties are Pm*, Pc* (which always equal zero) and Pw*. Thus we obtain
Shoot apical meristem with α = 3
Assuming α=3 the transition matrix P (eqn 2) for this four-state system is
where P13=0 if 2τγ<3 and P20=0 if τ=1 since there are too few cells of a given genotype to enable transitions to all conceivable states (cf. Fig. 2). The individual transition probabilities are derived from eqn 1 and simplified (cf. eqns 4–6) in the same manner as for α=2 (cf. eqns 7–9). Due to the cumbersome expressions we will not present the details here.
Assuming we start with one mutant initial (i=1) the limiting property of P is thus
Results and discussion
Our qualitative results show that a somatic mutation in one of the initial cells in the shoot apical meristem can go to fixation rapidly ( Figs 3 and 4). The probability and time to fixation depend on the number of apical initials (α), the time between each selection cycle (τ) and the difference in generation time (γ) between the wildtype and the mutant cell lineage. The most notable tendencies for both α=2 and α=3 is the dissipation of the chimeric condition ( Figs 3 and 4) with increasing number of selection cycles (n). For a given γ both α and τ influence the number of selection cycles n that it takes to reach Pm*.
Although γ potentially does not have an upper limit we have, however, for our purposes, limited γ to 1.3. It would not be of interest to let γ→∞ since the probability of fixation of the cell lineage asymptotically approaches 1. Moreover, a large difference in generation time between wildtype and mutant cell lineages increases the likelihood of intercellular interactions due to, for example, spatial constraints and resource limitations, which are outside the scope of this study.
Although our model only considers the fate of one single mutation, not the accumulation of recurrent mutations, it is still valid in the case of recurrent mutations as long as the mutation rates are sufficiently low. Otto & Orive (1995) showed that when mutation rates are low (approximately one somatic mutation per individual organism generation) recurrent mutations are of little importance. At low mutation rates (per cell generation) it is unlikely that more than one mutation will accumulate in the shoot apex prior to homogenization of the meristem, either by fixation of the mutant or by reverting to the wildtype state. Otto & Orive (1995) adapted the model by Klekowski & Kazarinova-Fukshansky (1984b) to include recurrent mutations that arise continuously. Their results showed that even weak selection among cell lineages, i.e. slightly deleterious mutations, acts strongly to reduce the mutation load under the assumption that a high mutation load entails an increased probability of extinction of a population ( Haigh, 1978; Lynch & Gabriel, 1990), thus reducing both the frequency of deleterious mutants and the observable mutation rate. These results agree well both with Klekowski and Kazarinova-Fukshansky’s results as well as ours.
The tacit assumption in the genetic mosaicism hypothesis is, however, that the mutations are transferred to the progeny through sexual reproduction only ( Whitham & Slobodchikoff, 1981; Callaghan et al., 1992 ), since vegetatively derived progeny are assumed to be ‘necessarily genetically identical with their parents’ ( Bell & Coombe, 1971, p.205). Thus, the prevailing view holds that a genetically unique individual, a genet, arises through sexual reproduction alone and that physically independent clones represent fragmented growth ( Harper, 1981).
Since the only source of new genetic variation in obligately asexual plants is somatic mutations, such plants were for a long time associated with low levels of genetic diversity ( Stebbins, 1941, 1950; Gustafsson, 1947; Bell & Coombe, 1971; Callaghan et al., 1992 ). Recent studies have shown that clonal plant populations often hold at least as much genetic diversity as sexually reproducing populations ( Ellstrand & Roose, 1987; Hamrick & Godt, 1989; Lindeskog, 1995; Widén et al., 1994 ). Some studies even demonstrate a higher genetic variation in clonal plant populations (cf. Silander, 1983). This variation is, however, assumed to be interclonal variation since plants belonging to the same clone are assumed to have no variation. In stoloniferous and rhizomatous plants, where the clones exist as physically separated units, it is often difficult to determine which clones have a common zygotic origin and it is assumed that plants that are genetically different have separate origins. There have been few attempts to measure genetic variability within plants, although the few studies that have been conducted suggest considerable genetic diversity within individuals ( Lewis et al., 1971 ; Klekowski, 1984). To find out the evolutionary role of somatic mutations within and between individuals, studies of levels of intraorganismal (organism in the physical sense) and intraclonal (physically separated clones) genetic variation are essential. Slatkin (1985) partly expressed the same idea although he, like many others, only mentioned the possibility of evolutionary change taking place within an individual – not between.
Our qualitative results indicate that somatic mutations could be an additional mechanism for such high levels of genetic variation and that this variation could potentially confer an evolutionary change without involving a meiotic cycle. Thus, such variation may not be due solely to the operation of Muller’s Ratchet, nor solely to the presence of hidden sexual reproduction ( Fagerström et al., 1998 ), but also to somatic mutations penetrating the population through meristematic cell lineages. In this case the prevailing thought that clones are genetically identical by descent does not necessarily hold.
We challenge this view in qualitative terms because evolutionary change sensu lato may be defined as the transition between two genetically unique, but different individuals, one being ancestral and one descendant. There is no need for sexual reproduction for this broader definition to apply.
Our study shows that there is a high probability of an advantageous somatic mutation going to fixation through a mitotic cell lineage in the presence of intraorganismal selection. Thus, as Fagerström et al. (1998 ) highlight, genetically different individuals may originate through a succession of chimeric ramet generations without involving sexual reproduction. While sexual reproduction confers a potential for ‘instant’ mutation fixation, i.e. a mutation in the germ line may either become fixed in the succeeding generation or lost through meiosis, the meristem in vegetative reproduction goes through a number of intermediate chimeric states prior to either mutation fixation or mutation loss. How often mutation fixation occurs depends on both the mutation rate and the extent of intraorganismal selection. The rapid fixation of either the wild type or the mutant arises in part because the mutation process is not explicitly modelled. With mutation as a continual process, there would be a mutation-selection or selection-drift equilibrium, with potentially different dynamics that could include the chimeric state at equilibrium. Several authors suggest that this rate may be higher than expected in plants ( Antolin & Strobeck, 1985; Charlesworth, 1989). Although the study of chimeric plants ( Steward, 1978; Whitham & Slobodchikoff, 1981; Buss, 1983; Sutherland & Watkinson, 1986) has provided the best evidence for intraorganismal selection among cell lineages, particularly for disadvantageous mutations (e.g. loss of function such as chlorophyll deficiency in variegated plants), the extent and evolutionary importance of intraorganismal selection in plants cannot be comprehensively assessed until further studies are conducted ( Sutherland & Watkinson, 1986; Otto & Orive, 1995). The issue is not as much ‘Do plants evolve differently?’ ( Sutherland & Watkinson, 1986) but rather how do plants evolve differently?
Our results suggest that deleterious mutations in the shoot apical meristem will, assuming the mutant trait is expressed at the cellular level, have a high probability of becoming eliminated through intraorganismal selection or through random drift (γ=1, i.e. when the mutant trait is selectively neutral at the cellular level). This stands in contrast to the presumed accumulation of deleterious mutations due to Muller’s Ratchet in asexual populations ( Haigh, 1978; Bell, 1988; Judson & Normark, 1996).
Traits expressed later in ontogeny, and at a different level of selection, will not be affected by the process of intraorganismal selection. Adding a second level of selection, e.g. the level of the ramet, leads to a 2×2 classification scheme, +/+,+/−,−/+,−/−, with the effect of the mutation on the cell given to the left and the effect of the mutation on the ramet given to the right ( Michod, 1996). Of these combinations, −/− mutations are trivial; they will go extinct. Mutations that by luck benefit both the fitness of cells and the fitness of whole ramets (+/+) will sweep through the population, the interesting problems being to understand the dynamics of this process. The most challenging cases are effects of conflicting multilevel selection, i.e. +/−, a cancer-like situation that can potentially threaten the developmental integrity of the ramet, and −/+, which implies that cells sacrifice fitness for the benefit of the whole ramet. Thus, a mutant cell genotype with a lower growth rate than the wildtype can potentially invade, provided it has fitness-increasing effects on the ramet level. Such mechanisms are likely to be instrumental in the evolution of developmental programmes and differentiation.
This article has benefited from discussions with Torbjörn Säll and Richard Michod. We are grateful to Anders Brodin and Kari Lehtilä for critical reading of the manuscript and Ziad Taib for helpful discussions and constructive criticism on the mathematical part of the manuscript. We also thank two anonymous referees for their comments. This work was partially financed by grants from the Royal Swedish Academy of Science.