# Extinction-recolonization dynamics in the mycophagous beetle Phalacrus substriatus.

Over the last decade it has been increasingly recognized that the temporal scale over which many populations persist is rather short. This has in turn led to a redefinition of the concept of a population. Many species are now viewed as consisting of a large set of local populations that are ephemeral, but where the regional persistence of a species is attained by a balance between extinctions of local populations and the subsequent recolonization of empty habitat patches (Andrewartha and Birch 1954; Levins 1969; Harrison 1991). The local populations show large temporal and spatial variation in a number of important demographic parameters, such as population size and migration rates, due to environmental fluctuations (Andrewartha and Birch 1954). These fluctuations greatly influence evolutionary change of the populations since they affect processes such as genetic drift within and gene flow among populations and provide the background on which natural selection operates.Extinction-recolonization dynamics have several consequences for the way in which genetic variation is structured within and among populations (Slatkin 1987). The founder events associated with colonization introduce an additional opportunity for genetic drift to act (Wright 1940), since founding populations are often relatively small and the effects of genetic drift are proportional to the inverse of the effective population size (Crow and Kimura 1970; Slatkin 1987; Wade and McCauley 1988; Whitlock and McCauley 1990; Whitlock 1992b). Deviations from a 1:1 sex ratio (Crow and Kimura 1970), variation in reproductive success among colonizers (Wright 1938) and the probability of common origin of the colonizers (Whitlock and McCauley 1990) further reduce the effective size of the founding population and increase the effect of the founding event. When population turnover is fairly frequent, most local populations will have experienced a bottleneck rather recently, regardless of their current population sizes (McCauley 1989). Since founding events are associated with a perturbation away from genetic equilibrium, population turnover will be important for determining the overall population genetic structure. The rate of gene flow among local populations is equally important since it determines the rate at which the disturbed populations move toward equilibrium (Whitlock 1992b).

Whether population turnover enhances the genetic differentiation among populations depends on how the genetic variation is structured in the newly founded populations compared to older and more established populations. If the genetic variance among newly founded populations is larger than among older populations, population turnover is expected to increase the genetic differentiation among populations (measured as [F.sub.ST], the proportion of genetic variation distributed among populations; Slatkin 1977; Wade and McCauley 1988; Whitlock and McCauley 1990). Theory states that if the (effective) numbers of colonizers are less than approximately twice the numbers of migrants among populations at equilibrium, the extinction-recolonization process will result in increased genetic differentiation relative to an island model at equilibrium (Wade and McCauley 1988; Whitlock and McCauley 1990). The effective number of colonizers is a function of both the size and the origin of the founding groups (Whitlock and McCauley 1990; Whitlock 1992a). Thus, as long as colonization is qualitatively the same process as migration, population turnover always leads to an increase in the genetic differentiation relative to the equilibrium case without population turnover (Wade and McCauley 1988; Whitlock and McCauley 1990; Whitlock 1992b). If, on the other hand, migrants preferably move into vacant habitat patches, the founding groups may be substantially larger than the number of migrants among extant populations. Population turnover then acts to increase gene flow among populations and thus leads to a reduction in the genetic differentiation among local populations (Slatkin 1977; Wade and McCauley 1988).

Whether extinctions and recolonizations results in an increase in the genetic differentiation among populations is thus reduced to the ecological question: "Is colonization a process that is fundamentally different from normal migration?" (Wade and McCauley 1988). There are currently only a few studies that have examined the effects of population turnover on the degree of genetic differentiation among local populations (Whitlock 1992a; Dybdahl 1994; Nurnberger and Harrison 1995; McCauley et al. 1995; Giles and Goudet 1997). The available data on ecological parameters such as local population sizes, migration rates, size and structure of founding populations, as well as extinction and colonization rates are even more limited. Whitlock (1992a) studying extinction-recolonization dynamics in the forked fungus beetle, Bolitotherus cornutus, was able to estimate the relevant demographic parameters by combining several different techniques. He subsequently used the parameter estimates to predict the expected degree of genetic differentiation in the total population. The expected value was in close agreement with an estimate of the genetic differentiation obtained from electrophoretic data. By comparing the estimates obtained with the expected degree of differentiation in a model without extinctions and recolonizations, he concluded that population turnover increased genetic differentiation among populations by 12%, a figure that was further increased to 49% if the effects of current population size were eliminated.

In this study, we present data from a detailed study of the extinction-recolonization dynamics of the mycophagous beetle Phalacrus substriatus. We have followed populations of P. substriatus over a four-year period (1992 to 1995) and noted any naturally occurring extinction and colonization events. By using mark-recapture techniques we have also estimated a number of demographic parameters, such as rates and patterns of migration among local populations and the rate of colonization of new populations. We have further created a number of artificial populations to study specifically the effects of distance on colonization and to determine the origin of the individuals founding new populations. We use these parameter estimates in combination with recent theoretical models to make predictions about how population turnover will affect the genetic structure of P. substriatus. The predictions based on the demographic data are then tested by performing an electrophoretic analysis on beetles collected from a large number of local populations.

Study Organisms

Phalacrus substriatus Gyll. (Phalacridae, Coleoptera) is mycophagous, like most of the beetles in the family Phalacridae (Steiner 1984). The adults are small (1.0-2.0 mm), shiny black, and are found on plants of various Carex species at the onset of flowering in early June. The adults feed on overwintering teliospores and germinating basidiospores of smut fungi of the genus Anthracoidea and on Carex pollen. Adult beetles are active for approximately three weeks. The female lays eggs either on the surface of or in a hole bitten in the perigynium. Larvae hatch after approximately one week and feed in the developing smut sori (Kontkanen 1936). The larval period lasts three to four weeks after which pupation occurs in the sorus. Adult beetles emerge after three weeks and appear to overwinter as adults at the base of the tussock (Kontkanen 1936; P. K. Ingvarsson pers. obs.). Phalacrus substriatus is univoltine in the study area and there is no overlap between parent and offspring generations since all adult beetles die before larval pupation occurs (P. K. Ingvarsson pers. obs).

Individual P. substriatus beetles do not show any flight tendencies either in the field or in the lab, even though they have fully developed wings (P. K. Ingvarsson pers. obs.). Thus, dispersal is probably archieved by beetles crawling between tussocks. There is also the possibility that some beetles are passively dispersed by water, since P. substriatus beetles have been found in drift material that is transported around the archipelago during periods of high water levels (Frey 1937; Palmen 1944). For a more thorough description of the interaction between P. substriatus and the smut fungus A. heterospora, see Ingvarsson and Ericson (in press).

MATERIAL AND METHODS

Natural Extinctions and Recolonizations

In 1992, 50 C. nigra tussocks were individually marked on an island in the Skeppsvik archipelago (63 [degrees] 44-48[minutes] N, 20 [degrees] 31-33[minutes] E) outside Umea, northern Sweden (for a general description of this area, see Ericson 1981). The tussocks were distributed along an approximately 75-m long and 10-m wide area of the shoreline of the island. All individual tussocks were checked for the presence of P. substriatus beetles at regular intervals (2-4 d) by sweep-netting, beginning the second week in June. The tussocks were censused regularly for approximately 3 wk, the period during which P. substriatus is active. All P. substriatus beetles caught were counted and the tussocks where they were found were noted. Hereafter we will refer to the beetles captured in a single tussock as a local beetle population. If no P. substriatus beetles were found on a tussock during the entire season we regarded the population in that tussock as extinct. In the same manner, we regarded the presence of P. substriatus beetles in a tussock that did not support any beetles the previous year as a colonization event. To ensure that the colonization event was successful, we only used observed colonizations where the new population persisted for at least two years (with the exception of colonizations in 1995). This census was repeated in June to early July in each year of the period 1993 to 1995. During the period of the study only two of the 50 censused tussocks did not support a beetle population in at least one year. For a population to be recorded as either extinct or recolonized we required that it had been either extant or extinct in the previous year, respectively (Mason 1977). Extinction and colonization rates are calculated by dividing the observed number of extinctions and colonizations by the maximum possible number of occasions where an extinction or colonization event could have occurred (Mason 1977).

Mark-Recapture Experiment

In June 1994, we studied the movement patterns of individual P. substriatus beetles by doing a mark-recapture experiment. Adult beetles caught on a tussock were sexed and individually marked with permanent color (Edding 751) by applying a three-color code on the elythra. Marked beetles were released at the base of the tussock where they were originally captured. We regularly censused all tussocks in the C. nigra population as described above and all new beetles found were marked as described above. For beetles already marked, we noted the tussock on which they were recaptured. The experiment was continued until the first week of July, when beetles could no longer be found within the study area. All mark-recapture data were analyzed using the Jolly-Seber method (Jolly 1965; Begon 1980). We used the program JOLLY (Pollack et al. 1990) to estimate population sizes, residence rate (survival rate), and recruitment into the population.

Estimating Migration Rates

Data obtained from the mark-recapture experiment provide a raw estimate of the migration rate in the population, [m.sub.r]. This estimate has to be corrected for the time span over which the study was conducted and can be estimated by using the formula (Whitlock 1992a):

[m.sub.d] = 1 - [(1 = [m.sub.r]).sup.1/t], (1)

where [m.sub.d] is the daily migration rate and t is the average time span between the first and last capture of an individual. The weighted average migration rate in the population can then be found by applying the formula (Whitlock 1992a):

[Mathematical Expression Omitted]. (2)

Here [Xi] denotes the survival rate of individuals, a quantity that is estimated from mark-recapture data. We must also correct for the fact that if migration is independent of age, on the average only half of the reproductive effort of an individual will be spent in the new population.

Colonization Experiment

In early June 1995 before the emergence of P. substriatus, 15 new C. nigra tussocks were artificially created by transplanting C. nigra tussocks from an island where P. substriatus had not been observed during the previous three years. The tussocks were placed at 0, 10, and 20 m from the original study population, to examine whether there were any distance effects in colonization of new tussocks. The placement of the tussocks was chosen to reflect distances that beetles would move with decreasing probability, based on the mark-recapture experiment the previous year. For tussocks situated at 0 m (i.e., within the study population) we expected frequent movements, whereas 10 m represents a distance that only few individuals would move over a season; 20 m was used as a distance representing extreme, long-distance dispersal for individual P. substriatus beetles and we therefore did not expect any beetles to disperse this far. The newly created tussocks continued flowering throughout the study period and could not be distinguished visually from tussocks already present in the population. The transplanted tussocks were regularly sweep-netted and the numbers and sexes of all P. substriatus beetles found were noted. At the same time, all beetles caught in the regular censuses were marked with a population-specific color code to determine the origin of the beetles caught on the new tussocks.

Electrophoretic Analysis

In 1995 we repeated the sweep-netting in the same manner described above. In late June, after egg laying had progressed for about two weeks, we started to collect beetles to be included in the electrophoretic analysis. We repeated the sweep-netting of the tussocks over a period of approximately two weeks until no additional beetles could be found. Beetles were sampled from a total of 42 tussocks. Collected beetles were put in Eppendorf tubes and kept alive until they were sexed. They were subsequently frozen at -70 [degrees] C and stored until they could be processed for electrophoresis. We analyzed seven different enzyme systems: aconitate hydratase (Acn), diaphorase (Dia), isocitrate dehydrogenase (Idh), malate dehydrogenase (Mdh), phosphoglucoisomerase (Pgi), phosphoglucomutase, (Pgm) and Triose-phosphate isomerase (Tpi). Staining recipes were modified after May (1992). The entire beetle was ground in 15 [[micro]liter] of distilled water and the enzymes were resolved on a 12% starch gel made from a 14: 1 dilution of a Tris-citrate buffert (pH 7.0) (Meizel and Markert 1967). We scored the individual genotypes and the data were analyzed by using the program FSTAT v1.2 (Goudet 1995), which calculates Wright's F-statistics using the Weir and Cockerham (1984) estimators. This method facilitates the calculation of multilocus estimates and their variance using jackknifed procedures. F-statistics were calculated for genetic variation among individuals in the total sample [Mathematical Expression Omitted], inbreeding within populations [Mathematical Expression Omitted], and the differentiation among subpopulations [Mathematical Expression Omitted]. The FSTAT program also provides significance tests for the different estimates using permutation procedures (Goudet 1995).

Before the analysis, we divided our populations into two categories: young, recently founded populations (n = 32) and old populations (n = 10). In the category young we included populations that the annual survey indicated had been colonized during the previous two years, while the category old included the rest of the populations from which beetles were collected. The choice of including populations that were founded over the last two years as opposed to populations founded only during the previous year of the study was done to increase the sample size of young populations. We estimated the degree of differentiation among populations, measured as [Mathematical Expression Omitted], for the young and old populations separately (hereafter denoted [Mathematical Expression Omitted] and [Mathematical Expression Omitted]). We tested these estimates, to determine whether there were any difference in the level of genetic differentiation between the two subgroups, by a Wilcoxon's signed-ranks test with the individual loci as replicates.

RESULTS

Population Size

A total of 298 P. substraitus beetles were marked in the mark-recapture experiment. The recapture rate varied between 14% and 45% over the study period, with a mean of 33%. The estimated proportion of beetles caught was 45.0% and the daily residence (or survival rate), [Xi], was estimated to be 0.834. The average residence (or survival) time, [Mathematical Expression Omitted], can be obtained by using the formula (Lawrence 1988):

[Mathematical Expression Omitted]. (3)

This yields an estimate of the average residence time of 5.5 d. From the mark-recapture data it is possible to estimate the number of beetles present in each tussock (or beetle population). This value is obtained by dividing the number of beetles recorded in each single tussock with the estimated proportion of beetles caught. Figure 1 shows the distribution of population sizes obtained in this way for 1994. The arithmetic mean population size is 11.9, but the distribution is skewed toward small sizes, indicated by the harmonic mean population size that is substantially lower, 4.9. The harmonic mean is the quantity that is the most appropriate measure in relation to the effective size of the population (Karlin 1968; Whitlock 1992b). Populations consisting of only one or two individuals rarely represent viable populations, but they strongly influence the average population size, especially the harmonic mean. If these populations are excluded, the arithmetic mean population size increases to 19.0 and the harmonic mean to 11.1.

Extinction and Recolonizations

Over the course of the four years of the study, we recorded 23 extinctions of previously populated tussocks, which translates into an extinction rate of 0.235. There were no indications of a deviation from randomness in extinction rates among populations with regard to population size (goodness-of-fit, G = 2.64, df = 3, P [greater than] 0.1, [ILLUSTRATION FOR FIGURE 2 OMITTED]). Classes with an expected value of less than 5 were pooled according suggestions in Sokal and Rohlf (1981). During the same period we recorded 27 new successful colonizations, or a colonization rate of 0.275. A total of 101 beetles were recorded in previously uninhabited tussocks. The number of colonists per tussock was generally small, with an arithmetic mean of 3.6 and a harmonic mean of 1.9 [ILLUSTRATION FOR FIGURE 3 OMITTED]. Of the 61 colonizing beetles for which sex data are available, only 7 were males (11.4%). The sex ratio among colonizers is significantly different from the population sex ratio of 27% males, estimated from the mark-recapture data (goodness-of-fit, G = 7.45, df = 1, P [less than] 0.01). In the genetic models mentioned above (Slatkin 1987; Wade and McCauley 1988; Whitlock and McCauley 1990), extinction rates and colonization rates are equal since all populations that go extinct are immediately recolonized. Since it is not clear which estimate is most appropriate when the two rates differ, we simply used the average of the two estimated rates. This yields a value of [e.sub.0] = 0.255.

In the colonization experiment a total of 11 beetles were recorded in the artificially created tussocks. Only tussocks that were situated within the studied population (distance class 0 m) received colonizers. The arithmetic mean number of colonizers was 3.5, while the harmonic mean was slightly lower, 2.0. These values are similar to values obtained from the regular survey. The average distance from the newly colonized tussocks to the nearest neighboring tussock supporting a P. substriatus population was 0.81 m, comparable with the mean nearest neighbor distance in the population of 0.71 m. Only one of the beetles that colonized a tussock was male. This female-biased sex ratio is comparable to the data obtained from natural colonizations. In no case did the colonizing beetles come from more than two different tussocks. When the beetles did come from two different tussocks, they always came from the closest neighboring tussocks. The individuals in the founding groups thus represent only a small subset of the entire set of populations.

Migration Patterns and Rate

The mean distance moved by P. substriatus beetles over an entire season was 0.91 m. The distribution of distances moved was skewed and 35% of the beetles did not move at all [ILLUSTRATION FOR FIGURE 4 OMITTED]. The mean distance moved is of the same order of magnitude as the average distance between tussocks in the population, 0.71 m. Thus, beetles that emigrated from a tussock in general moved to one of the closest neighboring populations. There were no evidence that the migration probability of individuals declined with age (Pearson r = 0.389, P [greater than] 0.15). In the mark-recapture experiment, 35% of all marked beetles did not move from the tussock where they were originally caught and the raw estimate of the migration rate in the population, [m.sub.r], is thus 0.65. The average time span between the first and last capture of an individual is 5.05 d, yielding an estimate of the daily migration rate, [m.sub.d], of 0.188. Using the survival rate estimated from the mark-recapture data ([Xi] = 0.834) yields a migration rate of 0.735. Correcting for the fact that, on the average, only half of the reproductive effort of an individual will be spent in the new population provides a final estimate of the migration rate in the population of [Mathematical Expression Omitted].

TABLE 1. Overall gene frequencies for the seven different enzyme systems. Enzyme systems Allele Acn Dia Idh Mdh Pgi Pgm Tpi 1 0.005 0.658 0.978 0.030 0.796 0.101 0.848 2 0.365 0.342 0.017 0.970 0.204 0.813 0.152 3 0.450 - 0.05 - - 0.043 - 4 0.043 - - - - 0.043 - 5 0.130 - - - - - -

Electrophoretic Analysis

A total of 201 beetles from 42 different tussocks (populations) were collected for the electrophoretic analysis. All enzyme systems studied were polymorphic at the 99% level and five were polymorphic at the 95% level (Table 1). A total of 22 alleles were found. Both Dia and Pgm produced very fuzzy and weak banding on the gels with the buffer system used, and for both enzyme systems it was hard to accurately score the alleles. They further produced results that were inconsistent with the other five loci analyzed, as both showed a significant deficit of heterozygotes (i.e., [Mathematical Expression Omitted], Table 2). Since we cannot exclude the possibility that we have misinterpreted the Pgm and Dia genotypes for some beetles, these loci were excluded from subsequent analysis. However, the qualitative features of the results remain unchanged if Dia and Pgm are included in the analysis.

With Pgm and Dia excluded, there were an excess of heterozygotes within local populations, as evidenced by the negative estimate of [Mathematical Expression Omitted]. This estimate is significantly different from zero (P = 0.043). The estimated degree of genetic structuring among local populations, measured by [Mathematical Expression Omitted], was 0.077 (Table 2). Only two of the individual loci were significant, but these were two of the most informative loci and the overall estimate was highly significant (P = 0.0002, Tables 1 and 2). There is thus evidence for a local structuring among different populations of P. substriatus. However, the combined estimate of deviation from Hardy-Weinberg, over the entire metapopulation, is small [Mathematical Expression Omitted] and not significantly different from zero. A negative [Mathematical Expression Omitted], positive [Mathematical Expression Omitted], and [TABULAR DATA FOR TABLE 2 OMITTED] [Mathematical Expression Omitted] close to zero is what would be expected when local populations consists largely of sibs. This also seems to be the case, at least in the smaller populations of P. substriatus (Ingvarsson, unpubl.).

The data were subsequently reanalyzed with the material grouped into the two categories young populations and older populations. The young populations were more differentiated that the old ([Mathematical Expression Omitted], [Mathematical Expression Omitted]; Table 2). This difference in degree of differentiation was also significant (Wilcoxon's signed rank test, N = 5, t = 0, P = 0.031). The young populations are consequently more differentiated that the older populations, indicating that the extinction-recolonization dynamics result in an increased overall genetic differentiation.

Discussion

The data presented here indicate P. substriatus populations are characterized by a population structure with many small, local populations interconnected by migration. Each local P. substriatus population has a relatively short expected persistence time, but persistence of the species occurs due to a balance between local extinctions and recolonizations, much in the manner suggested by Harrison (1991). The spatial structuring is also reflected in the degree of genetic differentiation among tussocks, measured as [Mathematical Expression Omitted]. The present estimate, 0.077, falls within the range of estimates of differentiation over much larger spatial scales from other, more mobile, beetle species (see review in McCauley and Eanes 1987). The frequent local extinctions and recolonizations also influences the genetic structuring of P. substriatus and lead to higher degrees of differentiation than expected without population turnover. An extinction rate on the order of a few percent will result in a significant increase in the genetic differentiation among local populations, but the actual degree of increase depends on the values of a number of ecological parameters, such as population size and migration, and extinction rates (Wade and McCauley 1988). It is therefore crucial to have good estimates of these parameters.

Local population sizes in P. substriatus are generally small, on the order of 10 individuals, but considerably larger populations can be found. There will be strong sampling effects each generation and this will result in an increased differentiation among local populations. There is also a large among-population variability in population size, on both spatial and temporal scales. This can have a number of ecological and genetic consequences. First, large populations may be crucial for the persistence of the species over a longer time scale. Second, if the migration is triggered by local density effects (Herzig 1995), large populations will act as sources for migrants, while small populations act as migrant sinks (Pulliam 1988; Harrison 1991; McCauley 1995). If the migration rate is high enough, migration from sources can maintain viable populations in sinks even though mortality rates otherwise exceed rates of reproduction (Pulliam 1988). This leads to spatial variation in the migration rate as well. This spatial heterogeneity will also have profound effects on the genetic structuring, since spatial variation in demographic parameters, such as migration rate and local population size, in general results in much higher degrees of differentiation than does temporal variation (Whitlock 1992b).

Recolonization seems to be a frequent event for local P. substriatus populations, but founding groups are small, which results in an additional opportunity for genetic drift to act at the colonization event. The biased sex-ratio among colonizers further reduces the effective population sizes in the newly founded populations (Wright 1938), but since single female colonizers successfully founded at least some populations, dispersing females must be preinseminated. This reduces the effects of the biased sex ratio (Wade and McCauley 1988) and results in a substantially higher number of colonizers than observed. The harmonic mean number of colonizers was 2.0, but if we assume that most females mated at least once in their source population, the estimated number of colonizers is approximately 4.0. McCauley and Reilly (1984) found successful colonizations in the milkweed beetle, Tetraopes tetraophtalmus, although there were only female colonizers. They suggested that these females probably did carry sperm from two or more males. Phalacrus substriatus colonizers also have a high probability of common origin since they come from populations in the immediate vicinity of the newly colonized population. Whether this probability is further increased by the fact that females have already mated in the source population before dispersal, depends, for example, on the number of matings in the new population and on sperm precedence, factors which are currently unknown for P. substriatus. The probability of common origin, [Phi], is an important variable in determining the effect of population turnover on the genetic differentiation among populations (Wade and McCauley 1988; Whitlock and McCauley 1990). The data on colonizations in P. substriatus suggest that the probability of common origin among colonizers is high and an estimate of [Phi] = 0.5 is probably highly conservative. Although the data set is limited, the artificial colonization experiment together with migration estimates from the mark-recapture experiment suggests that long distance migration and colonization is a rare event in P. substriatus. Comparing the results from the colonization events with migration patterns estimated from the mark-recapture experiment, it seems like colonization is no different from migration. There is a close correspondence between average migration distance and the average distance moved by colonizers, and the two processes also involved comparable numbers of individuals. The two processes are probably the same and colonization is only migration into a patch that happens to be uninhabited. Since colonization is spatially limited, it is only reasonable to assume that the same applies to migration as well. The models, however, assume that once a population has been colonized migration follows the island model (Slatkin 1977; Wade and McCauley 1988; Whitlock and McCauley 1990). Spatially limited migration will generally inflate the levels of differentiation (e.g., Slatkin 1993), but the magnitude of this effect in the present case is unknown.

Theory predicts an increase in genetic differentiation if migration and colonization occur at comparable rates (Wade and McCauley 1988; Whitlock and McCauley 1990). There is substantial ecological evidence that population turnover will result in an increase in the overall genetic differentiation in P. substriatus. Data from the genetic analysis show that this is indeed true since the genetic variation among newly founded populations [Mathematical Expression Omitted] was significantly larger than among older populations [Mathematical Expression Omitted]. It is possible to calculate the theoretically expected [F.sub.ST] value given the extinction-recolonization process. Using the estimates of the demographic parameters obtained above (N = 11.1, [Mathematical Expression Omitted], k = 4.0, [Phi] = 0.5, e = 0.255 and by assuming that [m.sub.p], migration prior to sampling, is equal to [Mathematical Expression Omitted]) and equation (1) in Whitlock (1992a), a predicted [F.sub.ST], value of 0.070 is obtained. This should be compared to the overall estimate from the electrophoretic data of 0.077. There is thus a good agreement between the empirical results and the theoretical prediction. By comparing the results obtained with the equilibrium levels of differentiation in the traditional island model (i.e., [F.sub.ST], = 1/2N(1 - L), where [Mathematical Expression Omitted]; Wright 1951; Wade and McCauley 1988) the direct effects of population turnover can be obtained. The expected levels of differentiation for an island model at equilibrium, given the parameter values above, is 0.049. The extinction-recolonization process thus results in an approximately 40% increase in the overall genetic differentiation.

One important property that helps predict the evolutionary future of a species is the variance effective size (see for instance Crow and Kimura 1970). This quantity is the size of an ideal population that experiences the same rate of change in genetic variance per generation as the studied population. The consequences of population subdivision for the effective size is currently the focus of much theoretical work (Slatkin 1977; Maruyama and Kimura 1980; Chesser et al. 1993; Barton and Whitlock in press; Whitlock and Barton in press). Whitlock and Barton (in press; see also Barton and Whitlock in press) have derived a formula for the effective population size of a structured population that takes into account the effects of extinctions and recolonizations. If we assume the mutation rate to be negligible, the ratio of the effective (subdivided) population size, [N.sub.e], to the expected population size in a completely panmictic population (nN) is given by (from eq. [24] in Whitlock and Barton in press):

[N.sub.e]/nN [approximately equal to] 1 + 4Nm + 2eN(1 - [Phi](1 - 1/2k)) / 4N(m + e)(1 - eN/k). (4)

By substituting the parameters above into equation (1) and by assuming that n, the number of local populations present, is equal to 41, it can be shown that population turnover reduces the effective population size by about 55%. While this should not be viewed as an exact estimate, it gives an indication that the effects of the extinction-recolonization dynamics can lead to dramatic reductions in the global effective population size.

It is apparent from the results that population turnover can have profound effects on how genetic variation is structured within and among local populations. The extinction-recolonization dynamics in P. substriatus lead to an increased genetic differentiation among local populations, but also to a reduction in the global effective population size. One important point should be stressed here: the theoretical models discussed above all refer to genetic differentiation measured as [F.sub.ST] (Slatkin 1977; Wade and McCauley 1988; Whitlock and McCauley 1990). However, [F.sub.ST] measures the proportion of the genetic variation that is distributed among populations. Thus, even though turnover results in an increase in the variation among populations (measured as [F.sub.ST]) it does not necessarily say anything about the absolute magnitude of genetic variation. In fact, as long as the number of populations is finite, the extinction-recolonization process will increase the rate of loss of genetic variation, both within single populations and from the metapopulation as a whole (McCauley 1991; Harrison and Hastings 1996). This is further illustrated by the reduction in the global effective populations size due to the extinction-recolonization process (Gilpin 1991; Harrison and Hastings 1996; Barton and Whitlock in press).

Whether the process of population turnover and the associated effects have any influence on the long-term evolution of the P. substriatus is still an open question. To obtain a more complete understanding on how the extinction-recolonization process affects the evolutionary dynamics of P. substriatus one has to consider a whole range of processes, including genetic drift, mutation, migration, and natural selection, all acting simultaneously.

ACKNOWLEDGMENTS

We thank B. Giles for helpful discussions and constructive criticism during the entire course of the work. We would also like to thank J. Goudet, M. Whitlock, J. Agren, and an anonymous reviewer for providing comments on earlier versions of the manuscript that led to notable improvements. The study was funded by a grant from the Swedish Natural Science Research Council (NFR) to LE and grants from the Hierta-Rezius foundation (The Royal Swedish Academy of Sciences) and the Bjorkman foundation to PKI.

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Author: | Ingvarsson, Par K.; Olsson, Katarina; Ericson, Lars |
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Publication: | Evolution |

Date: | Feb 1, 1997 |

Words: | 6548 |

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