Testing Equivalence Simultaneously for Location and Dispersion of two Normally Distributed Populations

In clinical trials with an active control usually therapeutical equivalence of a new treatment is investigated by looking at a location parameter of the distributions of the primary efficacy variable. But even if the location parameters are close to each other existing differences in variability may be connected with different risks for under or over treatment in an individual patient. Assuming normally distributed responses a multiple test procedure applying two shifted one-sided t-tests for the mean and accordingly two one-sided F-tests for the variances is proposed. Equivalence in location and variability is established if all four tests lead to a rejection at the (one-sided) level α. A conservative procedure “correcting” the t-tests for heteroscedasticity is derived. The choice of a design in terms of the global level α, the global power, the relevant deviations in the population means and variances, as well as the sample size is outlined. Numerical calculations of the actual level and power for the proposed designs show, that for balanced sample sizes the classical uncorrected one-sided t-tests can be used safely without exaggerating the global type I error probability. Finally an example is given.     

EFFECTS OF POPULATION BOTTLENECKS ON GENETIC DIVERSITY AS MEASURED BY ALLOZYME ELECTROPHORESIS

Low levels of allozyme heterozygosity in populations are often attributed to previous population bottlenecks; however, few experiments have examined the relationship between heterozygosity and bottlenecks under natural conditions. The composition and number of founders of 55 experimental populations of the eastern mosquitofish (Gambusia holbrooki), maintained under simulated field conditions, were manipulated to examine the effects of bottlenecks on three components of allozyme diversity. Correlations between observed and expected values of allozyme heterozygosity, proportions of polymorphic loci, and numbers of alleles per locus were 0.423, 0.602, and 0.772, respectively. The numbers of polymorphic loci and of alleles per locus were more sensitive indicators of differences in genetic diversity between the pre-bottleneck and post-bottleneck populations than was multiple-locus heterozygosity. In many populations, single- and multiple-locus heterozygosity actually increased as a result of the founder event. The weak relationship between a population's heterozygosity and the number and composition of its founders resulted from an increase in the variance of heterozygosity due to drift of allele frequencies. There was little evidence that selection influenced the loss of allozyme variation. When it is not possible to estimate heterozygosity at a large number of polymorphic loci, allozyme surveys attempting to detect founder events and other types of bottlenecks should focus on levels of locus polymorphism and allelic diversity rather than on heterozygosity.     

Allozyme diversity in Chinese,Seguin and American chestnut (Castanea spp.)

Allozyme genetic variability in three chestnut (Castanea) species was investigated using 19 loci from ten enzyme systems. G-tests of heterogeneity of isozymic allele distribution showed significant differences between the three species at 15 of the 19 loci, and between the 13 C. mollissima populations at 13 of the 19 loci examined. C. mollissima was found to possess a significantly-higher value of mean gene heterozygosity (H=0.3050±0.0419), the percentage of polymorphic loci (P=84.21%) and the average number of alleles per locus (A=2.05), than any other species in the Castanea section Eucastanon. When the genetic variability of populations of C. mollissima from four regions in China was investigated, the population from the Changjiang river region showed a markedly higher mean gene heterozygosity (H=0.3480±0.0436) than populations from the other regions. Genetic relationships among the four regions were assessed by Nei's genetic identity I and standard genetic distance D. An approximately-identical distance between the population from the Changjiang river region and populations from the three other regions was observed, while populations from the latter regions showed almost the same genetic distance from each other. These data, when considered with information existing prior to this study, contribute to an understanding of the possible origin and progenitor of the chestnut species.     

MATING SYSTEM IN NATURAL POPULATIONS OF JEFFREY PINE

The mating system and allozyme variation at 20 loci in three Klamath Mountains and two Sierra Nevada populations of Jeffrey pine (Pinus jeffreyi Grev. & Balf.) were investigated. On average, multilocus estimates of the proportion of viable progeny due to outcrossing (t_m) were high in all populations (mean t_m = 0.935, range 0.881 to 0.971). Despite differences in stand structure, t_m did not differ (P > 0.05) between the Klamath (mean t_m = 0.933) and Sierra Nevada (mean t_m = 0.937) populations. At all but one locus in one population and at two in another, genotype frequencies fit (P > 0.05) Hardy-Weinberg expectations. Mean estimates of observed heterozygosity in Klamath (0.182) and Sierra Nevada (0.327) populations were comparable to values reported for other conifers.     

Comparison of t-tests for differences in sexual dimorphism between populations

A t-test that can be used for evaluating the significance of differences in metric sexual dimorphism between populations is derived directly from mathematical considerations of the differences between distributions. It is compared with the t-test derived by Relethford and Hodges (1985), which was based upon linear regression with sex as a dummy variable. Both are determined to be mathematically equivalent, though the one derived here is more similar in form to traditional t-tests of differences and therefore may be simpler to employ. Both tests require only summary statistics for comparisons between populations and comparisons between generations within populations.     

Genic variation in the coyote,Canis latrans,in Tennessee,U.S.A.

Protein variation, levels of heterozygosity, and interlocality gene variation were studied in the coyote, Canis latrans, using starch gel electrophoresis. Canis latrans were obtained from 27 counties in Tennessee. Eleven of 20 loci examined were found to be polymorphic with the remaining nine loci fixed for the same gene in all populations. Mean heterozygosity (\-H) varied from 0.0% to 1.9% with a mean of 0.9%. These values are low for a mammal. Significant heterozygote deficiencies occurred in most groups. Results of F-statistics indicated a significant degree of population differentiation at four loci (Gdh, Idh-1, Mdh-2, 6-Pgd). Rogers' coefficients of genetic similarity ranged from 0.950 to 1.000 and showed C. latrans to be genetically homogenous in that portion of the range investigated.     

Microsatellite Variation in Two Populations of Free-Ranging Yellow Baboons (Papio hamadryas cynocephalus)

We investigated genetic variation at six microsatellite (simple sequence repeat) loci in yellow baboons (Papio hamadryas cynocephalus) at two localities: the Tana River Primate Reserve in eastern Kenya and Mikumi National Park, central Tanzania. The six loci (D1S158, D2S144, D4S243, D5S1466, D16S508, and D17S804) were all originally cloned from and characterized in the human genome. These microsatellites are polymorphic in both baboon populations, with the average heterozygosity across loci equal to 0.731 in the Tana River sample and 0.787 in the Mikumi sample. The genetic differentiation between the two populations is substantial. Kolmogornov–Smirnov tests indicate that five of the six loci are significantly different in allele frequencies in the two populations. The mean F _ST across loci is 0.069, and Shriver's measure of genetic distance, which was developed for microsatellite loci (Shriver et al., 1995), is 0.255. This genetic distance is larger than corresponding distances among human populations residing in different continents. We conclude that (a) the arrays of alleles present at these six microsatellite loci in two geographically separated populations of yellow baboons are quite similar, but (b) the two populations exhibit significant differences in allele frequencies. This study illustrates the potential value of human microsatellite loci for analyses of population genetic structure in baboons and suggests that this approach will be useful in studies of other Old World monkeys.     

RAPD and Allozyme Analysis of Genetic Diversity in Panax ginseng C.A. Meyer and P. quinquefolius L.

Inter- and intraspecific variation of two ginseng species Panax ginseng and P. quinquefolius was estimated by studying 159 RAPD and 39 allozyme loci. Parameters of polymorphism and genetic diversity were determined and a tree was constructed to characterize the differences between individual plants, samples, and species. Genetic variation in P. ginseng proved to be lower than in P. quinquefolius. Gene diversity in the total P. ginseng sample was comparable with the mean expected heterozygosity of herbaceous plants. This suggests that wild P. ginseng plants in various areas of the currently fragmented natural habitat and cultivated plants of different origin have retained a significant proportion of their gene pool. The mean heterozygosity calculated per polymorphic locus for the RAPD phenotypes is similar to that of the allozyme loci and may be helpful in estimating gene diversity in populations of rare and endangered plant species.     

Molecular genetics of peripheral populations of Nova Scotian Unionidae (Mollusca: Bivalvia)

Peripheral populations of eight species of freshwater bivalves (Unionidae.) extending their geographic ranges into Nova Scotia, Canada, were examined electrophoretically to determine both the extent of genetic variability within such populations, and whether the hypothesized pathway of colonization across the Isthmus of Chignecto is reflected in patterns of genetic resemblance among these populations. The Nova Scotian species examined could be separated into two groups based on levels of observed heterozygosity and levels of variability in allele frequencies. The first group is characterized by low levels of heterozygosity and polymorphism compared with north-eastern American populations, and in the case of one species, Elliptio complanala, considerable variability in allele frequencies among populations occurring in similar habitats in different drainages. Populations of E. complanata from Nova Scotia can be differentiated from conspecific populations on the southern Atlantic Slope by possession of fast alleles at two loci. Multivariate analyses define subgroups within populations of E. complanata consistent with hypothesis that the species invaded Nova Scotia by way of the Isthmus of Chignecto, and then split into two groups, one of which colonized Cape Breton to the north and the other of which colonized southern areas of the Province. The second group of Nova Scotian species is characterized by little reduction in heterozygosity and polymorphism compared with values observed among north-eastern American conspecifics or congeners, little variability in allele frequencies from population to population, and little evidence to suggest that these species were dependent on the land bridge to invade the Province. The type of dispersal is hypothesized to be responsible, in part, for these differences: larvae of species in the first group rely on a parasitic attachment to fish with territorial habits limited to fresh water, and are thus likely to invade new drainages separated by salt water by chance, in small numbers, and in stepping-stone fashion. Species in the second group parasitize anadromous or saltwater tolerant hosts, are likely to be introduced into new habitats in greater numbers and/or receive greater amounts of gene flow subsequent to colonization, and seem less dependent on land-bridges to colonize new habitats.     

Genetic Differentiation of the Tuva Population with Respect to the AluInsertions

Polymorphism of three rural populations of the Tuva Republic was examined using a set of five autosomal Aluinsertions at the ACE, PLAT, PV92, APOA1,and F13Bloci. The allele frequency distribution patterns revealed in Tuvinians were typical to Mongoloid populations of Asia and were characterized by relatively high frequency of the Alu-repeat insertion at the PV92and F13Bloci along with relatively low insertion frequency at the APOA1locus. With respect to the test systems used, Tuvinian populations examined displayed high levels of genetic diversity. The mean expected heterozygosity values in the populations of Kungurtug, Toora-Khem, and Teeli were 0.433, 0.407, and 0.437, respectively. The level of genetic diversity in the pooled Tuvinian sample was 0.432. The coefficient of genetic differentiation in the three populations studied was 1.4% pointing to relatively low level of genetic subdivision of the indigenous Tuvinian populations. However, estimates of genetic differentiation of the Tuvinian gene pool made by use of the Alu-repeat system were higher compared to those performed using classical protein systems, mtDNA, or Y-chromosomal haplotypes. Even though Tuvinian populations were characterized by common gene pool, some features specific to Western Tuvinian population could be distinguished. These features could be associated with higher contribution of the Caucasian component to the gene pool of this population. Phylogenetic analysis demonstrated close genetic relationships between the Tuvinian and Altaic ethnic populations.     

Electrophoretic variability in natural populations of Drosophila melanogaster and Drosophila simulans

Genetic variation at 59 gene loci coding for enzymes (50) and larval proteins (9) has been studied in sympatric populations of Drosophila melanogaster and D. simulans from insular and continental origin. The average number of alleles per locus, the mean proportion of polymorphic loci and the mean heterozygosity are similar both within and between species. There are however some significant differences between D. simulans populations in the genotypic frequencies for four polymorphic loci.     

Microsatellite DNA evidence for genetic drift and philopatry in Svalbard reindeer

Mainland populations of Arctic reindeer and caribou Rangifer tarandus often undergo extensive movements, whereas populations on islands tend to be isolated and sedentary. To characterize the genetic consequences of this difference, levels of genetic diversity and subdivision of Svalbard reindeer (R. t. platyrhynchus) from two adjacent areas on Nordenskjiöldland, Spitsbergen were estimated using data from up to 14 microsatellites. The mean number of alleles per locus in Svalbard reindeer was 2.4 and mean expected heterozygosity per locus was 0.36. The latter value was significantly lower than in Canadian caribou and Norwegian reindeer but higher than in some other cervid species. Large samples of females (n = 743) and small samples of males (n = 38) from two sites ≈ 45 km apart showed genetic subdivision, which could be due to local population fluctuations or limited gene flow. To our knowledge, this is the first study to report significant differentiation at microsatellite loci in Rangifer at such short geographical distances. Neither population showed genetic evidence for recent population bottlenecks when loci unbiased with respect to heterozygosity were analysed. In contrast, false signals of a recent bottleneck were detected when loci upwardly biased with respect to heterozygosity were analysed. Thus, Svalbard reindeer appeared to conform to the paradigm of island populations made genetically depauperate by genetic drift.     

Genetic diversities of four little-known species of Malesherbia (Malesherbiaceae) endemic to the arid inter-Andean valleys of Peru

Few studies of genetic variation have been conducted on plants of the Pacific coastal desert and neighboring Andes of Peru, although the region has many endemic taxa. Enzyme electrophoresis was employed to examine allozyme diversities of four species of the family Malesher-biaceae, an endemic to the arid Andes and coastal desert. One population ofMalesherbia splendens and two ofM. tubulosa, both endemics of the department of Lima, one population ofM. weberbaueri var.weberbaueri, an endemic of the Andean department Huancavélica, and the two Lima populations ofM. scarlatiflora were studied. Fifteen loci were examined for all populations and an additional seven loci were resolved forM. weberbaueri andM. splendens. Malesherbia splendens, which is known from three populations, has a low mean number of alleles per locus (A), proportion of polymorphic loci (P), and expected heterozygosity (H_s) (A=1.214, P=0.214, H_s=0.057).Malesherbia weberbaueri (A=1.231, P=0.154, H_s=0.079) andM. scarlatiflora (A=1.364, P=0.273, H_t=0.083) both have average expected heterozygosities and relatively low mean numbers of alleles per locus and proportions of polymorphic loci. InM. tubulosa, all measures of genetic diversity are high in comparison with other endemics (A=1.818, P=0.364, H_t=0.206).Malesherbia tubulosa has high interpopulation differentiation, whereasM. scarlatiflora has low among-population diversity. The relatively low allozyme diversities, restricted habitats, narrow ranges ofM. splendens andM. weberbaueri, and the morphological similarities of all four species suggest that they evolved recently by founder events. Greater allozyme diversities inM. tubulosa could be attributable to its maintenance of larger populations in a greater variety of habitats.     

Identification of microsatellite DNA markers for population structure analysis in Indian major carp, Cirrhinus mrigala (Hamilton-Buchanan, 1882)

Forty‐four primer sequences available for four cyprinid fishes were tested to amplify microsatellite loci in Indian major carp, Cirrhinus mrigala. A total of 12 loci were successfully amplified with clear scorable patterns and five thereof were polymorphic. Suitability of the identified polymorphic loci in population structure analysis of C. mrigala was assessed. Genetic variation was examined in 76 specimens collected from five different rivers. The mean observed heterozygosity ranged from 0.247 to 0.333. Significant heterogeneity in allele frequencies was detected, indicating that the samples analysed did not belong to homogenous populations. The identified microsatellite markers are promising for the analysis of intraspecific divergence in C. mrigala across its distribution range.     

BREEDING SYSTEM OF THE FERN DRYOPTERIS EXPANSA: EVIDENCE FOR MIXED MATING

The levels and distribution of genetic variation within and among populations of the homosporous fern Dryopteris expansa were assessed using enzyme electrophoresis. Twelve loci representing six enzymes were examined in 502 sporophytes from nine populations. Values of P, H, and mean number of alleles per locus are much lower in D. expansa compared to values for other fern species. Values of F varied from –0.014 to 0.745 with an average F of 0.335. There was also considerable population to population variation in F. In three populations the observed heterozygosity closely approximated that expected at Hardy-Weinberg equilibrium, whereas in the remaining populations observed heterozygosity was significantly lower than the expected heterozygosity. In D. expansa the major component of F_IT is F_IS; the relatively high F_ST value suggests a high degree of interpopulational differentiation. Electrophoretic data suggest that this species possesses a mixed mating system. This study, in conjunction with other investigations, indicates that just as in angiosperms, a variety of breeding systems operates in homosporous ferns, ranging from extreme inbreeding, through mixed mating to outcrossing.     

Genetic and clonal diversity in Korean populations ofVitex rotundifolia (Verbenaceae)

Vitex rotundifolia L.f. is a woody perennial and has sexual and asexual modes of reproduction. Allozyme study was conducted on 550 plants in 13 Korean populations. The levels of genetic variability and divergence within and among populations, respectively, are considerably lower and higher than the mean values for woody plants with similar life history tralts. Mean percentage of polymorphic loci (P _P), mean number of alleles per locus (A _P), and mean genetic diversity (He _P) within populations ofV. rotundifolia were: 16.7%, 1.21, and 0.047. On average, about 79% of the total variation inV. rotundifolia was common to all populations (meanG _ST=0.208). In addition, significant differences in allele frequencies among populations were found in all polymorphic loci examined (P<0.001). On the other hand, levels of genotypic diversity within and among populations were moderate. About 44% (18/41) of multilocus genotypes were “local genotypes” (genotypes occurring in only one population), whereas only one “widespread genotype” (genotypes occurring in more than 75% of the populations) were detected. The mean number of multilocus genotypes per population (G) and mean genotypic diversity index (D _G) were 8.4 and 0.74, respectively. Most common multilocus genotypes found in populations were homozygous for five polymorphic loci. The abundance of ramets of these genets is responsible for the low levels of expected heterozygosity within populations. The results indicate that clonal reproduction may act as an enhancer of genetic drift by reducing effective size of local populations ofV. rotundifolia.     

The effects of sample size on population genetic diversity estimates in song sparrows Melospiza melodia

To empirically determine the effects of sample size on commonly used measures of average genetic diversity, we genotyped 200 song sparrows Melospiza melodia from two populations, one genetically depauperate (n=100) and the other genetically diverse (n=100), using eight microsatellite loci. These genotypes were used to randomly create 10,000 datasets of differing sizes (5 to 50) for each population to determine what the effects of sample size might be on several estimates of genetic diversity (number of alleles per locus, average observed heterozygosity, and unbiased average expected heterozygosity) in natural populations of conservation concern. We found that at small sample sizes of 5 to 10 individuals, estimates of unbiased heterozygosity outperformed those based on observed heterozygosity or allelic diversity for both low- and high-diversity populations. We also found that when comparing across populations in which different numbers of individuals were sampled, rarefaction provided a useful way to compare estimates of allelic diversity. We recommend that standard errors should be reported for all diversity estimators, especially when sample sizes are small. We also recommend that at least 20 to 30 individuals be sampled in microsatellite studies that assess genetic diversity when working in a population that has an unknown level of diversity. However, research on critically endangered populations (where large sample sizes are impossible or extremely difficult to obtain) should include measures of genetic diversity even if sample sizes are less than ideal. These estimates can be useful in assessing the genetic diversity of the population.     

Comparing molecular measures for detecting inbreeding depression

Correlations between heterozygosity and components of fitness have been investigated in natural populations for over 20 years. Positive correlations between a trait of interest and heterozygosity (usually measured at allozyme loci) are generally recognized as evidence of inbreeding depression. More recently, molecular markers such as microsatellites have been employed for the same purpose. A typical study might use around five to ten markers. In this paper we use a panel of 71 microsatellite loci to: (1) Compare the efficacy of heterozygosity and a related microsatellite‐specific variable, mean d², in detecting inbreeding depression; (2) Examine the statistical power of heterozygosity to detect such associations. We performed our analyses in a wild population of red deer (Cervus elaphus) in which inbreeding depression in juvenile traits had previously been detected using a panel of nine markers. We conclude that heterozygosity‐based measures outperform mean d²‐based measures, but that power to detect heterozygosity‐fitness associations is nonetheless low when ten or fewer markers are typed.     

Identification and characterization of nuclear microsatellite loci in Abies alba Mill.

Eleven polymorphic nuclear microsatellite markers for Abies alba Mill. were developed from an enriched genomic library. An average of 5.2 alleles per locus and a mean expected heterozygosity of 0.532 were found in a sample of 24 Abies alba individuals from different populations within Europe. These loci can be used in studies of genetic diversity for parentage analysis and for estimation of gene flow in silver fir populations. Moreover, successful amplifications were obtained for eight other Mediterranean Abies species, suggesting that these loci may be useful for similar applications in other fir species.     

Genetic Variation in Remnant Populations of the Woolly Spider Monkey (Brachyteles arachnoides)

The muriqui or woolly spider monkey (Brachyteles arachnoids) is an endangered primate endemic to the Atlantic Forest of Brazil, <5% of which remains. The known muriqui population consists of <700 individuals separated into approximately 15 geographically isolated forest fragments. I present data on the distribution of genetic variation within and between two such remnant populations (FE and FBR) and summarize the implications of these results for long-range management of species genetic diversity. Eleven of 32 allozyme loci were polymorphic, representing an overall level of polymorphism of 34.4% and a mean heterozygosity per locus of 11%. Both values are among the highest reported for New World monkeys. Genetic differentiation between the two localities is highly significant (F_ST = 0.413, p < 0.001). Genetic distance between them is an order of magnitude greater than that between other populations of platyrrhine subspecies, but this could be an artifact of the small sample size from FBR. High levels of genetic diversity apparently characteristic of this species persist because (1) fragmentation and size reduction of muriqui populations has occurred very rapidly relative to the muriqui life span—although both polymorphism and heterozygosity were lost between generations in the largest population, the high genetic diversity present in the parent population was still in evidence; and (2) genetic diversity before population fragmentation by human activity was not distributed uniformly throughout the species' historic distribution. Thus, remnant muriqui populations are important genetic reservoirs of alleles that are unique or rare in the species gene pool as a whole. These results emphasize the need for the integration of conservation management efforts throughout the species range.