The genetic consequences of long distance dispersal during colonization

Received 6 September 1993 Heredity 72 (1994) 312—317 Genetical Society of Great Britain The genetic consequences of long distance dispersal during colonization RICHARD A. NICHOLS* & GODFREY M. HEWITTI School of Biological Sciences, Queen Mary and Westfield College, University of London, Mile End Road, London El 4NS and tSchool of Biological Sciences, University of East Anglia, Norwich NR4 771, UK. Rare long distance dispersal may have little impact on gene frequencies in established populations but it can dramatically increase gene flow during episodes of range expansion. We model the invasion of new territory by genetically distinct populations of the same species to investigate the dynamics of such episodes. If long distance dispersal is sufficiently frequent, the populations do not spread as a wave of advance but instead found intermingled isolates. We argue that this process can explain many otherwise puzzling patterns in the geographical distribution of alleles. Keywords: colonization, dispersal, founder events, gene flow, hybrid zone, travelling wave. Introduction zations have been implicated in the spread of organ- In most species, populations from different parts of the (Pytophophthora infestans) to cheat grass (Bromus tectorum) and oak trees (Quercus spp.) (Pyle, 1969; Cliff et al., 1981; van der Plank, 1967; Mack, 1981; isms ranging from cholera and potato blight species range are genetically distinct. It has become increasingly apparent that in order to interpret this geographical variation we need to understand the history Hengeveld, 1989). Indeed, the post-glacial advance of many organisms seems to have been very rapid, with clear evidence from fossil pollen and beetles (Huntley & Birks, 1983; Bennett, 1988; Coope, 1990). The theory of the dynamics of range expansion has of a species' distribution (Hewitt, 1989; Avise et al., 1987) and episodes of range expansion have particularly dramatic genetic consequences. The process of range expansion can produce genetic patterns that persist for many hundreds or thousands of generations; for example the present day distribution of human blood groups can be traced back to the consequences of the been extensively studied by Mollinson (1977). He identifies an important transition in the behaviour of an expanding population depending on the form of the function relating dispersal to distance: V(x). If V has Neolithic agricultural revolution (Ammerman & exponentially bounded tails then the population spread tends to proceed as a wave of advance. In stochastic simulations where V has thicker tails then the population tends to spread in leaps and bounds. Cavalli-Sforza, 1984), and hybrid zones in many plants and animals seem to have formed soon after the last ice age (Barton & Hewitt, 1985). Fisher's (1937) influential model characterized the spread of an advantageous gene through a population as an advancing wave. Subsequently population expan- In this paper we investigate the genetic consequences of this difference in dispersal behaviour when two genetically distinct populations meet. The work was stimulated by surveys which revealed genetic mix- sion has also been modelled as an advancing wave (Skellam, 1951; van den Bosh et al., 1988). In such models the dispersal is characterized by the variance (a2) in parent-offspring distance (Hengeveld, 1989). However, natural examples of range expansion often ing between races of the grasshopper Chorthippus paralielus in the Pyrenees. The measured rate of dispersal (a = 30 m) is insufficient to account simply for the penetration of allozyme markers, morphological do not involve a simple wave of advance; instead long distance colonizations set up new populations distant and behavioural characters some 20 km into the range of the other race (Butlin & Hewitt, 1 985a,b; Hewitt, 1989; Butlin et al., 1991). We therefore developed a simulation that could emulate the two types of range expansion. from the parent population. These new populations then act as foci for local spread. Long distance coloni*Correspondence 312 LONG DISTANCE DISPERSAL DURING COLONIZATION 313 A model of range expansion The model incorporates migration and population growth with selection and/or genetic drift acting on two alleles at a single locus. It consists of a rectangular array of demes, 79 by 40. The direction of the shorter axis is designated North. Migration The number of migrants from each deme is drawn from the binomial distribution with parameters m (migration rate) and N (the number of adults in the deme). Migrants are chosen at random from the deme and moved to their new population. A dispersal function (see below) specifies the distribution of displacements for the new population from the old. For each migrant a random direction was chosen uniformly from 0 to 360° and a displacement drawn from the dispersal distribution. Migrants crossing the eastern and western boundaries were discarded. The northern and southern boundaries were connected, so that a migrant crossing to the north appeared in the south and vice versa. Population growth The population in a deme grows until it reaches the carrying capacity according to the equation: N+1N+ rN(k—N5/k, (1) during colonization. In the light of Mollinson's (1977) results, a dispersal function was chosen for which the tails of the distribution could be modified but the variance kept constant. This was achieved using the weighted sum of two normal distributions: (1 —a)N[0,1}+ aN[0,b]. N[x,u] represents the normal distribution with mean x and variance cr2. The unit of distance was the spacing between demes. The series of distributions used here was chosen to have a range of values for a, and a value of b such that the variance remained 25. The proportion of individuals that migrate (m) was set to 0.3 and the rate of population growth (r) was set to 0.9 so that there was some lag (approximately seven gener- ations) between colonization and a deme growing to full size. These combinations lead to colonization of the array of demes in around 25 generations which was sufficiently short for repeated simulation. The range of values of interest makes ln(a) (hereafter a) a convenient measure (Table 1). Figure 1 illustrates the function for the two extreme values and one intermediate: a =0, 2 and 4.5. The intermediate and larger values of a proTable I The set of parameter values for the dispersal function a 0 0.5 1.0 1.5 b 5 5.7 6.9 8.5 3.0 2.0 2.5 10.7 13.5 17.1 6 10 3.5 4.0 4.5 21.9 28.9 46.3 where N is the population size after migration, N is the adult population size in the next generation, r is the intrinsic rate of increase and k is the carrying capacity (20 individuals in these simulations). 0.9 0.8 Genetic drift and selection 0.7 The two alleles in the population can be designated A and B. The frequency of A in adults after migration 0.6 determines the frequency in the gamete pooi. Each () allele in the foll (...truncated)