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Population structure of Dipodomys ingens (heteromyidae): the role of spatial heterogeneity in maintaining genetic diversity.

The ability to reconstruct the historical events that have given rise to the current structure of natural populations is a major goal of population biologists. However, because many different historical events are likely to have affected the genetic structure of an extant population, it is difficult to isolate and distinguish such processes from one another. A natural population may be founded by colonization or range expansion from another population and, after this initial sampling event, its genetic structure may be affected by such factors as range contraction, subdivision, dispersal, migration, selection, and mating system. Even though we can often predict the pattern of genetic differentiation that each of these processes should leave behind, it is not always possible to identify which of them have contributed to the current genetic structure because many have been involved. Moreover, most of the models that examine different aspects of population structure assume that populations are in equilibrium with respect to drift, migration, and mutation, but this condition may not hold if populations have only recently subdivided or expanded or if the mutation rate at the locus under examination is high (Neigel and Avise 1993). Consequently, reconstructing the factors responsible for determining natural population structure has proven difficult.

The development of coalescent theory for use in population genetics is enhancing our ability to reconstruct the genealogical relationships among individuals and the population processes that could lead to the current genetic structure of a population (Watterson 1975; Tavare 1984; Hudson 1990). Until recently, the structure of populations was assessed using Wright's F-statistics (or derivations of them) (Wright 1969). Although the theory behind Wright's F-statistics implicitly assumed genealogical processes, it was not until the development of molecular tools that permitted the estimation of key parameters (such as the mutation rate) that the connections between population structure and genealogical processes as coalescent processes have been explored. Coalescent theory assumes that for a neutral gene the accumulation of mutations along a given DNA lineage is Poisson distributed and independent of population structure, size, and linkage to selected loci. However, the number of alleles present in the population at a specific time will depend on population size, structure, and linkage to selected loci. Therefore, if we can assume that there is no recombination and that mutations follow the infinite sites model, the coalescent branches of the genealogy and the mutations occurring along each branch can be reconstructed for a given sample of alleles. Moreover, the reconstruction should enable us to infer the geographic or selective forces that have led to the specific allelic distribution in the sample.

Templeton et. al (1995) developed another technique to explore the historical processes giving rise to current population structure. Their method combines information from a parsimony haplotype network with measurements of the geographic distance between populations and then uses a series of statistical hypothesis tests to determine if current levels of population subdivision have been created by processes of isolation by distance, contiguous range expansion, restricted gene flow, or other processes. Although we have not followed this approach per se, we have drawn upon its criteria to draw some of our conclusions.

Our study examines the population structure of the giant kangaroo rat, Dipodomys ingens, and aims to infer the historical processes that may have created it. Dipodomys ingens is an endangered species of kangaroo rat endemic to the Tulare Basin and some adjacent areas in south-central California (US Fish and Wildlife Service 1987). Grinnell (1932) performed a survey of the species and described the lower Tulare Basin as covered with millions of the large, distinctive burrows of the giant kangaroo rat. Dipodomys ingens was widespread in the Tulare Basin until the late 1960s but its habitat has now mostly been lost due to the development of the San Joaquin Valley for agricultural purposes: its current distribution has been estimated to represent only 3% of its historic range (Williams et al. 1993). The remaining populations of the rodent are on the eastern foothills of the western edge of the Basin and in the Carrizo Plain at the southern end of the valley [ILLUSTRATION FOR FIGURE 1 OMITTED].

We collected samples from the remaining sites of this, once massive, Tulare Basin population (SJV population, [ILLUSTRATION FOR FIGURE 1 OMITTED]). As recently as 25 years ago, this population occupied thousands of hectares more than it does today, stretching at least 80 km to the south of where we collected. We also have samples from several populations to the west of the basin [ILLUSTRATION FOR FIGURE 1 OMITTED]. These populations were not described by Grinnell (1932), although he probably did not visit these areas. There is some cattle grazing in the area but this has little impact on giant kangaroo rats (Williams et al. 1993). However, giant kangaroo rats prefer flat terrain and the existence of gulches, hills, and uneven topography in the Ciervo and Tumey Hills [ILLUSTRATION FOR FIGURE 1 OMITTED] has led them to be patchily distributed throughout this area (Williams 1992). In addition, we collected samples from several populations that lie on the western side of the Coastal Range mountains, roughly 150 km to the southwest of the Tulare Basin populations, in the Carrizo Plain [ILLUSTRATION FOR FIGURE 1 OMITTED]. The Carrizo Plain is large, nearly flat, and relatively uniform, making it possible for a continuous and large population to exist there. It has supported populations of giant kangaroo rats since recorded history some 100 years ago. The land was used for livestock grazing, and use of the land for grain farming reduced habitat for the giant kangaroo rats by 20-40% (Williams 1992). The area is now protected and habitat for giant kangaroo rats is increasing through secondary succession of abandoned farmland.

Several aspects of the life history of giant kangaroo rats are pertinent to developing models to describe their population structure. The giant kangaroo rat is a solitary, territorial rodent. Population sizes of giant kangaroo rats can fluctuate markedly as consecutive seasons of drought or plentiful rain cause sharp declines or explosions in their number. Females generally mate at their own burrow, while male breeding dispersal distance is predominantly circumscribed to the precincts of neighboring females in estrus (10-20 m; Evon Hekkala, unpubl. data). Female giant kangaroo rats can reproduce in their first year, but the number of litters per year may vary from zero to three depending, principally, on the amount of rainfall. In other species of kangaroo rat, the length of time young remain in the mothers burrow and the natal dispersal distance are influenced by population density because both are dependent on the availability of empty burrows for colonization (see, e.g., Waser and Elliott 1991). This is also probably also true for giant kangaroo rats because their burrows are more extensive than most other species of kangaroo rat, and the time and risk of constructing a new burrow is probably considerable (Williams et al. 1993). Consequently, the existence of a variable reproductive rate and short natal and mating dispersal distances probably also affect the genetic structure and effective population size ([N.sub.e]) of giant kangaroo rats as they do other species of kangaroo rat (Jones 1988, 1989; Jones et al. 1988; Waser and Elliott 1991).

The effect that different mammalian social structures have on dispersal patterns, local population structure, and effective size has long been of interest to mammalian population biologists (Chepko-Sade and Halpin 1987). Some studies have found that strong territoriality, natal philopatry, or episodes of low density (as in species with fluctuating population densities) leads to genetic subdivision between demes or populations (Selander 1970; Schwartz and Armitage 1980; Patton and Feder 1981; Bowen 1982; Chesser 1983; Plante et al. 1989), while others have found that such social structures did not create intrademic genetic subdivision (Jones et al. 1988; Waser and Elliott 1991). Several studies have also examined the effect of spatial subdivision and biogeography on genetic structure using molecular markers (Plante et al. 1989; Thomas et al. 1990; Patton and Smith 1992; Riddle et al. 1993; Stewart et al. 1993; Nachman et al. 1994; Jaarola and Tegelstrom 1996). Studies of the effect of spatial heterogeneity on genetic structure are of practical concern for endangered species. Theoretical results have shown that spatial subdivision directly influences population persistence (Hanski and Gilpin 1991), and that episodes of extinction and recolonization are predicted to reduce [N.sub.e] and hence genetic variability (Gilpin 1987). However, it is also becoming clear that a knowledge of the historical connections and ongoing relationships between extant populations of endangered species, in other words, the historical processes that have led to the current genetic structure, is valuable for designing management strategies because species loss is not only a question of loss of genetic diversity but also a question of the loss of habitat essential for maintaining gene-flow and other patterns (Avise and Hamrick 1996).

Here, we address several aspects of the effect of spatial heterogeneity on the genetic population structure of giant kangaroo rats. In particular we address the following questions: (1) What is the relationship between northern and southern populations and do they show different patterns of genetic differentiation? (2) What is the relationship between the San Joaquin Valley population and the Panoche Valley populations that lie to their west? (3) Are the small hill populations in the north depauperate in genetic variation or is there evidence of gene flow between them and the larger populations in the north? (4) To what extent are existing levels of genetic variation attributable to ongoing gene flow versus the maintenance of ancestral polymorphism? To address these questions we sequenced 295 base-pair segments of the control region in 95 individuals from nine natural populations. To analyze the data we have used models derived from coalescent theory to estimate: the hierarchical structure of populations (Holsinger and Mason-Gamer 1996); the migration rate between populations (Slatkin and Maddison 1989), the population genetics parameter, 0 = 2[N.sub.f]u for mitochondrial genes (Watterson 1975; Tajima 1989), and to examine the age of allelic classes (Crandall and Templeton 1993).


Sampling Locations. - In the northern part of their geographic range we collected in Fresno and San Benito Counties at sites in the San Joaquin Valley (SJV), the Panoche Valley (PV) and in the Tumey (TH) and Ciervo (CH) Hills [ILLUSTRATION FOR FIGURE 1 OMITTED]. In the southern part of their geographic range we collected in the Carrizo Plain from two sites situated 25 km apart, the Elkhorn Plain Ecological Reserve (EP) and Painted Rock (PR) [ILLUSTRATION FOR FIGURE 1 OMITTED]. We also collected from a third site, a colony near Soda Lake (SL), which is composed of individuals translocated from both the EP and PR populations and was established for conservation purposes. The sequences from this population could not be used for the population structure analysis. All collections were made using Sherman live traps, positioned in disparate locations. Individual samples of ear wedges and of tail hairs were collected for DNA extraction.

DNA Extraction. - A 2-4-[mm.sup.2] ear wedge was cut into small pieces and incubated at 50 [degrees] C with constant shaking for 20 h in 500 [[micro]liter] of genomic extraction buffer. Protein and lipids were phenol-chloroform extracted and genomic DNA was ethanol precipitated (Thomas et al. 1990). The quantity of high-weight molecular DNA on each sample was estimated by inspection on a 0.8% agarose gel using a molecular marker of known weight and quantity.

Amplification and Sequencing. - A small quantity of total DNA (50-100 ng) was used to amplify a 370-bp fragment of the 5[prime] end of the control region in 100 [[micro]liter] PCR reactions containing 100 mM TrisHCl (pH 8.3); 2 mM Mg[Cl.sub.2]; 500 mM KCl; 0.02% gelatin, 250 [[micro]meter] each of dATP, dCTP, dGTP, and dTTP; 2[[micro]gram]/mL bovine serum albumin (Sigma, fraction V); and 4.0 Units of Taq DNA polymerase (Perkin Elmer-Cetus). Amplifications were performed with 5 [[micro]liter] of two 10 [[micro]meter] primers, one designed for kangaroo rats (TAS; Villablanca 1994) and a generalized vertebrate d-loop primer (H16498; Kocher et al. 1989). For each individual, two amplifications were required; one with one primer phosphorylated and another with the other phosphorylated. Amplifications were carried out for 40 cycles using a denaturing temperature of 94 [degrees] C for 1 min, an annealing temperature of 50 [degrees] C for 1 min and an extending temperature of 72 [degrees] C for 2 min. Ten [[micro]liter] of the product was run on a 2% agarose gel to quantify and verify size. Negative controls were run for all amplifications. The remainder of the product was subjected to exonuclease digestion to remove the strand with the phosphorylated primer and then cleaned with centricon-100 (AMICON) microconcentrators. Seven [[micro]liter] of the resultant volume was direct-sequenced using the dideoxynucleotide chain termination method and Sequenase enzyme (United States Biochemical; Sakai et al. 1988; Higuchi and Ochman 1989; Sambrook et al. 1989). The nucleotide sequence was determined for both strands for all individuals.

Alignment. - Sequences were assembled with the SEQMAN program (DNASTAR, Madison, WI), and the resulting consensus sequences were aligned manually with the Eyeball Sequence Editor (ESEE, Vers. 3.0; Cabot and Beckenbach 1989). A total of 293 base pairs were obtained for each of 95 individuals. No gaps were detected.

Statistical Analysis

Phylogenetic Trees. - To determine whether the variable sites in the control region follow a Poisson distribution, we performed a heuristic search using parsimony analysis (Swofford 1989) to obtain a consensus parsimony tree. This tree was used to ascertain the number of multiple hits (substitutions per site). We removed two sites from further analysis (leaving 293 sites) because they introduced substantial homoplasy. From the number of multiple hits we estimated the mean and variance of the number of substitutions and discovered that mutations were not Poisson but negative binominally distributed. Therefore, we calculated the gamma-parameter of this distribution and used it to construct trees with gamma-corrected distances (Kocher and Wilson 1991). We then constructed neighbor-joining trees (Saitou and Nei 1987) using both the Jukes-Cantor correction for multiple hits (Jukes and Cantor 1969) and the Tamura-Nei distance which provides a gamma-correction for negative binominally distributed mutations and corrects for GC content and transition-transversion bias (Tamura and Nei 1993).

Population Structure. - Genetic diversity and its variance were calculated for each population as in Lynch and Crease (1990). Their estimate of nucleotide diversity corrects for multiple hits and it considers each site as a different locus (Lynch and Crease 1990). Therefore, it should be robust to the biases introduced by rate variation in the control region.

Hierarchical population structure was estimated using the method of Holsinger and Mason-Gamer (1996). Their method defines a new parameter for genetic differentiation, [Mathematical Expression Omitted], as the proportion of diversity in the sample due to differences among populations, which is simply an unbiased version of Nei's statistic, []. It is based upon the fact that Wright's [] can be defined as the ratio of the average coalescence time for pairs of genes taken from within and between populations (Slatkin 1991). It involves creating a hierarchical "tree" of relationships among populations and placing populations on the tree to reflect their natural hierarchical position. At each node, the degree of genetic differentiation between one population and all populations higher up on the hierarchy is determined and a rank statistical test performed to test for its significance.

To test for genetic differentiation between specific pairs of populations, we used the method of Lynch and Crease (1990). Their estimate of the degree of genetic differentiation between populations, [], employs a Jukes-Cantor correction for multiple hits and incorporates stochastic error due to the sampling of haplotypes, populations, and nucleotides. To determine whether an []-value is significant, they employ a test statistic, D, that is chi-square distributed under the null hypothesis of no genetic differentiation. For both Holsinger and Mason-Gamer's (1996) and Lynch and Crease's (1990) methods, we randomly sampled 10 individuals to represent the TH population, so that all populations were equally weighted.

We also examined population structure by constructing a minimum spanning network using Tamura-Nei gamma-corrected distances (see above) with the aid of the statistical package NTSYS (Rohlf 1988). This network is similar to a neighbor-joining tree, except that the constraint of bifurcating branches is removed.

Migration. - To examine migration patterns, we assigned population numbers to the eight populations used for this analysis and determined between which populations migration events were required to explain the topology of a neighbor-joining tree (following the method of Slatkin and Maddison 1989). This method makes use of the information inherent in a phylogenetic tree and reveals between which populations gene flow has occurred. For nonrecombining molecules, such as mtDNA, it is preferable to []-based estimates of migration (Slatkin 1991). The tree was rooted by selecting the most ancestral haplotype among our sample of alleles, deduced by determining the most basal D. ingens haplotype on a phylogenetic tree constructed with D. panamintinus as the outgroup (Thomas et al. 1990; D. panamintinus was too divergent to be used as the outgroup). This analysis indicated that haplotype 21, individual PVA.2, was the best intraspecific outgroup.

[Theta] Estimation. - [Theta] (= 2[N.sub.f]u for mitochondrial genes) and its variance were calculated on distance-corrected estimates based on the number of segregating sites, [[Theta].sub.s], following Watterson (1975) and the average number of pairwise differences, [[Theta].sub.k], between all sequences (following Nei [1987] eqs. 10.6 and 10.9). By assuming that the mutation rate is constant, and by selecting individuals or populations that are not genetically structured, differences between [[Theta].sub.s] and [[Theta].sub.k] should reflect historical differences in population size (Tajima 1989).


Haplotype and Nucleotide Diversity. - We identified 50 unique haplotypes in 95 individuals (Table 1). Among these 50 haplotypes, 54 variable nucleotide sites occurred in the 293-base pair segment of mtDNA we analyzed. Seventeen of these positions harbored singletons, leaving 37 parsimony-informative sites. There were 39 haplotypes among the 68 individuals sampled in the north and 11 haplotypes in the sample of 25 individuals from the south (Table 2). Two northern haplotypes (33 and 37) found in isolated populations (populations TH and CH) had relatively high frequency, but most of the haplotypes in the north had low frequency. Haplotype frequencies in the southern populations were somewhat higher (Table 2), and the EP and PR populations share two haplotypes despite being separated by 25 km. Several haplotypes are shared between the SL and the EP and PR populations, but this was expected because SL is the translocation colony.

If populations have been isolated for significant periods of time and have maintained constant size, the amount of nucleotide diversity in a given population should be correlated with its size. Table 2 does not indicate this trend. Assuming a given mutation rate, the relationship between nucleotide diversity, [Pi], and the number of females (the population size for a mitochondrial gene) can be modeled for an equilibrium population. Figure 2 shows the results of a simulation by Villablanca (1994), who modeled this relationship using [Mu] = 1.5 x [10.sup.-.8], a rate calculated for a section of the control region sequenced in D. panamintinus (Villabianca 1994). The segment of the control region sequenced in this study probably evolves at a slightly higher rate, because it does not include a conserved segment at the 5[prime] end of the gene used in the D. panamintinus study, and later we use an estimate of 5.0% per million years or [Mu] = 2.5 x [10.sup.-8] as another estimate concluded (Thomas et al. 1990); however, the results of this simulation are still of utility. Interpolation from Figure 2 reveals that there is greater nucleotide diversity, [Pi], than expected given the current population sizes in the north (taking [N.sub.f] [similar to] 1/2N in Table 2) and that the EP population has the expected amount of nucleotide diversity for its size. This indicates that extant populations of giant kangaroo rats are not in equilibrium and that population processes such as changes in size, subdivision, and gene flow patterns must have affected their genetic structure. These processes will now be examined in more detail.

Variation in the Rate of Substitution in the Control Region. - If mutations occur at equal rate across the genome, their frequency is expected to be Poisson distributed. However, if the probability of mutation is not equal across sites, then the distribution of mutations approximates a negative binomial distribution (Kocher and Wilson 1991). Comparison of the observed and expected number of mutations by chi-square analysis indicates that the observed pattern of mutation is negatively binomially distributed (Table 3). To correct for the negative distribution of mutations, we calculate the gamma-parameter following Kocher and Wilson (1991), to be a = [m.sup.2]/([s.sup.2] - m) = 0.27, where m is the mean and [s.sup.2] the variance of the number of substitutions.

Nonetheless, the negative binomial distribution of substitutions does not introduce substantial error into the phylogenetic tree. The topography of a neighbor-joining tree based on Tamura-Nei gamma-corrected distances [ILLUSTRATION FOR FIGURE 3 OMITTED] and one based on distances corrected only for multiple hits (the Jukes-Cantor correction; not shown) were identical with the exception that one individual, haplotype 36, is closest to haplotype 15 on the Tamura-Nei tree but closer to haplotype 35 on the Jukes-Cantor tree. The primary distinction between trees corrected or uncorrected for the non-Poisson distribution [TABULAR DATA FOR TABLE 1 OMITTED] of mutations is that the branch lengths on the gamma-corrected tree were about 0.3% greater.

Population Structure. - Most of the methods employed to examine population structure assume a specific model of migration. In addition, all of the models based on Wright's [] or coalescent theory assume a Poisson distribution of mutation, which does not fit this dataset. However, because the difference between a phylogenetic tree that corrects for the non-Poisson distribution and one that does not is minimal, the use of models that assume a Poisson distribution of mutation should be reliable for this dataset.

The hierarchical relationship among populations [ILLUSTRATION FOR FIGURE 4 OMITTED] reveals that the EP population is significantly subdivided from all the other populations grouped collectively, but is [TABULAR DATA FOR TABLE 2 OMITTED] most closely related to the PR population. A test for significant differentiation between the EP and PR populations, using the method of Lynch and Crease (1990), does not reject the null hypothesis of no geographic subdivision ([v.sub.w][mean] = 0.0225 [+ or -] 0.0049; [v.sub.b][EP - PR] = 0.00675 [+ or -] 0.00508; [] = 0.231, D = 0.000[n.s.]). However, the two southern populations (EP and PR) grouped together are significantly subdivided from the northern ones [ILLUSTRATION FOR FIGURE 4 OMITTED].

The structure of the northern populations is more complicated. The SJV population is significantly differentiated from the other northern populations grouped collectively at the 10% level (P = 0.062) and the most closely related to the southern ones. The PVC population is significantly differentiated from populations CH, TH, PVA, and PVB grouped collectively at the 10% level (P = 0.095). The phylogenetic tree [ILLUSTRATION FOR FIGURE 3 OMITTED] shows that the PVC and the CH populations share similar haplotypes with each other, some of which are also shared with the PVA/PVB populations, but all of which are distinct from the TH and SJV haplotypes. The CH population is significantly subdivided from populations TH, PVA and PVB grouped collectively (P = 0.0003): even though it clearly shares a phylogenetic history with the Panoche Valley populations [ILLUSTRATION FOR FIGURE 3 OMITTED], especially population PVC, its structure still is unique.
TABLE 3. The observed and expected number of substitutions per site
if mutations are considered to be Poisson or negatively binomially
distributed. Comparison of the observed pattern of substitution
with that expected for a Poisson and negative binomial distribution
of mutations indicates that the pattern of substitution across the
region is negatively binomially distributed. For the negative
binomial [[[Chi].sup.2].sub.obs] = 1.4623,
[[[Chi].sup.2].sub.3,0.5] = 7.185, while for the Poisson
[[[Chi].sup.2].sub.obs] = 134.67, [[[Chi]2].sub.3,0.5] = 7.815.

tutions                                           Expected:
per site                          Expected:       negative
(hits)                Observed     Poisson        binomial

0                        239        214.03           237.0
1                         28         67.097           33.51
2                         14         10.54            12.14
[greater than] 3          12          1.10            10.38

A negative value of [Mathematical Expression Omitted] was obtained at the final two nodes. This should be precluded by the Wahlund effect (Hartl and Clark 1989), but negative [Mathematical Expression Omitted] have been observed in other recent, yet unpublished, studies, in particular when a locus with a high mutation rate, such as microsatellites, has been used (pers. obs., SVG). The two negative [Mathematical Expression Omitted] observed here [ILLUSTRATION FOR FIGURE 4 OMITTED] are probably due to different causes. Population TH has a negative degree of differentiation [Mathematical Expression Omitted] with populations PVA and PVB and it is significantly subdivided from them (P = 0.001). It seems possible that this negative [Mathematical Expression Omitted] is due to nonequilibrium between drift, mutation and migration in these populations. The TH population is geographically isolated from the Panoche Valley and from the Tulare Basin (due to the hilly terrain and gulches between them), yet there is evidence of gene flow between these regions (see section on migration). It also is small (N [similar to] 135), isolated, and has an unusual character to its genetic variation (unequal allele frequencies and diverse ones) - all characteristics indicating that it may not be in equilibrium. Neigel and Avise (1993) found evidence for a nonequilibrium between drift, mutation, and migration using mtDNA sequence data in three rodent species and discuss how this can occur when the marker used to infer population processes has a high rate of mutation.

On the other hand, population PVA has a negative [Mathematical Expression Omitted] distinguishing it from population PVB, but it is not statistically significant [ILLUSTRATION FOR FIGURE 4 OMITTED], that is, it is effectively zero. This negative [Mathematical Expression Omitted] was probably obtained because these two populations effectively act as a single population and, therefore, should not be treated as distinct. They are large populations situated close to one another and there are no serious barriers to gene flow between them; it is probable that during times of high density they have been connected.

Mistakes about the population structure of natural populations can be made because the wrong population genetic model is assumed (Barton and Clark 1990). An important advantage of Holsinger and Mason-Gamer's (1996) method is that it reveals the hierarchical relationships underlying populations rather than having the investigator decide, a priori, which populations to compare. Since Figure 4 provides a depiction of the hierarchical relationship among populations, it should also represent a rough hierarchy of the age-order of populations with the oldest lying at the most basal branch (EP) and the youngest at the tip (populations PVA and PVB). This age-order of populations makes geographic sense because the three oldest populations, EP, PR and SJV, are situated in large regions of flat terrain where large populations of giant kangaroo rats persisted in the past. The overall order of populations within the hierarchy also makes phylogeographic sense: in a general way the hierarchy proceeds from populations in the south to the northern basin and then westward into the foothills of the coastal range [ILLUSTRATION FOR FIGURE 1 OMITTED]. However, this pattern does not reflect some of the more complex current population processes, which will be discussed at a later point.

If we overlay the structural genetic hierarchy [ILLUSTRATION FOR FIGURE 4 OMITTED] on the position of populations in Figure 1, it appears that differentiation between south and north is due, primarily, to isolation by distance. To a lesser degree this characterizes differentiation in the northern populations. For example, population PVA/PVB are the furthest apart in the genetic hierarchy from population SJV [ILLUSTRATION FOR FIGURE 4 OMITTED] yet they are relatively close geographically. Using the method of the Lynch and Crease (1990) the hypothesis of no genetic differentiation between PVA/PVB and SJV was rejected at the 5% level . They are connected primarily through Panoche Creek, which connects the Panoche Valley to the Tulare Basin but provides limited opportunities for gene flow [ILLUSTRATION FOR FIGURE 1 OMITTED]; isolation by barrier seems a likely cause for their genetic differentiation. Still, their degree of differentiation is somewhat surprising given that they are large populations, each harboring substantial genetic diversity, and would be expected to maintain ancient polymorphism. This suggests that there has been sufficiently little recent historical contact that substantial lineage sorting has occurred. The TH population also appears to be differentiated through isolation by barrier: it is geographically close to the PVA/PVB and the SJV populations, yet significantly differentiated from them [ILLUSTRATION FOR FIGURES 1, 4 OMITTED]. However, the CH population appears to be isolated by both distance and barrier. The phylogenetic tree shows that it contains a small subset of alleles closely related to several of those in the Panoche Valley and to one SJV haplotype but it has little other genetic diversity [ILLUSTRATION FOR FIGURE 3 OMITTED]. Therefore, in the northern colonies both geographical substructuring and unique migration (or colonization) events (as in the CH population) have had an affect on the structure of genetic diversity.

To examine the relationship between geographic location and population structure in more detail we constructed a minimum spanning tree (MST) among all haplotypes and overlaid the geographic position of haplotypes on it [ILLUSTRATION FOR FIGURE 5 OMITTED]. This shows that the southern haplotypes (triangles) are derived from two northern haplotypes (11 and 32), which are close derivatives of one another, but that the southern haplotypes are distinct from the northern ones and nearly monophyletic. The southern haplotypes have as many mutational steps connecting them to the northern haplotypes as some northern haplotypes have between themselves; this, once again, underscores the diversity inherent in the northern populations. The southern haplotypes also have relatively few tip haplotypes and long internal branches.

The haplotypes from the Panoche Valley (circles) are represented on almost every branch of the tree except those leading to the southern haplotypes and one containing exclusively TH haplotypes. This suggests that the Panoche Valley contains old haplotypes, because the geographic variance of alleles has been shown to be highly correlated to allele age (Neigel and Avise 1993). In addition, the cluster containing several single-step mutations between haplotypes is composed exclusively of PV and CH individuals, strongly suggesting that the CH population has been colonized from a PV mtDNA lineage. However, there are two haplotypes in the CH population that do not fall in this cluster (haplotypes 38 and 39); therefore more than one female had to establish the population.

The TH population (dotted squares) contains more diverse haplotypes than one would predict given its small, relatively isolated, geographic range [ILLUSTRATION FOR FIGURE 5 OMITTED]. However on the MST the haplotypes are clustered even though there are often a large number of mutational steps between them. A large number of mutational steps separating haplotypes may indicate that there has been insufficient geographic sampling (Templeton et al. 1995), but it definitely indicates that the TH population contains diverse haplotypes given its small size. Furthermore, some of these haplotypes appear to be old (they are in interior positions and have many mutational derivatives; Crandall and Templeton 1993), suggesting that there must either be restricted gene flow with the larger, presumably older, populations in the Panoche and San Joaquin Valleys or stepping stones of small populations near the TH population. Given that the TH population shares two haplotypes with the Panoche Valley [ILLUSTRATION FOR FIGURE 5 OMITTED], the latter may be more likely as the former would require there to have been several long-distance natal dispersal events. A combined behavior and intensive sampling scheme in the northern foothills would be necessary to reveal the structural dynamics of these small, isolated populations.

Finally, the SJV haplotypes (squares) cluster primarily as derivatives of haplotype 30 (only haplotype 1 does not), and are connected to many of the haplotypes from the Panoche Valley (although the latter are more diverse). This suggests that the Panoche Valley populations are differentiated from the San Joaquin Valley population because, in part, more mitochondrial lineages have survived in the Panoche Valley. This could be due to the recent reduction in habitat for giant kangaroo rats in the SJV, or to differences in genetic structure between the two areas (i.e., the SJV could be less subdivided). However, there is evidence of shared polymorphism of recent origin between the SJV and PV populations (there is one shared haplotype and several haplotypes that are joined by only a few mutational steps) suggesting that there may be limited gene flow connecting these two populations, possibly through the Panoche Creek as mentioned above.

Migration. - Following the method of Slatkin and Maddison (1989) we estimated the mean number of migrants per generation, M (= [N.sub.e]m), from a neighbor-joining tree using Tamura-Nei gamma corrected distances, and haplotype 21 (PVA.2) as the outgroup (see methods). From Slatkin and Maddison (1989), we estimate an average of 7.5 migrants per generation for all populations. This is higher than some previous estimates in rodents but lower than a recent estimate calculated for Mus domesticus (Nachman et al. 1994).

Table 4 presents the populations between which migration events are required to explain the topology of the phylogenetic tree [ILLUSTRATION FOR FIGURE 3 OMITTED]. If we treat each population independently, there are 28 possible pairs of populations between which migration could have occurred, of which 14 are represented. If we join populations PVA and PVB (1 and 2 in Fig. 3) as suggested by the hierarchical population analysis (above), then migration events between the Panoche Valley and all other populations account for 21 of the 30 events on the tree. Therefore, genetic variation in populations of giant kangaroo rats can often be traced to extant mitochondrial lineages in the Panoche Valley.

To distinguish whether this is because the PV population harbors ancestral haplotypes or if there is ongoing gene flow, it is necessary to compare the genetic diversity between populations with the number of haplotypes they share. In this way we can tentatively distinguish between lineage sorting and migration. If populations are highly differentiated, geographically isolated, but share haplotypes, it seems reasonable to conclude that there is some ongoing gene flow. Using this logic, it seems probable that the PV and CH populations share a recent episode of gene flow or even that there has been a founder event from PV to the CH. There may also be gene flow between the TH and PV populations (see above) but it must be restricted, or occur via a stepping stone of other populations. On the other hand, the inference of five migration events (Table 4) between the PV and SJV is more likely due to shared ancestry.
TABLE 4. The populations between which migration events are
required to explain the topology of the neighbor-joining tree,
Figure 3 (see text for details).

                                   No. of migration
Population                             events

PVA-PVB                                  3
PVA-PVC                                  2
PVA-SJV                                  3
PVA-TH                                   3
PVA-CH                                   1
PVB-PVC                                  2
PVB-SJV                                  1
PVB-TH                                   2
PVB-CH                                   3
PVB-SJV                                  1
SJV-TH                                   3
SJV-CH                                   1
SJV-EP                                   1
TH-PR                                    1
EP-PR                                    3

Change in Population Size. - Tajima (1989) has shown that two estimates of [Theta] (where [Theta] = 2[N.sub.f]u for cytoplasmic genes) are differentially sensitive to changes in population size; this fact may be used to infer a change in population size from DNA sequence data. Specifically, [[Theta].sub.s] based on segregating sites (Watterson 1975) reflects more the current effective population size, whereas [[Theta].sub.k] based on the average number of pairwise differences (Tajima 1989) reflects the effective population size over historical time (note also [[Theta].sub.k] = [Pi]).

Using individuals from populations SJV, PVA, PVB, and PVC (the largest populations, so as to minimize the effect of population subdivision) we calculate [[Theta].sub.s] for the 293 base-pair segment to be 13.97 [+ or -] 3.49 and [[Theta].sub.k] to be 8.66 [+ or -] 4.15. Though these estimates are not statistically different (the variance for [[Theta].sub.k] is usually large), they suggest that there may have been an increase in population size in the northern colonies, a result that agrees with recent census data (Williams et al. 1994). This view is corroborated by both the migration analysis and the negative [Mathematical Expression Omitted] result obtained in the nested populations structure analysis. The migration analysis indicated that mtDNA haplotypes from all northern populations can often trace their lineage to one extant in the PV, which would be expected during a range expansion because rare alleles do not have the same probability of being lost (Slatkin and Hudson 1991). Second, during a population expansion negative [Mathematical Expression Omitted] would be more likely due to the possibility of nonequilibrium among migration, mutation, and drift.

[[Theta].sub.s] for the southern population (individuals from EP, PR, and SL) is 7.02 [+ or -] 3.32, while [[Theta].sub.k] is 7.06 [+ or -] 4.08. This estimate of [[Theta].sub.k], corresponds to a nucleotide diversity, [Pi], of 0.02. Interpolation from Figure 2 indicates that this value of [Pi] is a little higher than expected for a population of 10,000 females. However, population sizes in the south have fluctuated dramatically: in 1996 there were about 200,000 individuals ([similar to]100,000 females) as opposed to the 20,000 (10,000 females) at the time of sampling in 1993. A nucleotide diversity of 0.02 could also describe a population that fluctuates between 10,000 and 100,000 females because the effective size of a populations that fluctuates in size is equal to the harmonic of its population sizes over time (Nei 1987). The MST [ILLUSTRATION FOR FIGURE 5 OMITTED] and the phylogenetic tree [ILLUSTRATION FOR FIGURE 3 OMITTED] both revealed that there are long internal branches and relatively few tip branches in the south compared to the north. Given that [[Theta].sub.s] and [[Theta].sub.k] are indistinguishable for the southern populations, it is possible that they are in equilibrium with respect to mutation and drift. However, the fact that most southern haplotypes are separated by many mutational steps lends support to the hypothesis that the south was undergoing a population decline at the time of sampling; that is, young mutational types have been eliminated while older, more common, allelic lineages have been preserved.


Our study has found that despite a recent reduction in the range of giant kangaroo rats, both intra- and interpopulation variabilities are high. Intuitively, one might have expected that the patchy distribution of kangaroo rats in the north would lead to reduced genetic variation there. One might also have expected the primary determinant of existing patterns of variation to be restricted gene flow and to find a substantial genetic distance between northern and southern populations. None of these expectations were borne out by our analyses. This reveals why genetic studies can be useful for conservation: the current distribution of a population may not reflect the historical processes that have shaped its genetic structure. Because species persistence is greatly affected by changes in population structure (Avise and Hamrick 1996; Holsinger 1996), a knowledge of the historical patterns of gene flow and population structure can be useful for designing management strategies.

We have found more mitochondrial DNA lineages (i.e., ancestral polymorphism) and greater genetic diversity in populations of giant kangaroo rats that inhabit complex topographical terrain. This indicates that increased spatial heterogeneity of populations can maintain greater genetic diversity even when the total population size of a heterogeneously distributed population is less than that of continuously distributed one. Avise et al. (1984) demonstrated that the principal factors determining the number of mtDNA lineages surviving over time are the number of founding mtDNA lineages, the growth rate of the population, and the degree of population subdivision. They calculated that for a panmictic population of size N, most individuals will trace their mtDNA ancestry to a single female lineage after 4[N.sub.f] generations. If there is population subdivision, while diversity may decay within subpopulations more mtDNA lineages will survive in the total population. This second situation is an extension of the phenomenon that more alleles are maintained in a subdivided population than in one of the same size that is panmictic (Maruyama 1970).

We can observe this phenomena in our sample of alleles. If we consider each internal node in the phylogenetic tree to be a distinct mtDNA lineage there are, conservatively, eight extant mtDNA lineages represented in our sample of alleles [ILLUSTRATION FOR FIGURE 3 OMITTED]. All eight lineages have descendants in the north, while only two do in the south despite a larger total population size in the south and that the southern population has probably experienced fewer human-induced changes. Moreover, we find extensive genetic structuring in the north and none in the south and that there is a greater genetic distance between certain northern haplotypes than there is between any northern and southern haplotype [ILLUSTRATION FOR FIGURE 4 OMITTED]. Taken together these results attest to the importance of geographic structuring in preserving genetic variation.

Relationship between Northern and Southern Populations. - This leads us to the question of the historical relationship between northern and southern populations. Our analyses have uncovered two apparently contradictory results with respect to the relative age of northern and southern populations. The hierarchical relationship among populations [ILLUSTRATION FOR FIGURE 4 OMITTED] indicates that the EP and PR populations contain, on average, the most basal haplotypes, which means that they are most likely the oldest populations. However, the migration and Minimum Spanning Tree analyses suggest that the northern populations contain the oldest haplotypes. These apparently contradictory results underscore the role of population structure in maintaining ancient polymorphisms because allelic diversity is dependent upon allele turnover rate that, in turn, is dependent on population structure. It appears that the northern populations have maintained more ancestral polymorphisms than the southern populations but that the southern populations were established prior to or at a similar time as the northern ones.

To examine the relationship between northern and southern populations in more detail we can estimate the time since divergence between the populations by estimating the number of mutational differences between them. Using four-cluster analysis (Rzhetsky et al. 1995) we can estimate the branch length separating north from south. In lieu of the TamuraNei gamma-correction, we use a Kimura two-parameter distance correction (Kimura 1980) to estimate the distance between populations SJV and PVA/PVB (grouped together) to represent the north and populations EP and PR in the south. This analysis gives an interior branch length estimate of 0.0048 [+ or -] 0.0024 separating north from south, with P = 0.045 that this branch length is significantly different from zero. Assuming an approximate mutation rate of 5% per million years (see above) this leads to an estimate of 100,000 [+ or -] 50,000 years for the divergence time between northern and southern populations of giant kangaroo rats.

Second, we can ask whether this divergence time is less than or greater than the coalescent time of all haplotypes in either the north or south. This will allow us to examine if populations of giant kangaroo rats were first in the south and then moved north or vice versa. We can estimate [N.sub.f] for a given sample of alleles because the expected number of nucleotide differences per site between haplotypes, [Pi], is estimated by [[Theta].sub.k], which is equal to 2[N.sub.f][Mu] for a mitochondrial gene. Therefore, we can estimate the number of females in the south by grouping individuals from populations EP, PR, and SL (because there is no detectable genetic differentiation between them) and calculating [Pi]. This gives [Pi] = 0.021, and using [Mu] = 2.5 x [10.sup.-8] we arrive at [N.sub.f] = 210,000 in the south. This gives us a coalescent time for all haplotypes of about 800,000 generations (4[N.sub.f]), or 400,000 years. It will also hold that the coalescent time of all northern haplotypes will be [greater than or equal to] 400,000 years since all of the main northern populations have a [Pi] [greater than or equal to] 0.021. The precision of these estimates is not particularly good; the variance of [Pi] is large and the numbers we arrive at are highly dependent upon [Mu]. Nevertheless, because both the time since divergence between north and south and the coalescent time of all haplotypes in the north or south are both dependent upon [Mu], the relative value of these estimates should answer the question of the historical relationship between north and south.

Given that the coaslescent time of all haplotypes in the south and the north is greater than the time since divergence between north and south, we cannot determine whether the northern or southern populations existed prior to the other, although we can say that populations of giant kangaroo rats must have been continuously enough distributed throughout the Tulare Valley that alleles could pass (via other populations) between north and south after the two areas were already colonized by giant kangaroo rats. This is supported both by the relationship of northern and southern haplotypes [ILLUSTRATION FOR FIGURE 5 OMITTED] and by the phylogeographic position of populations [ILLUSTRATION FOR FIGURE 4 OMITTED], since the southern populations are genetically closest to the SJV and any historic connection between the northern and southern populations would have been through the Tulare Basin.

Nevertheless, the dates given above are commensurate with geological data. Davis and Cophen (1989) have determined that 725,000 to 615,000 years ago the Coastal Range (on the west side of the Tulare Basin) uplifted and closed the southern outlet of the basin to the Pacific Ocean. Therefore, parts of the Tulare Basin and the Carrizo Plain could have been dry enough 725,000 years ago to provide suitable habitat for giant kangaroo rats. However, prior to 615,000 B.P. there was a large lake in the southern half of the basin that would have prevented contact between the current northern and southern populations of giant kangaroo rats, if they then inhabited the region. About 615,000 B.P. this lake dried up and from 200,000 to 10,000 B.P. the basin increased in aridity and probably provided suitable habitat for giant kangaroo rats throughout its entire lower part. It is possible that the current northern and southern populations of giant kangaroo rats were, essentially, continuously distributed during this time, a point that agrees with our estimate of 100,000 [+ or -] 50,000 years for the separation of northern and southern populations. Finally, the above times for the divergence between northern and southern populations and the coaslescent age of all haplotypes are commensurate with historical mtDNA patterns found in populations of D. panamintinus, another species of kangaroo rat endemic to California just east of the range of D. ingens. Villablanca (1994) estimated the time since separation of two D. panamintinus populations to be between 200,000 to 400,000 years; it seems possible that the expansion of desert rodents throughout this region occurred within this time scale.

The Northern Populations. - Our analyses revealed extensive substructuring within the northern populations that, we have argued above, is partly maintained by the geographic complexity in the north. This substructuring, however, takes several forms. First, although the SJV and PVA/PVB populations are close geographically and harbor substantial nucleotide diversity, they are significantly subdivided from one another. Moreover, the haplotypes in the SJV population appear primarily as derivatives of one haplotype (number 30), while the PV haplotypes are found throughout the MST [ILLUSTRATION FOR FIGURE 5 OMITTED]. Second, the theory of random genetic drift would dictate that small populations, such as those in the Tumey and Ciervo Hills, would be depauperate in genetic diversity. Although both of these populations contained less genetic diversity than larger populations and had an uneven allele frequency both suggestive of the results of drift (Table 1), the nature of that diversity was somewhat unexpected.

Neigel and Avise (1993) and Crandall and Templeton (1993) have demonstrated that the correlation between lineage age and geographic range and the correlation between haplotype position (i.e., on the tip or interior of a phylogenetic tree) and allele age, respectively, are robust. Applying their conclusions to the Tumey and Ciervo Hills populations demonstrates that different population genetic processes are affecting the two populations. The haplotypes in the Ciervo Hills population are primarily tip haplotypes [ILLUSTRATION FOR FIGURE 5 OMITTED], that is, young, and there are few mutational connections between them and other haplotypes, suggesting that the CH is a young population. Because the CH population is both significantly subdivided and geographically isolated from the Panoche Valley populations [ILLUSTRATION FOR FIGURE 4 OMITTED] it argues that there were recent dispersal events from the Panoche Valley to the Ciervo Hills, but that only a small subset of the alleles from the larger populations were involved. On the other hand, the existence of several interior haplotypes in the Tumey Hills population [ILLUSTRATION FOR FIGURE 5 OMITTED] and the large number of mutational derivatives between Tumey Hills haplotypes indicates that the Tumey Hills population is neither as young nor as isolated as the Ciervo Hills population. We have argued that there may be ephemeral populations of giant kangaroo rats in the Tumey Hills, enabling restricted ongoing gene flow between them and the Panoche Valley.

Are existing levels of genetic diversity in northern populations due to ongoing gene flow or to the maintenance of ancestral polymorphisms? Our results indicate that there has been little ongoing gene flow between the San Joqauin and Panoche Valleys. It appears that they have been reproductively isolated for sufficient time that lineage sorting of ancestral polymorphism has left them with distinct mtDNA diversity [ILLUSTRATION FOR FIGURE 3 OMITTED]. However, the SJV population appears to have lost (or the PV maintained) more mtDNA lineages that the PV (see results). This may indicate that either the SJV population has declined in size or that the PV population has expanded. However, there is some strong evidence of ongoing gene flow between the Panoche Valley and Ciervo Hills, good evidence for gene flow between the Tumey Hills and the Panoche Valley and, perhaps, with the San Joaquin Valley, and weak evidence for gene flow between the Panoche and San Joaquin Valleys.

Finally, our analyses have suggested that there may be a range expansion occurring in the northern populations with the Panoche Valley as its primary source. The Panoche Valley populations harbor considerably more diversity than would be predicted from their size. This alone could be evidence of a recent population decline or expansion (because new mutations have a lower probability of being lost during a population expansion). Panoche Valley haplotypes are distributed throughout the phylogenetic tree, a haplotype found in the PV population was determined to be the best intraspecific outgroup, and many of its haplotypes occupied interior positions on a haplotype spanning network [ILLUSTRATION FOR FIGURE 5 OMITTED]. These things indicate that it is an old population. However, there is evidence that it may be the principal source of a recent expansion. Panoche Valley haplotypes are frequently separated by only one mutation from another existing haplotype (an excess of tip haplotypes is expected during a population expansion), many migration events between the Panoche Valley and other populations are required to explain the current genetic structure (Table 4) and our inference of a historical change in population size suggests [[Theta].sub.s] [greater than] [[Theta].sub.k] - all of these results suggest that there may be an expansion of giant kangaroo rats throughout the Panoche Valley and neighboring foothills.

The Southern Populations. - In contrast, we cannot reject the hypothesis that the southern populations act, as a whole, as a single population and that they are in genetic equilibrium. However, there is some indication that the structure of the southern population is affected by episodes of changing population size. Recent census data has revealed that the population size of giant kangaroo rats can change by an order of magnitude within a short period of time. When we sampled there were approximately 20,000 giant kangaroo rats in the Carrizo Plain, while in 1996 that number had increased to at least 200,000. Although we found no genetic subdivision between the EP and PR populations, the high number of mutational steps between all southern haplotypes and the existence of a cluster of haplotypes unique to Painted Rock suggests that some lineage sorting and loss of young alleles had occurred prior to sampling, both of which may accompany a population decline. The fact that there was no evidence of a change in population size by the comparison of [[Theta].sub.s] and Ok is consistent with the hypothesis that the southern population has not changed in size. However, it also seems logical that a population which fluctuates in size would have similar estimates of [[Theta].sub.s] and [[Theta].sub.k] because the effective size of such a population is equal to the harmonic mean of the population sizes over time (Nei 1987). However, it may be possible to detect fluctuating population size from the information in a phylogenetic tree. For example, if a population that fluctuates in size is sampled during a population explosion one would observe an excess of tip (i.e., young) branches, while if it is sampled during a population decline one would observe longer internal branches (indicative of older haplotypes).

In summary, our investigation into the population processes affecting the genetic structure of D. ingens has found that (1) all populations (except the EP population) harbor more genetic diversity than expected for random mating, nonstructured populations; (2) the topographical complexity (in addition to any untested effects of social structure) of the north helps to maintain high levels of substructuring, diversity and ancestral polymorphism; (3) the time since separation of northern and southern colonies is probably less than the coalescent age of all haplotypes in the north or south; (4) the Panoche Valley population has maintained more ancestral polymorphisms than any other population, and it may also be undergoing a range expansion; (5) the Ciervo Hills population has been founded by a recent migration event from a Panoche Valley mtDNA lineage; (6) there is restricted gene flow to the Tumey Hills from the Panoche and San Joaquin Valleys but there may also be, unsampled, populations throughout the Tumey Hills that contribute to the surprisingly high genetic diversity found there; and (7) the southern populations act, effectively, as one large population, although fluctuations in size may affect their genetic structure.


We thank M. Davis, L. Hamilton, and S. Nelson for assistance with the fieldwork. K. Holsinger kindly performed the computer analysis for the hierarchical genetic structure and provided helpful discussions on the use of the method. Thanks to P. Mosquin for reading an earlier version of this manuscript, and for several helpful discussions, and to S. Kumar for providing help with computer programs. Partial funding was provided by Section-6 funds from the California Department of Fish and Game (CDFG) to DFW (FG-1256) and by Section-6 funds to KR and RCF. We acknowledge R. Schlorff of CDFG for his part in funding the research and the US Fish and Wildlife Service, Sacramento Field Office, and the Bureau of Reclamation, Mid-Pacific Region, for their support, with special thanks to R. Faubion at the Bureau of Reclamation, through the Endangered Species Recovery Planning Program.


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