Effects of Colonization Processes on Genetic Diversity: Differences Between Annual Plants and Tree Species

Corresponding author: Frédéric Austerlitz, Rm. 152, ENRS Bldg., 14 College Farm Rd., Rutgers University, New Brunswick, NJ 08901-8551., austerlitz{at}aesop.rutgers.edu (E-mail)

Communicating editor: R. G. SHAW

	ABSTRACT

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX A APPENDIX B LITERATURE CITED

Tree species are striking for their high within-population diversity and low among-population differentiation for nuclear genes. In contrast, annual plants show much more differentiation for nuclear genes but much less diversity than trees. The usual explanation for this difference is that pollen flow, and therefore gene flow, is much higher for trees. This explanation is problematic because it relies on equilibrium hypotheses. Because trees have very recently recolonized temperate areas, they have experienced many foundation events, which usually reduce within-population diversity and increase differentiation. Only extremely high levels of gene flow could counterbalance these successive founder effects. We develop a model to study the impact of life cycle of forest trees, in particular of the length of their juvenile phase, on genetic diversity and differentiation during the glacial period and the following colonization period. We show that both a reasonably high level of pollen flow and the life-cycle characteristics of trees are needed to explain the observed structure of genetic diversity. We also show that gene flow and life cycle both have an impact on maternally inherited cytoplasmic genes, which are characterized both in trees and annual species by much less diversity and much more differentiation than nuclear genes.

THE present distribution of genetic variability in forest tree species is peculiar. Isozyme data, collected by HAMRICK et al. 1992 and HAMRICK and GODT 1996 on a large number of species, indicate that trees maintain a significantly higher level of genetic diversity within species (0.177 on average) and within populations (0.148 on average) than annual plants (respectively 0.154 and 0.101 on average) for nuclear genes. Forest trees also show a lower level of genetic differentiation among populations, measured with G_ST (NEI 1973 ), a coefficient of gene differentiation equivalent to WRIGHT's (1951) F_ST: 0.084 on average for woody long-lived perennial species and 0.355 on average for annual plants. The low differentiation observed with isozymes has recently been confirmed by molecular data for several species (for instance, the oak Quercus petraea; LE CORRE et al. 1997A ).

Analysis with cytoplasmic markers of chloroplast DNA, which is maternally inherited in most angiosperms, gives completely different results: a clear geographic structure is observed. For two European species of oaks, the estimations of G_ST are 0.905 for Q. robur and 0.925 for Q. petraea (PETIT et al. 1993A ). Comparable values are given for various tree species in ENNOS 1994 . Genetic structure is clearly much higher for maternally inherited cytoplasmic markers than for nuclear ones. Data on the structure of cytoplasmic genetic diversity in annual or short-lived plants are very rare. For Silene alba, a short-lived perennial, F_ST is 0.613 for chloroplast genes and 0.128 for nuclear genes on a regional scale in a recently colonized region (MCCAULEY 1994 , MCCAULEY 1997 ). The values are, respectively, 0.624 and 0.222 for S. vulgaris (MCCAULEY 1998 ). There are also few data for paternally inherited chloroplast genes in gymnosperms. They usually show much less differentiation than maternally inherited mitochondrial genes (DONG and WAGNER 1994 ; LATTA and MITTON 1997 ).

The high within-population diversity and low differentiation of trees' nuclear genes is unexpected. During the last glacial period of ~100,000 years (ANDERSEN and BORNS 1994 ), tree species from the Northern Hemisphere were confined to a few southern refuges completely isolated from one another. About 15,000 years ago, they began to recolonize all temperate areas and some species have only recently reached their modern range limits (HUNTLEY and BIRKS 1983 ; HUNTLEY 1990 ). As pointed out by KREMER 1994 , because of trees' long life span, there have been only 100–1000 generations (depending on the species) since the end of the last glacial period. Our previous results (AUSTERLITZ et al. 1997 ) showed that the successive foundation events that occur during colonization yield a strong genetic differentiation and low within-population diversity, especially in populations far from refuges. This is the classically denoted founder effect: the loss of diversity in newly founded populations due to a small number of founders.

Various authors have experimentally investigated the impact of recent colonization events on genetic diversity, both on annual plants and tree species, on a more local scale. They show that colonization events usually yield strong founder effects in plant species (WESTERBERGH and SAURA 1994 ; RAYBOULD et al. 1996 ), but it is not the case for several tree species (MARIETTE et al. 1997 ; RASPE and JACQUEMART 1998 ).

The usual explanation for the limited differentiation of nuclear genes in trees and for their high differentiation for maternally inherited cytoplasmic genes is that there is much more migration through pollen than through seeds. ENNOS 1994 showed that the difference between nuclear and cytoplasmic gene differentiation in oaks could be explained by a 200:1 ratio between gene flow through pollen and seeds, respectively. Nevertheless, his results are calculated for an island model at equilibrium. Equilibrium hypotheses seem unrealistic because recolonization is recent for forest tree species, and an island model on the scale of most temperate areas is doubtful. To be more realistic, LE CORRE 1997 simulated the process of European recolonization with a two-dimensional (2D) stepping-stone model with nonoverlapping generations. To explain the observed F_ST values, she had to take an even higher ratio of pollen flow vs. seed flow.

None of these studies take into account an important feature of tree species. Unlike short-lived annual and perennial plant species, trees have a long life span and grow vegetatively for a long period before reproduction. Birches, alders, elms, and poplars reproduce at ~10 years; maples and chestnuts between 20 and 30 years; and oaks and beeches at ~50 years. Great longevity, several age or size classes, overlapping generations, and a long juvenile phase are the main characteristics of the life cycle of trees.

The first aim of this article is to show the impact of this life-cycle difference between trees and short-lived plants on genetic diversity and population structure during colonization. Our hypothesis is that due to the duration of the juvenile phase, a newly founded tree population will grow for many years only through the arrival of new migrants, increasing the number of founders of a population and therefore decreasing the founder effect. The second aim is to study the impact of the persistence of several refuges, isolated from one another during the glacial period.

We develop a Markovian approach that follows the evolution of genetic structure for nuclear and maternally inherited cytoplasmic genes of plants with a tree life cycle during and after a colonization period, following long isolation. Our colonization starts from one or several refuges and is one- or two-dimensional. In previous models of tree populations, only long generation time was taken into account, trees being thus modeled as semelparous long-lived plants with no overlap between generations (bamboo-like models; PETIT et al. 1993B ; ENNOS 1994 ; LE CORRE et al. 1997B ). Here trees are also characterized by a juvenile phase and overlapping generations. They are compared with plants having no juvenile phase or nonoverlapping generations, with either a 1-year generation (annual plants) or the same generation time as trees. In the latter case, all plants in a cohort reproduce and die simultaneously. This corresponds to "trees" as modeled in previous studies, but not to any existing plant, and it allows us to characterize the effect of life cycle independently of generation length. To also separate the effects of life cycle from other effects, all the comparisons are made with the same effective size, the same amount of gene flow through seeds and pollen, and the same population growth rate.

	MATERIALS AND METHODS

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX A APPENDIX B LITERATURE CITED

Demographic model within each population:
We simulate a tree life cycle of several size classes and include a density-dependence factor. In classical models of population dynamics, the transition from one population state to another is based on a matrix that gives annual survival and reproduction rates. These models were originally used by LEWIS 1942 and LESLIE 1945 for human demography and dynamics of animal populations that were age structured.

They were adapted to populations of forest trees, either natural (for example, BOSCH 1971 ) or managed (USHER 1966 , USHER 1969 ). Following these models, we structured populations according to the size of the individuals rather than the age, as in LEFKOVITCH 1965 . If A is the annual transition matrix and N(t) and N(t + 1) are the vectors of the numbers of trees in each size class, respectively, at years t and t + 1, we write N(t + 1) = A · N(t).

where P_ii is the proportion of trees that stay alive and remain in class i from t to t + 1; P_ii+1 is the proportion of trees of class i that stay alive and move from the class of size i to i + 1 during the time interval t to t + 1; and f is the number of offspring per individual of the last class at each generation. Thus, we have k - 1 classes of juveniles and only one class of adult trees that can reproduce. The proportion of individuals that die in class i in one time unit is 1 - P_ii - P_ii+1.

However, models based on the Leslie matrix yield exponential growth or decrease of the size of each class, which is not realistic enough if long-term predictions are required. Therefore we include a density-dependent growth regulation function, adapted from BUONGIORNO et al. 1995 . This regulation acts as follows: when density increases, the probabilities of moving to the next class and fecundity decrease, whereas mortality increases. This is performed by assigning to the individuals of each class a given stand basal area (which is a measure of the space occupied by an individual). Then, at each time t, all P_ii+1 and f are multiplied by a reduction coefficient (t) (0 (t) 1), which is computed so that the total stand basal area of the whole population grows logistically to an equilibrium value (see details in Appendix A).

The demographic data available (see, for instance, BUONGIORNO and MICHIE 1980 ; HARCOMBE 1987 ) subdivide tree populations into a small number of classes and are very specific for a given species in a given area. Because we were interested in features that are common to all forest tree species, we chose parameters that were representative of the main characteristics of forest trees. The number of classes (k) is 25, so trees can never reproduce before the age of 25, and fecundity is high in the absence of density dependence (f = 250). The other parameters of the projection matrix A are given in Appendix A, and they were chosen so that at equilibrium an individual reaches the adult class on average at 50 years and the average age of the individuals in the adult class is 100 years. An important point of this model is that, for a newly founded population, due to low density, trees reaching the adult class are much younger. With the chosen parameter, tree populations are filled to carrying capacity within a few hundred years (i.e., a few generations).

The results obtained for trees are compared with those obtained for plants with no juvenile phase and nonoverlapping generations. For these plants, the population size at equilibrium is set at the effective size of tree populations at equilibrium (N_e), which is calculated using the method of ORIVE 1993 . These plants are modeled with a single class (k = 1). All individuals are born, reproduce, and die within a single generation (that is, P₁₁ = 0). The population grows logistically toward its equilibrium size. The initial growth rate r is directly related to the fecundity f: f = 1 + r. The generation time can be either 1 year (annual plants) or 100 years, which is approximately the generation time of trees in our model. Various values of the fecundity were tested: f = 1.01, 1.1, 1.5, or 3. It is difficult to compare precisely the growth of trees and plants with nonoverlapping generations. The value of 1.1 is the fecundity necessary for the population of annual plants to grow approximately at the same rate as trees, as defined in our model. The value of 3 is the corresponding value for the plants with nonoverlapping generations of 100 years. These values were determined by empirical comparison of the growth of stand basal area in both cases.

Colonization models:
In each case, we have a total of d populations connected by seed and pollen flow in a one- or two-dimensional stepping-stone model (see Fig 1).

View larger version (47K): In this window In a new window Download PPT slide   Figure 1. Schematic representation of the 1D and 2D colonization processes. In both cases, the arrows indicate the populations that are connected by gene flow through seeds and pollen. In the 1D colonization (A), only the first population is full and at demographic and genetic equilibrium; all other populations are empty. The simulation begins with the colonization of the second population, and one population is colonized subsequently every 100 years. In the 2D colonization (B), starting from a given value of differentiation, the three groups of four refuge populations drift independently, one from another, over 80,000 years (isolation period). Then the whole space is colonized in the y direction, one line of populations every 500 years (colonization period, which lasts 7000 years). Then, we let the system evolve until time t = 95,000 years is reached (postcolonization period).

We wanted to first study the interaction between the colonization process and tree life cycle from a theoretical point of view. We thus modeled colonization for a one-dimensional stepping-stone metapopulation (in which seeds and pollen migrate unidirectionally to the neighboring populations; see Fig 1A). At the beginning of a simulation, all sites are empty, except for the refuge, within which there is a population at demographic and genetic equilibrium (this is obtained by letting this population evolve alone until it reaches equilibrium). The total number of sites (d) is 15. Colonization is then one-dimensional and unidirectional. Every 100 years a new site is opened to colonization, as a consequence of progressive warming, making the total colonization period last 1400 years. Subsequently, we let the populations evolve after the colonization period until time t = 5000 years.

The second model of colonization is a two-dimensional stepping-stone model (see Fig 1B). Because the process is highly computer intensive, the total number of populations was set at only 102 (6 along the x-axis times 17 along the y-axis). We started with three refuge areas. In each refuge there were 4 populations. Several initial conditions for genetic diversity and differentiation were tested; in most cases we started with the expected equilibrium value for the 102 populations, connected by gene flow, as indicated. Before starting the colonization, we let the 12 populations evolve during 80,000 years (the average length of glacial periods, see HAYS et al. 1976 ; PAILLARD 1997 ), with no gene flow through seeds or pollen among them. After the isolation period, the colonization starts, with 1 new area of populations being open for colonization every 500 years. This new area consists of 6 populations on a line (see Fig 1B). This yields a colonization period of 7000 years. Then the populations evolve, remaining at their equilibrium size, for a postcolonization period of 8000 years. The entire process lasts 95,000 years. The length of the different periods is realistic (HUNTLEY and BIRKS 1983 ; KREMER 1994 ), but due to the limitations in the number of populations, the interval between two colonization events had to be long.

In each case the migration parameters are m_s and m_p, the proportion of seeds and pollen produced by the adults of a population p that exit the population. Migrants arrive with equal probability to each of the populations to which p is connected. Regulation by density dependence acts on migrant seeds in the population in which they arrive in the same way that it acts on local seeds.

Computation of genetic parameters:
The mutation rate is set at 10^-6 for nuclear and cytoplasmic genes. We use a Markovian approach to calculate the probabilities of identity by descent (IBD) iteratively from one generation to the next, assuming an infinite allele model. Time is expressed in units of years, except for the plants with long nonoverlapping generations, where it is expressed in units of generations. Individuals are diploid for their nuclear genes and haploid for their cytoplasmic ones, which are strictly maternally inherited. We assume a panmictic reproduction among all the individuals of the adult class. The probabilities f^c_p,i,q,j and fⁿ_p,i,q,j of identity by descent at time t for two cytoplasmic or nuclear genes belonging, respectively, to individuals of population p and class i and of population q and class j, are calculated iteratively every unit of time, after migration and reproduction occur, for all populations p and q that are not empty at time t and all classes i and j between 1 and k (see details in Appendix B). The following computations are the same for nuclear or cytoplasmic genes, and f_p,i,q,j denotes both f^c_p,i,q,j or fⁿ_p,i,q,j in this subsection.

The expected diversity H_p in each population p is then calculated as follows: H_p = 1 - f_p,p, where f_p,p is the average probability of identity by descent within population p,

where N_p,i is the number of individuals in each population p and each class i, and N_p is the total number of individuals in population p. This allows us to calculate the average within-population diversity H_S by averaging H_p over every population in , the set of populations that are not empty at time t. In the same way, we can calculate the average probability of identity by descent f_p,q for two genes chosen respectively in populations p and q, p q,

The average identity by descent f_T for two genes chosen in any population is then calculated

where d denotes the number of populations in . The expected global diversity is H_T = 1 - f_T and the expected F_ST can be deduced using F_ST = 1 - .

	RESULTS

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX A APPENDIX B LITERATURE CITED

Evolution of within-population diversity in the one-dimensional colonization process:
For annual plants (Fig 2A), there was very strong founder effect: diversity in each population decreased substantially during the first generations after each colonization event. A great proportion of diversity was lost due to founder effect but was then recovered relatively quickly. Fig 2A gives the case of no pollen flow. For the case of high pollen flow, the founder effect was almost of the same magnitude, but the recovery of diversity was much faster (data not shown).

View larger version (24K): In this window In a new window Download PPT slide   Figure 2. Within-population diversity of annual plants (A) and trees (B) for the first five populations of the 1D colonization process. The founder effect is much greater for annual plants than for trees. Parameters are as follows: ms = 0.0002, mp = 0, Ne = 1000, d = 15.

For trees, the situation was very different. Even with no pollen flow, the foundation event had a very limited effect: genetic diversity decreases only slightly in the newly founded populations (Fig 2B). Afterward, it increased only very slowly. Nevertheless, trees reached the same equilibrium value as annual plants after several hundred thousand years (data not shown). There was almost no founder effect and each founded population retained almost all the diversity of its ancestral population. Increasing pollen flows reduced the founder effect even further (data not shown).

Evolution of among-population differentiation (F_ST) in the one-dimensional colonization process:
For annual plants, F_ST strongly increased during the colonization period (Fig 3, A–C), followed by a gradual decrease and again a slow increase toward its equilibrium value. With N_e = 1000 and m_s = 0.0002, even in the case of high pollen flow (m_p = 0.01), F_ST for nuclear genes reached a maximum value of 0.13 (Fig 3A). This maximum value was higher when pollen flow decreased: 0.28 when m_p = 0 (Fig 3B). The value was 0.36 for cytoplasmic genes (Fig 3C).

View larger version (14K): In this window In a new window Download PPT slide   Figure 3. FST plotted against time since the beginning of the colonization period in the 1D colonization process, for trees (thin lines) and annual plants (thick lines), for nuclear genes (A and B), or maternally inherited cytoplasmic genes (C). In all cases, d = 15, ms = 0.0002, Ne = 1000. For nuclear genes, the pollen flow mp was, respectively, 0.01 (A) and 0.00 (B).

For trees, F_ST for nuclear genes increased only very slowly during the colonization period. It then increased even slower toward its equilibrium value, which was the same for trees and annual plants. Even with no pollen flow, the F_ST value at the end of the colonization period was only 0.036, much lower than the final equilibrium value. For cytoplasmic genes, the increase in differentiation was slightly larger in the colonization period, yielding an F_ST of 0.07 at the end of the period. Again, this value was much lower than the equilibrium value. In all cases the rate of increase of F_ST decreased during colonization. The founder effect was decreased for increasing fecundity of annual plants, but it remained higher than the one to which trees were subjected (result not shown).

Evolution of among-population differentiation (F_ST) in the two-dimensional colonization process:
Several features appeared when two-dimensional processes were taken into account (Fig 4).

View larger version (27K): In this window In a new window Download PPT slide   Figure 4. FST plotted against time for the 2D colonization process, with 6 x 17 populations (see details in MATERIALS AND METHODS), for trees (thin lines), and annual plants (thick lines). A, B, C, and D represent cases of nuclear genes with different values of the initial differentiation FST0 (which is in some cases the equilibrium value) and the others parameters. (A) ms = 0.0005, mp = 0.1, Ne = 1000, FST0 = 0.02 (equilibrium value); (B) ms = 0.0005, mp = 0.01, Ne = 1000, FST0 = 0.02; (C) ms = 0.0005, mp = 0.01, Ne = 1000, FST0 = 0.17 (equilibrium value); (D) ms = 0.005, mp = 0.1, Ne = 100, FST0 = 0.17 (equilibrium value). E and F correspond to cytoplasmic genes: (E) ms = 0.0005, Ne = 1000, FST0 = 0.82 (equilibrium value); (F) ms = 0.0005, Ne = 1000, FST0 = 0.17.

Nuclear genes: First, F_ST increased during the isolation period of 80,000 years. The increase was much stronger for annual plants in all cases. For example, in Fig 4A, with N_e = 1000, m_s = 0.0005, and m_p = 0.1, starting from equilibrium value, F_ST of nuclear genes only increased from 0.021 to 0.093 for trees during the isolation period, whereas for annual plants it increased from 0.021 to 0.92, having almost reached equilibrium.

For trees, the rate of increase during this isolation period depended slightly on pollen flow: if we started from 0.021, it increased up to 0.093 for m_p = 0.1 during the isolation period (Fig 4A) and up to 0.12 for m_p = 0.01 (Fig 4B). The rate of increase of F_ST during the isolation period depended much more on population effective size (N_e), when the comparisons were made with the same number of migrants (i.e., the same values of N_em_s and N_emm_p). For the nuclear genes of trees, with N_em_s = 0.5 and N_emm_p = 10, starting from the initial equilibrium value of F_ST of 0.17, F_ST increased only to 0.23 in 80,000 years when N_e = 1000 (Fig 4C), whereas when N_e = 100 it increased much more, to 0.63 (Fig 4D).

Second, F_ST for annual plants decreased during the colonization period that followed. For trees, it decreased with high pollen flow (Fig 4A) or low effective population size (Fig 4D); otherwise it increased slightly (Fig 4B and Fig C). Third, during the postcolonization period, there was a decrease of F_ST that was very sharp in the case of annual plants but smooth for trees. As a consequence, the F_ST for annual plants fell quickly below that of trees. The rate of decrease also depended on the effective population size, a smaller N_e making F_ST decrease much faster. Therefore, F_ST of annual plants declined almost immediately below that of trees in the case of N_e = 100 (Fig 4D).

Cytoplasmic genes: Concerning cytoplasmic genes (Fig 4E and Fig F), with an N_em_s of 0.5, the equilibrium value of F_ST was already very high, >0.8. If we started at t = 0 from this value (Fig 4E), the isolation period brought almost no change for trees, whereas it yielded an increase for annual plants. Then, as for nuclear genes, F_ST for annual plants fell rather quickly below that of trees.

However, if we started with an F_ST of 0.17 (Fig 4F), as for nuclear genes (Fig 4C), even with an N_e value of 1000, F_ST of trees for cytoplasmic genes increased much more than for nuclear genes during the isolation period. It increased even more sharply during the colonization period and then slowly approached the equilibrium.

Comparison with long-living plants with nonoverlapping generations in the two-dimensional colonization process:
For a plant with nonoverlapping generations and a generation time similar to that of trees, the isolation period had the same impact as on forest trees for nuclear (Fig 5) or cytoplasmic genes (data not shown). The colonization period yielded a stronger increase in F_ST of nuclear genes for the plant with nonoverlapping generations than that for the tree species. This difference was very low when pollen flow was very high (m_p = 0.1, Fig 5A). It was much higher and remained so long after the colonization period was over, when pollen flow had a lower value (m_p = 0.01, which still makes N_emm_p = 10, Fig 5B). Again, the founder effect decreased when increasing the fecundity of these plants, but it remained higher than that to which trees are subjected (results not shown).

View larger version (17K): In this window In a new window Download PPT slide   Figure 5. FST plotted against time for the 2D colonization process with 6 x 17 populations for trees (thin lines) and plants with nonoverlapping generations and the same generation length as trees (thick lines), with a fecundity f of 3. The given values correspond to nuclear genes with, for A, ms = 0.0005, mp = 0.1, Ne = 1000, FST0 = 0.02 (equilibrium value); and for B, ms = 0.0005, mp = 0.01, Ne = 1000, FST0 = 0.17 (equilibrium value).

	DISCUSSION

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX A APPENDIX B LITERATURE CITED

Our results, which are summarized in Table 1, are useful for understanding the impact of various demographic parameters that have influenced the present distribution of genetic diversity in forest trees and annual plants. We show that the founder effect can be dramatically reduced when the life cycle of trees is taken into account, even with limited pollen flow. Therefore we did not need to introduce very high levels of pollen flow to explain the contrast between low differentiation of nuclear genes and the high differentiation of maternally inherited cytoplasmic genes.

Thanks to the one-dimensional colonization process, we showed that the founder effect seems to be much more limited for trees than for annual plants. This can be explained as follows: when a tree population is founded, growth for the first several years is because of new juvenile migrants (seed flow) and not because of reproduction. Therefore, when the first trees reach reproductive age in the newly founded population, a nonnegligible part of the space is already occupied by juveniles from seeds that arrived years before.

On the contrary, as we had shown in a previous work (AUSTERLITZ et al. 1997 ), the first annual plants that arrive in an empty site can reproduce the next year, and therefore the offspring of these first occupants have the opportunity to colonize the whole space. Therefore, the subsequent loss of diversity is greater for annual plants than for trees, and the differentiation among populations is also greater.

We emphasize that the key factor in avoiding the founder effect of trees species is not overlapping generations but delayed reproduction, which allows a large increase in the number of initial founders of a given population before reproduction begins. To check this more directly we made simulations with plants having overlapping generations but no juvenile phase, with the same growth rate and equilibrium effective population size. For these plants F_ST increased as for annual plants during colonization (results not shown). Therefore, even if some life-history traits, like the occurrence of a seed bank, can have an impact on annual plants similar to that of overlapping generations (TEMPLETON and LEVIN 1979 ), they cannot reduce the founder effect for those plants.

This process can be observed in well-described examples of recent colonization events. In a study on Prunus avium, MARIETTE et al. 1997 showed that a very young population (~120 years old) showed almost the same level of diversity as a long-established one, and neither population was differentiated (G_ST = 0.014). This is especially interesting because this species is insect-pollinated, so that a high level of gene flow through pollen is not expected. Seeds are dispersed at random by animals, so the number of seeds per year that fall and are able to germinate on a given site is presumably low. In spite of limited recruitment, the delay in reproduction allows genetic diversity to accumulate. A similar pattern can be observed in Sorbus aucuparia, another entomophilous tree species, where a recent colonization of a plateau in Belgium yielded only a small loss of genetic diversity (RASPE and JACQUEMART 1998 ).

By contrast, two species of Silene in Hawaii provide a good example of the impact of a recent colonization on genetic diversity and differentiation of perennial species with no juvenile phase (WESTERBERGH and SAURA 1994 ). The older populations of these species clearly show the highest level of internal diversity, and founder effect is extremely high for populations derived from recent colonization of lava beds. Also, as expected, these recent colonizations yield very high levels of F_ST (0.677). S. alba, which colonized Virginia ~200 years ago, does not show much differentiation for nuclear genes (F_ST = 0.13; see MCCAULEY 1994 , MCCAULEY 1997 ). This illustrates how subsequent homogenization can counterbalance initial founder events relatively quickly, the discrepancy with cytoplasmic genes (F_ST = 0.67) coming presumably from the differences between seed and pollen flow.

Our model also helps us to understand the general pattern of genetic diversity observed on a continental scale for temperate forest tree species: both the differences with annual plants as well as the opposite patterns of diversity of nuclear and cytoplasmic genes. On this last point, the two-dimensional colonization process shows that the differences between these two kinds of differentiation reflect not only differential gene flow during and after the colonization period, but also the fact that we have much differentiation between refuges for cytoplasmic genes and very little differentiation for nuclear genes during the isolation period.

In this two-dimensional process, pollen flow within refuges slows down differentiation by drift among the populations. Differentiation for nuclear genes only occurs among the refuges. For cytoplasmic genes, on the other hand, populations within refuges also diverge. This process is accelerated because the effective population size for cytoplasmic genes is half that of nuclear genes. Annual plants, because of their short generation time, have the time to diverge from one refuge to another for both nuclear and cytoplasmic genes. Effective population size is a very important parameter; tree refuges have the time to diverge genetically from one another during the glacial period if effective population size is ~100 but not if it is ~1000. This result is consistent with results (SLATKIN 1991 ) on the island model, for which the rate of convergence toward equilibrium is approximately governed by the smaller of 1/N_e and m/d, where N_e is the effective size of the demes, m the migration rate, and d the number of demes.

Provided that tree populations were already only slightly differentiated for nuclear genes when they entered the refuges and that the effective population sizes in the refuges were large enough, the tree populations might have maintained this low level of differentiation throughout the glacial period. Because recolonization does not yield a strong increase in differentiation for trees, F_ST would remain relatively low, without invoking a high level of pollen flow (between 1% and 10% of pollen coming from the neighbor populations, that is, between 20 and 200 times more than seed flow).

One of the most surprising results is the decrease of F_ST during the colonization period for the two-dimensional stepping-stone model for annual plants and also in some cases for trees. The explanation is probably that because F_ST had reached a very high value at the end of the isolation period, the restoration of gene flow between the refuges in the colonization period overwhelmed the effects of foundation events. LE CORRE et al. 1997B found a similar result. The number of founders of each new population was probably also important; other results (LE CORRE and KREMER 1998 ) have shown that F_ST can decrease during a colonization process if the number of founders is high enough.

The results obtained for trees are not just a consequence of their generation time. Plants with nonoverlapping generations and the same generation time as trees resembled trees in the change in their population structure during the isolation periods. However, they differentiated more during the colonization period (Fig 5) and did not return to equilibrium within the subsequent 8000 years, except in the case where pollen flow was very high.

The two-dimensional pattern of colonization also played a major role, increasing the number of source populations for each newly founded population and thus strongly reducing the founder effect. Also, when gene flow was high enough (Nm > 1), the rate of convergence was increased in a two-dimensional, compared to a one-dimensional, stepping-stone model (MARUYAMA 1971 ; SLATKIN 1991 ).

Another important factor is pollen flow. A key indicator of its role is that paternally inherited chloroplasts show much less differentiation than maternally inherited mitochondria in pines (LATTA and MITTON 1997 ). Nevertheless, Latta and Mitton show that while mitochondrial DNA is very differentiated between colonization lines coming from different refuges (F_ST = 0.679), it is almost not differentiated along a colonization line (F_ST = 0.005), well in agreement with the results of our one-dimensional colonization model.

Moreover, explanations based only on high pollen flow (ENNOS 1994 ) cannot account for the observation that the F_ST value for tree species does not depend on their pollen dispersal ability, because animal-pollinated species do not show more differentiation than wind-pollinated species (HAMRICK et al. 1992 ). On the other hand, low differentiation can be explained by life cycle, which does not depend on the level of pollen flow.

Our model reveals the complementarity of all processes. Fig 5 shows that if the tree life cycle was not taken into account, a huge level of pollen flow would be necessary to explain observed differentiation. Nevertheless, with the same level of seed and pollen flow, nuclear genes' F_ST for annual plants falls below that of trees at the end of the process because of the rapidity of homogenization of annual plant populations (see Fig 4). Therefore, higher levels of pollen flow or larger effective population sizes for trees than for annual plants are also necessary to explain the observed differences. Additionally, the two-dimensional process appears to be a key explanation for the lack of genetic differentiation.

Because the simulation is time intensive, we used a smaller number of populations than would be realistic in temperate areas. Increasing the number of populations may have increased the effect of colonization on differentiation, but probably not more for trees than for annual plants. With additional populations, more time would have been required to reach equilibrium, especially in a stepping-stone model. This could have generated a situation in which annual plants would not have had the time to return to equilibrium, therefore explaining in part why they have a high F_ST.

Several other features could be integrated into the model. For instance, LE CORRE et al. 1997B have shown by a simulation study that events of long distance dispersal of seeds by birds have to be invoked to explain the extremely high speed with which forest trees have recolonized the whole temperate zone after the last glacial period. This result agrees with direct observation (BOSSEMA 1979 ; DARLEY-HILL and JOHNSON 1981 ). For annual species, these long distance dispersal events would generate a founder effect that is much greater than that obtained by a stepping-stone colonization process, some newly founded populations remaining isolated for a long period. It will be of interest to see if tree population dynamics might reduce this high founder effect. These rare events of long distance dispersal could explain the observation of a very strong differentiation for chloroplast DNA at a local scale, as pointed out by PETIT et al. 1997 .

Our results have shown that the level of differentiation of trees is a consequence of the differentiation that existed before the last glacial period. The last million years have seen cycles of ~100,000 years with glacial periods of 80,000 years, followed by short warm periods (HAYS et al. 1976 ; PAILLARD 1997 ). There were probably successive events of isolation followed by colonization. Under our hypothesis, one might think that the particular life cycle of tree species permits them to pass through these successive events without suffering many changes in the structure of their nuclear gene diversity, while the cytoplasmic gene differentiation was more deeply shaped by the process. In some cases, the effective size of the refuges may not have been large enough, yielding much more among-population differentiation and much less within-population diversity (see, for instance, the case of Pinus pinea described by FALLOUR et al. 1997 ). The loss of diversity through fragmentation has been observed for some tree species (BILLINGTON 1991 ).

The method that we developed here is relatively specific to plant populations, because migration is presumed to occur through pollen and seeds. Nevertheless, the method could be adapted to the case of animals or humans, for which migration can also occur for adults or whole families. One might expect the same avoidance of founder effects during colonization for long-lived species, because even if the first migrants in a newly founded population can reproduce immediately, their descendants will then have to wait for many years before being able to reproduce, permitting the population to be filled by the arrival of new migrants as in the case for trees, thus limiting the founder effect.

This could help explain the low genetic differentiation of humans on a worldwide scale, which is rather surprising, because the colonization of the whole world by humans is probably very recent (CAVALLI-SFORZA et al. 1994 ) and could have involved major founder effects. Differences between populations account for only 15% of the global diversity (BARBUJANI et al. 1997 ; BARTON 1997 ), whereas the average F_ST of mammals is ~0.242 ± 0.030 (WARD et al. 1992 ).

	ACKNOWLEDGMENTS

We thank Evelyne Heyer, Bernard Jung-Muller, Mark Kirkpatrick, Antoine Kremer, Valérie Le Corre, and Jacquie Shykoff for helpful discussions and comments on the manuscript. We thank the associate editor and two anonymous reviewers for helpful comments. We also thank Liz Mason and Peter Smouse for their help with English usage. F.A. and S.M. have a Formation Complémentaire Par la Recherche grant from the French Ministère de l'Agriculture. This work was funded in part by the "Programme National Dynamique de la Biodiversité et Environnement" of the French Centre National de la Recherche Scientifique. Some simulations were performed on the SP2 and SGI computers of the Centre des Ressources Informatiques of the Université de Paris-Sud (Orsay).

Manuscript received May 15, 1999; Accepted for publication November 11, 1999.

	APPENDIX A

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX A APPENDIX B LITERATURE CITED

Regulation in each population occurs as follows. We denote by Y(t) the vector of the numbers of individuals in the population that would be potentially recruited in each size class from t to t + 1 if their was no regulation, and by S(t) the vector of the numbers of potential surviving individuals that remain in each size class during the interval t to t + 1. Y'(t) = (t)Y(t) and S'(t) = ß(t) S(t) are the corresponding vectors after regulation. (t) and ß(t) are regulation parameters comprised between 0 and 1, which depend on the total stand basal area of the population G(t); they are adjusted so that G(t) grows logistically to an equilibrium value.

S_i(t) = P_iiN_i(t) is the number of potential surviving trees in size class i during the interval t to t + 1 and the corresponding stand basal area is G(S(t)) = ^k_i=1G_iS_i(t), with G_i the stand basal area of a tree of class i, S(t) = (S₁(t), S₂(t), ... , S_k(t)). Y₁(t) = ^k_i=1f_iN_i(t) is the number of individuals that are potentially recruited in the first size class, Y_i+1(t) = P_ii+1N_i(t) is the number of trees that potentially pass from size class i to size class i + 1, and the corresponding stand basal area is G(Y(t)) = ^k_i=1G_i Y_i(t), with Y(t) = (Y₁(t), Y₂(t), ..., Y_k(t)).

S'(t) and Y'(t) are the corresponding vectors after regulation and N_i(t + 1) = S'(t) + Y'(t). (t) and ß(t) are the coefficients of regulation for Y(t) and S(t): Y'(t) = (t)Y(t) and S'(t) = ß(t)S(t). G(t) = G(S(t)) + G(Y(t)) - G(t) is the potential increase of stand basal area between t and t + 1 and G'(t) = G(S'(t)) + G(Y'(t)) - G(t) is the real increase of stand basal area. Regulation is introduced by limiting this increase: G'(t) = G(t)(1 - ) with G_eq the equilibrium G for the population.

This gives only one relation between (t) and ß(t). To calculate them completely, another relation has to be chosen arbitrarily; this will determine the proportion of the two categories of individuals (the ones that remain in the same class and the ones that move to the next class) that is affected by density dependence. The probabilities of transition between size classes are strongly affected by the basal area of the stand (BUONGIORNO et al. 1995 ). Therefore, for simplicity, we fixed ß(t) at 1, making density dependence act only on the number of individuals that move to the next class and on the number of offspring. This leads to the relation

We chose here the following parameters: k = 25, f = 250, G_eq = 91,912, P₁₁ = 0, P_ii = 0.54 for 2 i 24, P_25,25 = 0.98, P₁₂ = 0.1, P_i,i+1 = 0.4 for 2 i 24, G₁ = 0.01, G_i = 0.5 for 2 i 8, G_i = 1 for 9 i 16, G_i = 2 for 17 i 24, G₂₅ = 3. These values are somewhat arbitrary; they were adjusted principally to fulfill the main characteristics of tree species as indicated in the main text.

	APPENDIX B

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX A APPENDIX B LITERATURE CITED

ITERATION METHOD FOR COMPUTING THE PROBABILITIES OF IDENTITY BY DESCENT
Migration is defined by two matrices M_seed and M_poll, which are set according to Fig 2A or Fig B. M_seed(p,q) and M_poll(p,q) denote the proportion of seeds and pollen, respectively, that arrive in q coming from p. Demography behaves as follows for each population p and each class i:

where the c superscript denotes in each case the values corrected by density dependence. Thus, if we denote by P_c(p, i, q, j) the probability for a cytoplasmic gene of an individual of population p and class i at time t + 1 to have been in population p and class i at time t, this probability is

Then the IBD for two cytoplasmic genes in any population and any class can be deduced as

where ^c_{q,q',i,i',j,j'} denotes the probability that two genes are IBD because one is the parent of the other or that they both had the same parent at time t,

where µ denotes the mutation rate.

When reproduction is not involved, nuclear genes behave like cytoplasmic genes. Thus, if we denote by P_n(p, i, q, j) the probability for a nuclear gene of an individual of population p and class i at time t + 1 to have been in population q and class j at time t, this probability is

For the juvenile class (i = 1), an individual inherits half of his genes maternally and half paternally. When received maternally, the distribution of probability of origin for this gene is the same as for a cytoplasmic gene. When received paternally, we have to take into account pollen flow: for whatever population q and s, the proportion of pollen from s in the pollen cloud of q is

and then the probability for an individual of population p and class 1 to inherit a gene paternally from population q and class k will be

Altogether

Then as above,

where ⁿ_{q,q',i,i',j,j'} is the same as ^c_{q,q',i,i',j,j'} except that N_q,k(t) is replaced by 2N_q,k(t).

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