MATERNAL INHERITANCE AND ITS EFFECT ON ADAPTIVE EVOLUTION: A QUANTITATIVE GENETIC ANALYSIS OF MATERNAL EFFECTS IN A NATURAL PLANT POPULATION

A mother can influence a trait in her offspring both by the genes she transmits (Mendelian inheritance) and by maternal attributes that directly affect that trait in her offspring (maternal inheritance). Maternal inheritance can alter the direction, rate, and duration of adaptive evolution from standard Mendelian models and its impact on adaptive evolution is virtually unexplored in natural populations. In a hierarchical quantitative genetic analysis to determine the magnitude and structure of maternal inheritance in the winter annual plant, Collinsia verna, I consider three potential models of inheritance. These range from a standard Mendelian model estimating only direct (i.e., Mendelian) additive and environmental variance components to a maternal inheritance model estimating six additive and environmental variance components: direct additive and environmental variances; maternal additive and environmental variances; and the direct-maternal additive () and environmental covariances. The structure of maternal inheritance differs among the 10 traits considered at four stages in the life cycle. Early in the life cycle, seed weight and embryo weight display substantial , a negative , and a positive . Subsequently, cotyledon diameter displays and of roughly the same magnitude and negative . For fall rosettes, leaf number and length are best described by a Mendelian model. In the spring, leaf length displays maternal inheritance with significant and and a negative . All maternally inherited traits show significant negative . Predicted response to selection under maternal inheritance depends on and as well as . Negative results in predicted responses in the opposite direction to selection for seed weight and embryo weight and predicted responses near zero for all subsequent maternally inherited traits. Maternal inheritance persists through the life cycle of this annual plant for a number of size-related traits and will alter the direction and rate of evolutionary response in this population.     

RISK OF POPULATION EXTINCTION FROM FIXATION OF NEW DELETERIOUS MUTATIONS

The fixation of new deleterious mutations is analyzed for a randomly mating population of constant size with no environmental or demographic stochasticity. Mildly deleterious mutations are far more important in causing loss of fitness and eventual extinction than are lethal and semilethal mutations in populations with effective sizes, N_e, larger than a few individuals. If all mildly deleterious mutations have the same selection coefficient, s against heterozygotes and 2s against homozygotes, the mean time to extinction, , is asymptotically proportional to for 4N_es > 1. Nearly neutral mutations pose the greatest risk of extinction for stable populations, because the magnitude of selection coefficient that minimizes is about ? = 0.4/N_e. The influence of variance in selection coefficients among mutations is analyzed assuming a gamma distribution of s, with mean and variance . The mean time to extinction increases with variance in selection coefficients if is near ?, but can decrease greatly if is much larger than ?. For a given coefficient of variation of , the mean time to extinction is asymptotically proportional to for . When s is exponentially distributed, (c = 1) is asymptotically proportional to . These results in conjunction with data on the rate and magnitude of mildly deleterious mutations in Drosophila melanogaster indicate that even moderately large populations, with effective sizes on the order of N_e = 10³, may incur a substantial risk of extinction from the fixation of new mutations.     

THE MAINTENANCE OF POLYGENIC VARIATION IN FINITE POPULATIONS

Models of the maintenance of genetic variance in a polygenic trait have usually assumed that population size is infinite and that selection is weak. Consequently, they will overestimate the amount of variation maintained in finite populations. I derive approximations for the equilibrium genetic variance, in finite populations under weak stabilizing selection for triallelic loci and for an infinite “rare alleles” model. These are compared to results for neutral characters, to the “Gaussian allelic” model, and to Wright's approximation for a biallelic locus under arbitrary selection pressures. For a variety of parameter values, the three-allele, Gaussian, and Wrightian approximations all converge on the neutral model when population size is small. As expected, far less equilibrium genetic variance can be maintained if effective population size, N, is on the order of a few hundred than if N is infinite. All of the models predict that comparisons among populations with N less than about 10⁴ should show substantial differences in . While it is easier to maintain absolute when alleles interact to yield dominance or overdominance for fitness, less additivity also makes more susceptible to differences in N. I argue that experimental data do not seem to reflect the predicted degree of relationship between N and . This calls into question the ability of mutation-selection balance or simple balancing selection to explain observed . The dependence of on N could be used to test the adequacy of mutation-selection balance models.     

INBREEDING DEPRESSION IN PARTIALLY SELF-FERTILIZING DECODON VERTICILLATUS (LYTHRACEAE): POPULATION-GENETIC AND EXPERIMENTAL ANALYSES

Inbreeding depression is a major selective force favoring outcrossing in flowering plants. Some self-fertilization, however, should weaken the harmful effects of inbreeding by exposing genetic load to selection. This study examines the maintenance of inbreeding depression in partially self-fertilizing populations of the long-lived, herbaceous wetland plant, Decodon verticillatus (L.) Ell. (Lythraceae). Estimates from ten populations indicate that 30% of offspring are produced through self-fertilization. Population-genetic estimates of inbreeding depression (δ = 1 – relative mean fitness of selfed progeny) based on changes in the inbreeding coefficient for the same ten populations were uniformly high, ranging from 0.49 to 1.79 and averaging 1.11 ± 0.29 SE. Although confidence intervals of individual population estimates were large, estimates were significantly greater than 0 in six populations and greater than 0.5 in four. Inbreeding depression was also estimated by comparing growth, survival, and flowering of experimentally selfed and outcrossed offspring from two of these populations in a 1-yr glasshouse experiment involving three density regimes; after which offspring were transplanted into garden arrays and two field sites and monitored for two consecutive growing seasons. Overall for survival averaged 0.27 ± 0.01 in the glasshouse, 0.33 ± 0.04 in the garden, and 0.46 ± 0.04 in the field. The glasshouse experiment also revealed strong inbreeding depression for growth variables, especially above-soil dry weight ( = 0.42 ± 0.03). The fitness consequences of inbreeding depression for these growth variables approximately doubles if survival to maturity is determined by severe truncation selection. Despite substantial selfing, inbreeding depression appears to be a major selective force favoring the maintenance of outcrossing in D. verticillatus.     

THE EFFECT OF SOFT SELECTION ON THE VARIABILITY OF A QUANTITATIVE TRAIT

The equilibrium phenotypic variance of a normally distributed quantitative character P under soft selection is studied. This character is assumed to undergo Gaussian stabilizing selection W(p, x) = exp[–(p – x)²/2w²]. The environmentally determined optimum (x) is a normal variable with variance s². A stable equilibrium with is found, so that increases both with increasing environmental heterogeneity and with increasing local intensity of stabilizing selection. It is shown that both genetic and environmental components of the variance are selected until this equilibrium is reached. Habitat selection, supposed to be normal (with variance H²) around the optimum, also increases the value. Nevertheless, relatively intense local stabilizing selection (w < s) and accurate habitat choice (H < s) are required for the initial spread and the evolutionary stability of this habitat selection.     

Effective size of density‐dependent populations in fluctuating environments

Reliable estimates of effective population size are of central importance in population genetics and evolutionary biology. For populations that fluctuate in size, harmonic mean population size is commonly used as a proxy for (multi‐) generational effective size. This assumes no effects of density dependence on the ratio between effective and actual population size, which limits its potential application. Here, we introduce density dependence on vital rates in a demographic model of variance effective size. We derive an expression for the ratio in a density‐regulated population in a fluctuating environment. We show by simulations that yearly genetic drift is accurately predicted by our model, and not proportional to as assumed by the harmonic mean model, where N is the total population size of mature individuals. We find a negative relationship between and N. For a given N, the ratio depends on variance in reproductive success and the degree of resource limitation acting on the population growth rate. Finally, our model indicate that environmental stochasticity may affect not only through fluctuations in N, but also for a given N at a given time. Our results show that estimates of effective population size must include effects of density dependence and environmental stochasticity.     

LOCOMOTOR PERFORMANCE AT LOW TEMPERATURE AND THE EVOLUTION OF NOCTURNALITY IN GECKOS

Nocturnal geckos are active at body temperatures 10–35°C below the thermal optima for maximum rate of aerobic metabolism of diurnal lizards. Therefore, given ancestral (diurnal) lizard physiology, nocturnality causes a substantial thermal handicap in locomotor performance. In prior studies, we hypothesized that a low minimum cost of locomotion (C_min) in geckos was an adaptation that increased locomotor endurance capacity at low, nocturnal temperatures. However, C_min is only part of an integrated system that, in conjunction with the maximum rate of oxygen consumption, sets the maximum speed that can be sustained aerobically (termed the maximum aerobic speed or MAS). We conducted the first phylogenetic analysis of MAS and lizards and found that the greatest changes in MAS, C_min and (at activity temperatures) in the evolutionary history of lizards all coincided with the evolution of nocturnality in geckos. Geckos active at 15–25°C did not become optimized for nocturnal temperatures, or fully offset the thermal effects of nocturnality by evolving maximal rates of oxygen consumption comparable to diurnal lizards active at 35°C. Geckos did evolve MAS twice that of diurnal lizards running at low temperatures by evolving a remarkably low C_min. Allometric analysis and phylogenetically independent contrasts of , C_min, and MAS indicate a 72% evolutionary decrease in , (at activity temperatures) and a 50% evolutionary decrease in C_min concordant with the evolution of nocturnality in geckos. Experimental measurements show that decreased C_min in six species of gecko increased MAS by 50–120% compared to diurnal lizards at low temperatures. Thus, geckos sufficiently overcame the near paralyzing effects of nocturnal temperatures, but only offset about 50% of the decrease in MAS resulting from the low maximum rate of oxygen consumption. Although the nocturnal environment remains severely suboptimal, the evolution of a low cost of locomotion in the ancestor of geckos was highly adaptive for nocturnality. We also present a generalized approach to ecophysiological evolution that integrates phylogeny with the causal relationships among environment, physiology, and performance capacity. With respect to a clade, two hypotheses are central to our integrative approach: (1) a change of an environmental variable (e.g., temperature) causes a performance handicap; and (2) evolution of a physiological variable (e.g., minimum cost of locomotion [C_min]) increases performance in the derived environment. To test the hypothesis that evolution of a physiological variable is adaptive in nature, we suggest determining if individuals in nature perform at levels exceeding the performance capacity of their hypothetical ancestors and if this additional performance capacity is due to the evolution of the physiological variable in question.     

EPISTASIS,PLEIOTROPY, AND THE MUTATION LOAD IN SEXUAL AND ASEXUAL POPULATIONS

Mutation may impose a substantial load on populations, which varies according to the reproductive mode of organisms. Over the past years, various authors used adaptive landscape models to predict the long‐term effect of mutation on mean fitness; however, many of these studies assumed very weak mutation rates, so that at most one mutation segregates in the population. In this article, we derive several simple approximations (confirmed by simulations) for the mutation load at high mutation rate (U), using a general model that allows us to play with the number of selected traits (n), the degree of pleiotropy of mutations, and the shape of the fitness function (which affects the average sign and magnitude of epistasis among mutations). When mutations have strong fitness effects, the equilibrium fitness of sexuals and asexuals is close to ; under weaker mutational effects, sexuals reach a different regime where is a simple function of U and of a parameter describing the shape of the fitness function. Contrarily to weak mutation results showing that is an increasing function of population size and a decreasing function of n, these parameters may have opposite effects in sexual populations at high mutation rate.     

HEMOGLOBIN POLYMORPHISMS IN DEER MICE (PEROMYSCUS MANICULATUS): PHYSIOLOGY OF BETA-GLOBIN VARIANTS AND ALPHA-GLOBIN RECOMBINANTS

Wild populations of deer mice (Peromyscus maniculatus) contain hemoglobin polymorphisms at both alpha-globin (Hba, Hbc) and beta-globin (Hbd) loci. Population gene frequencies of beta-globin variants (d⁰ and d¹ haplotypes) are not correlated with altitude, whereas a¹c¹ alpha-globin haplotypes are fixed in low-altitude populations, and a⁰c⁰ haplotypes reach near fixation at high altitudes. We examined the effects of alpha- and beta-globin variants on blood oxygen affinity and on aerobic performance, measured as maximum oxygen consumption (). Exercise and cold exposure were used to elicit . Experiments were performed at low (340 m) and high (3,800 m) altitude to include the range of oxygen partial pressures encountered by wild deer mice. Beta-globin variants had little effect on blood oxygen affinity or . Oxygen-dissociation curves from a⁰c⁰ and a¹c¹ homozygotes and heterozygotes had similar shapes, but the P₅₀ of a⁰c⁰ homozygotes was significantly lower than that of other genotypes. Mice carrying a¹c¹/a¹c¹ genotypes had the highest at low altitude, but mice with a⁰c⁰/a⁰c⁰ genotypes had the highest at high altitude. Mice carrying rare recombinant alpha-globin haplotypes (a⁰c¹) had lower than nonrecombinant genotypes as a whole but in most cases were not significantly different from nonrecombinant heterozygotes (a⁰c⁰/a¹c¹). We conclude that genetic adaptation to different altitudes was important in the evolution of deer mouse alpha-globin polymorphisms and in the maintenance of linkage disequilibrium in the alpha-globin loci but was not a significant factor in the evolution of beta-globin polymorphisms.     

Additive genetic variance for lifetime fitness and the capacity for adaptation in an annual plant

The immediate capacity for adaptation under current environmental conditions is directly proportional to the additive genetic variance for fitness, V_A(W). Mean absolute fitness, , is predicted to change at the rate , according to Fisher's Fundamental Theorem of Natural Selection. Despite ample research evaluating degree of local adaptation, direct assessment of V_A(W) and the capacity for ongoing adaptation is exceedingly rare. We estimated V_A(W) and in three pedigreed populations of annual Chamaecrista fasciculata, over three years in the wild. Contrasting with common expectations, we found significant V_A(W) in all populations and years, predicting increased mean fitness in subsequent generations (0.83 to 6.12 seeds per individual). Further, we detected two cases predicting “evolutionary rescue,” where selection on standing V_A(W) was expected to increase fitness of declining populations (< 1.0) to levels consistent with population sustainability and growth. Within populations, inter‐annual differences in genetic expression of fitness were striking. Significant genotype‐by‐year interactions reflected modest correlations between breeding values across years, indicating temporally variable selection at the genotypic level that could contribute to maintaining V_A(W). By directly estimating V_A(W) and total lifetime , our study presents an experimental approach for studies of adaptive capacity in the wild.     

Effects of partial selfing on the equilibrium genetic variance,mutation load,and inbreeding depression under stabilizing selection

The mating system of a species is expected to have important effects on its genetic diversity. In this article, we explore the effects of partial selfing on the equilibrium genetic variance V_g, mutation load L, and inbreeding depression δ under stabilizing selection acting on a arbitrary number n of quantitative traits coded by biallelic loci with additive effects. When the ratio is low (where U is the total haploid mutation rate on selected traits) and effective recombination rates are sufficiently high, genetic associations between loci are negligible and the genetic variance, mutation load, and inbreeding depression are well predicted by approximations based on single‐locus models. For higher values of and/or lower effective recombination, moderate genetic associations generated by epistasis tend to increase V_g, L, and δ, this regime being well predicted by approximations including the effects of pairwise associations between loci. For yet higher values of and/or lower effective recombination, a different regime is reached under which the maintenance of coadapted gene complexes reduces V_g, L, and δ. Simulations indicate that the values of V_g, L, and δ are little affected by assumptions regarding the number of possible alleles per locus.     

EXTINCTION-RECOLONIZATION DYNAMICS IN THE MYCOPHAGOUS BEETLE PHALACRUS SUBSTRIATUS

The population structure of the mycophagous beetle Phalacrus substriatus is characterized by many small, local populations interconnected by migration over a small spatial scale (10 × 75 m²). Each local P. substriatus population has a relatively short expected persistence time, but persistence of the species occurs due to a balance between frequent local extinctions and recolonizations. This nonequilibrium population structure can have profound effects on how the genetic variation is structured between and within populations. Theoretical models have stated that the genetic differentiation among local populations will be enhanced relative to an island model at equilibrium if the number of colonizers is less than approximately twice the number of migrants among local populations. To study these effects, a set of 50 local P. substriatus populations were surveyed over a four-year period to record any naturally occurring extinctions and recolonizations. The per population colonization and extinction rate were 0.237 and 0.275, respectively. Mark-recapture techniques were used to estimate a number of demographic parameters: local population size (N = 11.1), migration rate , number of colonizers (k = 4.0), and the probability of common origin of colonizers (φ = 0.5). The theoretically predicted level of differentiation among local populations (measured as Wright's F_ST) was 0.070. Genetic data obtained from an electrophoretic survey of seven polymorphic loci gave an estimated degree of differentiation of 0.077. There was thus a good agreement between the empirical results and the theoretical predictions. Young populations had significantly higher levels of differentiation than old, more established populations . The extinction-recolonization dynamics resulted in an overall increase in the genetic differentiation among local populations by c. 40%. The global effective population size was also reduced by c. 55%. The results give clear evidence to how nonequilibrium processes shape the genetic structure of populations.     

The association between polyploidy and clonal reproduction in diploid and tetraploid Chamerion angustifolium

Clonal reproduction is associated with the incidence of polyploidy in flowering plants. This pattern may arise through selection for increased clonality in polyploids compared to diploids to reduce mixed‐ploidy mating. Here, we test whether clonal reproduction is greater in tetraploid than diploid populations of the mixed‐ploidy plant, Chamerion angustifolium, through an analysis of the size and spatial distribution of clones in natural populations using AFLP genotyping and a comparison of root bud production in a greenhouse study. Natural tetraploid populations (N = 5) had significantly more AFLP genotypes ( = 10.8) than diploid populations ( = 6.0). Tetraploid populations tended to have fewer ramets per genotype and fewer genotypes with >1 ramet. In a spatial autocorrelation analysis, ramets within genotypes were more spatially aggregated in diploid populations than in tetraploid populations. In the greenhouse, tetraploids allocated 90.4% more dry mass to root buds than diploids, but tetraploids produced no more root buds and 44% fewer root buds per unit root mass than diploids. Our results indicate that clonal reproduction is significant in most populations, but tetraploid populations are not more clonal than diploids, nor are their clones more spatially aggregated. As a result, tetraploids may be less sheltered from mixed‐ploidy mating and diploids more exposed to inbreeding, the balance of which could influence the establishment of tetraploids in diploid populations.     

SEX RATIO AND DENSITY AFFECT SEXUAL SELECTION IN A SEX‐ROLE REVERSED FISH

Understanding how demographic processes influence mating systems is important to decode ecological influences on sexual selection in nature. We manipulated sex ratio and density in experimental populations of the sex‐role reversed pipefish Syngnathus typhle. We quantified sexual selection using the Bateman gradient (), the opportunity for selection (I), and sexual selection (I_s), and the maximum standardized sexual selection differential (). We also measured selection on body length using standardized selection differentials (s′) and mating differentials (m′), and tested whether the observed I and I_s differ from values obtained by simulating random mating. We found that I, I_s, and , but not , were higher for females under female than male bias and the opposite for males, but density did not affect these measures. However, higher density decreased sexual selection (m′ but not s′) on female length, but selection on body length was not affected by sex ratio. Finally, I_s but not I was higher than expected from random mating, and only for females under female bias. This study demonstrates that both sex ratio and density affect sexual selection and that disentangling interrelated demographic processes is essential to a more complete understanding of mating behavior and the evolution of mating systems.     

GENETIC CONSEQUENCES OF OUTCROSSING IN THE CLEISTOGAMOUS ANNUAL,IMPATIENS CAPENSIS. I. POPULATION-GENETIC STRUCTURE

We examined the genetic structure of 11 populations of Impatiens capensis, a cleistogamous annual herb, using starch gel electrophoresis. We sampled both cleistogamous (CL) and chasmogamous (CH) progeny (if present) from maternal parents in each population to infer maternal genotypes and to estimate the extent and pattern of inbreeding within and among populations. Only eight of 31 loci were polymorphic, with one to six (mean = 3.1) loci varying within each population. Mean heterozygosity per individual is quite low (mean = 3.9%) and comparable to highly self-fertilized species. Gene flow is low, and genetic distances do not parallel geographical distances, suggesting a population structure similar to Wright's Island model with drift among the populations. Fixation indexes within populations (f? or F_IS) span the largest range yet reported for a plant species (0.26 to 0.94, mean = 0.57). Further inbreeding results from population substructuring , resulting in a total average inbreeding coefficient (F? or F_IT) of 0.77. Despite these high overall levels of inbreeding, chasmogamy significantly reduces fixation, which may account for the observed greater fitness of CH progeny.     

Comparing the strength of modular signal,and evaluating alternative modular hypotheses,using covariance ratio effect sizes with morphometric data

The study of modularity is paramount for understanding trends of phenotypic evolution, and for determining the extent to which covariation patterns are conserved across taxa and levels of biological organization. However, biologists currently lack quantitative methods for statistically comparing the strength of modular signal across datasets, and a robust approach for evaluating alternative modular hypotheses for the same dataset. As a solution to these challenges, we propose an effect size measure () derived from the covariance ratio, and develop hypothesis‐testing procedures for their comparison. Computer simulations demonstrate that displays appropriate statistical properties and low levels of mis‐specification, implying that it correctly identifies modular signal, when present. By contrast, alternative methods based on likelihood (EMMLi ) and goodness of fit (MINT ) suffer from high false positive rates and high model mis‐specification rates. An empirical example in sigmodontine rodent mandibles is provided to illustrate the utility of for comparing modular hypotheses. Overall, we find that covariance ratio effect sizes are useful for comparing patterns of modular signal across datasets or for evaluating alternative modular hypotheses for the same dataset. Finally, the statistical philosophy for pairwise model comparisons using effect sizes should accommodate any future analytical developments for characterizing modular signal.     

SMALL POPULATION GENETIC VARIABILITY AT LOCI UNDER STABILIZING SELECTION

Genetic variability at a locus under stabilizing selection in a finite population is investigated using analytic methods and computer simulations. Three measures are examined: the number of alleles k, heterozygosity H, and additive genetic variance Vg. A nearly-neutral theory results. The composite parameter S = NV_M/V_s (where N is the population size, V_M the variance of new mutant allelic effects and V_s the weakness of stabilizing selection) figures prominently in the results. The equilibrium heterozygosity is similar to that of strictly neutral theory, H = 4N_μc/ (1 + 4N_μc), except that μ_c = where c is about 0.5. Simulations corroborate except for very low N. Genetic variability attains similar equilibrium values at both a “lone” locus and at an “embedded” locus. This agrees with my earlier work concerning molecular clock rates. These results modify the neutralist interpretation of data concerning genetic variability and genetic distances between populations. Low H values are proportional not to N but to . This may explain the narrow observed range of H among species. Heterozygosities need not be highly correlated to genetic variances. Genetic variances are not highly dependent on population size except in very small populations which are difficult to sample without bias because the smallest populations go extinct the fastest. Nearly neutral evolution will not be easily distinguished from strictly neutral theory under the Hudson-Kreitman-Aguade inter-/intraspecific variation ratio test, since a similar effective mutation rate holds for genetic distances and D = 2μ_ct, where . As with strictly neutral theory, comparisons across loci should show D and H to be positively correlated because of the shared μ_c. But unlike neutral theory, for a given locus, comparisons across species should show D and H to be negatively correlated. There is no obvious threshold of population size below which genetic variability inevitably declines. Extinction depends on both genetic variation and natural selection. Neither theory nor observation presently indicates the measure of genetic variability (k, H, V_G or other) that best indicates vulnerability of a small population to extinction.     

A new proposal for measurement of the adjusted mean crowding through consideration of size variability in habitat units

The mean crowding has previously been measured under the assumption that all quadrats or habitat units have the same size, even though the actual habitat units such as seeds or leaves are generally variable in size. A new index, ‘adjusted mean crowding’, which is adjusted for this variability can be given as where Q is the total number of habitat units in the whole area, x_j the number of individuals in the jth habitat unit, and a_j is defined as the ‘relative size’ of the jth habitat unit, i.e. a_y=y_y/(∑y_j/Q) where y_j is the actually measured size of the jth habitat unit. It is expected that and for the uniform distribution and the random distribution ‘per unit size’, respectively. The comparison between and regressions ( analysis) for the egg distribution pattern of Callosobruchus chinensis or C. maculatus proved that the regression is biased by a positive correlation between the egg number per seed and seed size rather than by a density-dependent change in the ovipositional behavior.     

Activation of Terminal Components of Human Complement by a Trypsin-Activated Complex of Human Factor B and Cobra Venom Factor

Cleavage of C3 by CVF-B? was demonstrated by hemolytic, immunoelectrophoretic and immune adherence reactions. No cleavage of C5 was detected by immunoelectrophoresis, but C5 hemolytic activity, assayed with decreased although less than C3 hemolytic activity. The co-existence of C3 with limiting amounts of C5 did not reduce the final degree of hemolysis of guinea pig erythrocytes (GPE) induced by late-acting components C6 through C9 and CVF-B?. Thus, a CVF-B? hemolytic system composed of GPE, C5 through C9 and CVF-B? provided a method for titration of terminal components of human complement. CVF-B? was able to generate hemolytically active sites of on GPE by activation of C5, C6 and C7. The complex in the fluid-phase decayed within 1 min but on GPE was quite stable. Originally insensitive sheep erythrocytes became sensitive to the CVF-B? hemolytic system if C3b sites were present, suggesting that cell-bound C3b played a role in orienting the positions of to be fixed. CVF-B? could be recovered quantitatively from the supernatant of the reaction mixture in which the hemolytically active intermediate GPEC- had been formed through the interaction between C5 to C8 and CVF-B?.