Variation in carbon isotope discrimination in relation to plant performance in a natural population of <Emphasis Type="Italic">Cryptantha flava</Emphasis>

Few studies of phenotypic selection have focused on physiological traits, especially in natural populations. The adaptive significance of plant water-use efficiency, the ratio of photosynthesis to water loss through transpiration, has rarely been examined. In this study, carbon isotopic discrimination, Δ, an integrated measure of water-use efficiency, was repeatedly measured in juveniles and adults in a natural population of the herbaceous desert perennial Cryptantha flava over a 4-year period and examined for plasticity in Δ, consistency between years in values of Δ, and evidence for selection on Δ phenotypes. There was significant concordance in Δ values among the 4 years for adult plants and significant correlations in Δ values measured in different years for juveniles and adults combined. The wettest year of the study, 1998, proved an exception because Δ values that year were not correlated with Δ values in any other year of the study. Consistency in Δ measured on the same plants in different years could indicate genotypic variation and/or consistency in the water status of the microhabitats the plants occupied. Two forms of plasticity in Δ were also evident; mean seasonal values were correlated with precipitation the preceding autumn, and Δ values also declined with plant size, indicating increasing water-use efficiency. Phenotypic selection was evident because in the first year of the study juvenile plants that would survive until year five averaged lower Δ values than did those that failed to survive. During the driest year, 2000, Δ was significantly negatively correlated with adult plant size, measured as the number of leaf rosettes, but the negative relationship between Δ and the number of flowering stalks, a more direct measure of fitness, was not significant. These results suggest that the direction of phenotypic selection on Δ changes as plants grow.     

Ontogenetic and spatial variation in size‐selective mortality of a marine fish

Although body size can affect individual fitness, ontogenetic and spatial variation in the ecology of an organism may determine the relative advantages of size and growth. During an 8‐year field study in the Bahamas, we examined selective mortality on size and growth throughout the entire reef‐associated life phase of a common coral‐reef fish, Stegastes partitus (the bicolour damselfish). On average, faster‐growing juveniles experienced greater mortality, though as adults, larger individuals had higher survival. Comparing patterns of selection observed at four separate populations revealed that greater population density was associated with stronger selection for larger adult size. Large adults may be favoured because they are superior competitors and less susceptible to gape‐limited predators. Laboratory experiments suggested that selective mortality of fast‐growing juveniles was likely because of risk‐prone foraging behaviour. These patterns suggest that variation in ecological interactions may lead to complex patterns of lifetime selection on body size.     

Effects of size‐ and sex‐selective harvesting: An integral projection model approach

Harvesting is often size‐selective, and in species with sexual size dimorphism, it may also be sex‐selective. A powerful approach to investigate potential consequences of size‐ and/or sex‐selective harvesting is to simulate it in a demographic population model. We developed a population‐based integral projection model for a size‐ and sex‐structured species, the commonly exploited pike (Esox lucius). The model allows reproductive success to be proportional to body size and potentially limited by both sexes. We ran all harvest simulations with both lower size limits and slot limits, and to quantify the effects of selective harvesting, we calculated sex ratios and the long‐term population growth rate (λ). In addition, we quantified to what degree purely size‐selective harvesting was sex‐selective, and determined when λ shifted from being female to male limited under size‐ and sex‐selective harvesting. We found that purely size‐selective harvest can be sex‐selective, and that it depends on the harvest limits and the size distributions of the sexes. For the size‐ and sex‐selective harvest simulations, λ increased with harvest intensity up to a threshold as females limited reproduction. Beyond this threshold, males became the limiting sex, and λ decreased as more males were harvested. The peak in λ, and the corresponding sex ratio in harvest, varied with both the selectivity and the intensity of the harvest simulation. Our model represents a useful extension of size‐structured population models as it includes both sexes, relaxes the assumption of female dominance, and accounts for size‐dependent fecundity. The consequences of selective harvesting presented here are especially relevant for size‐ and sex‐structured exploited species, such as commercial fisheries. Thus, our model provides a useful contribution toward the development of more sustainable harvesting regimes.     

Cultural Disturbances and Local Ecological Knowledge Mediate Cattail (<Emphasis Type="Italic">Typha domingensis</Emphasis>) Invasion in Lake Pátzcuaro,México

The influence of local actors and socioeconomic constraints on biological invasions is often ignored. Wetland plant harvesters appeared to intentionally influence cattail (Typha domingensis) invasion around Lake Pátzcuaro, México, by altering their harvesting regimes, according to interviews with 44 expert respondents and botanical surveys. The oldest and most experienced harvesters reported controlling Typha initially, sometimes through organized eradication efforts, in order to protect Schoenoplectus californicus, an economically and culturally valuable wetland plant. Later, outsiders commoditized Typha by introducing new weaving designs popular with tourists, while industrial products and new livelihood activities reduced Schoenoplectus harvest. Harvesters from several communities began to promote Typha re-growth. Some harvesters, however, continued to combat Typha to maintain Schoenoplectus production, especially where supply was limited. Interviews suggested novel ecological cause–effect mechanisms and restoration strategies; some local harvesting regimes could efficiently conserve rare plants. An understanding of local ecological knowledge and incentives can inform invasive species control and conservation policy at a broader scale.     

Sustainable harvesting of bog myrtle (Myrica gale L.) in Scotland

Summary

Bog myrtle communities were surveyed to determine their accessibility for harvesting and the approximate number of harvestable stems. At least 45.1 million bog myrtle stems within Scotland may be both suitable (about 55 cm long) and easily accessible (< 1 km from a tarmac road) for harvesting. In a harvesting trial in Strath Avon, plants were subjected to five different cutting treatments with and without the addition of NPK. There were significant differences between cutting treatments, but no significant effects of fertilizer. Cutting all stems to half height produced the most rapid regeneration. Stems could take eight years to regenerate to a harvestable size if this cutting method were employed. On this basis, a harvest of 5.6 million stems could be sustained annually, compared with a current harvest of about 0.6 million.     

Field estimates of fitness costs of the pace‐of‐life in an endangered damselfly

Theory predicts that within‐population differences in the pace‐of‐life can lead to cohort splitting and produce marked intraspecific variation in body size. Although many studies showed that body size is positively correlated with fitness, many argue that selection for the larger body is counterbalanced by opposing physiological and ecological selective mechanisms that favour smaller body. When a population split into cohorts with different paces of life (slow or fast cohort), one would expect to detect the fitness–size relationship among and within cohorts, that is, (a) slower‐developing cohort has larger body size and higher fitness than faster‐developing cohort, and (b) larger individuals within each cohort show higher fitness than smaller individuals. Here, we test these hypotheses in capture–mark–recapture field surveys that assess body size, lifespan, survival and lifetime mating success in two consecutive generations of a partially bivoltine aquatic insect, Coenagrion mercuriale, where the spring cohort is slower‐developing than the autumn cohort. As expected, body size was larger in the slow‐developing cohort, which is consistent with the temperature‐size rule and also with the duration of development. Body size seasonal variation was greater in slow‐developing cohort most likely because of the higher variation in age at maturity. Concordant with theory, survival probability, lifespan and lifetime mating success were higher in the slow‐developing cohort. Moreover, individual body size was positively correlated with survival and mating success in both cohorts. Our study confirms the fitness costs of fast pace‐of‐life and the benefits of larger body size to adult fitness.     

Floral display, pollinator visitation and reproductive success in the dioecious perennial herb Wurmbea dioica (Liliaceae)

Floral traits that increase attractiveness to pollinators are predicted to evolve through selection on male function rather than on female function. To determine the importance of male-biased selection in dioecious Wurmbea dioica, we examined sexual dimorphism in flower size and number and the effects of these traits on pollinator visitation and reproductive success of male and female plants. Males produced more and larger flowers than did females. Bees and butterflies responded to this dimorphism and visited males more frequently than females, although flies did not differentiate between the sexes. Within sexes, insect pollinators made more visits to and visited more flowers on plants with many flowers. However, visits per flower did not vary with flower number, indicating that visitation was proportional to the number of flowers per plant. When flower number was experimentally held constant, visitation increased with flower size under sunny but not overcast conditions. Flower size but not number affected pollen removal per flower in males and deposition in females. In males, pollen removal increased with flower size 3 days after flowers opened, but not after 6 days when 98% of pollen was removed. Males with larger flowers therefore, may have higher fitness not because pollen removal is more complete, but because pollen is removed more rapidly providing opportunities to pre-empt ovules. In females, pollen deposition increased with flower size 3 days but not 6 days after flowers opened. At both times, deposition exceeded ovule production by four-fold or more, and for 2 years seed production was not limited by pollen. Flower size had no effect on seed production per plant and was negatively related to percent seed set, implying a tradeoff between allocation to attraction and reproductive success. This indicates that larger flower size in females is unlikely to increase fitness. In both sexes, gamete production was positively correlated with flower size. In males, greater pollen production would increase the advantage of large flowers, but in females more ovules may represent a resource cost. Selection to increase flower size and number in W. dioica has probably occurred through male rather than female function. Received: 15 June 1997 / Accepted: 12 February 1998     

Effects of population size on performance and inbreeding depression in <Emphasis Type="Italic">Lupinus perennis</Emphasis>

We investigated the relationships among population size, offspring performance, and inbreeding depression (δ) in Lupinus perennis by examining the effect of population size category (large vs. small) on seed production and offspring performance for three pollination treatments (open pollination, hand crossing and hand selfing). In each of our four pairs of populations, one member of the pair was substantially larger than the other. We then grew seeds from this factorial design (2 sizes × 4 pairs × 3 pollination treatments) in the greenhouse to investigate whether population size affects offspring performance in a common environment, and how small size affects purging of the inbreeding load. Multiplicative performance across four early life-stage components (seed production, seedling emergence, seedling survival and seedling growth) of smaller populations was not significantly lower, although biomass of seedlings declined in smaller populations. Self-pollination reduced seed production, seedling emergence and seedling growth, reflecting substantial inbreeding depression (δ = 0.404 ± 0.043). Population size categories did not consistently differ in levels of inbreeding depression, suggesting that purging of genetic load in smaller populations has been limited, and that all populations still harbor inbreeding load. We also found a significant decrease in log performance with increases in the population inbreeding coefficient. These results indicate that even in seemingly large populations, lupines are susceptible to considerable fitness declines through both inbreeding load within populations, and drift load via genetic erosion and fixation of deleterious alleles between populations.     

The effects of sexual selection on life‐history traits: an experimental study on guppies

Sexual selection is often prevented during captive breeding in order to maximize effective population size and retain genetic diversity. However, enforcing monogamy and thereby preventing sexual selection may affect population fitness either negatively by preventing the purging of deleterious mutations or positively by reducing sexual conflicts. To better understand the effect of sexual selection on the fitness of small populations, we compared components of female fitness and the expression of male secondary sexual characters in 19 experimental populations of guppies (Poecilia reticulata) maintained under polygamous or monogamous mating regimes over nine generations. In order to generate treatments that solely differed by their level of sexual selection, the middle‐class neighbourhood breeding design was enforced in the monogamous populations, while in the polygamous populations, all females contributed similarly to the next generation with one male and one female offspring. This experimental design allowed potential sexual conflicts to increase in the polygamous populations because selection could not operate on adult‐female traits. Clutch size and offspring survival showed a weak decline from generation to generation but did not differ among treatments. Offspring size, however, declined across generations, but more in monogamous than polygamous populations. By generation eight, orange‐ and black‐spot areas were larger in males from the polygamous treatment, but these differences were not statistically significant. Overall, these results suggest that neither sexual conflict nor the purging of deleterious mutation had important effects on the fitness of our experimental populations. However, only few generations of enforced monogamy in a benign environment were sufficient to negatively affect offspring size, a trait potentially crucial for survival in the wild. Sexual selection may therefore, under certain circumstances, be beneficial over enforced monogamy during captive breeding.     

Death without sex—the ‘problem of the small’ and selection for reproductive economy in flowering plants

Most of the resident plants within vegetation fail to leave descendants because of death without sex—i.e. sexual reproduction fails (zero fecundity), primarily because of relatively small plant size. I propose that this ‘problem of the small’ represents one of the principal driving forces of evolution by natural selection, and that the main product of this selection is ‘reproductive economy’, manifested by several plant traits that are widely distributed among angiosperms: sexual maturity at a relatively young age and small size, relatively small seed size, selfing (including through mixed mating), and of particular interest here, clonality. In non-clonal species, an offspring develops from a zygote into a single ‘rooted unit’, i.e. a distinct vascular transition point between live shoot and root tissue. Clonal species can produce an indeterminate number of these rooted unit offspring asexually, all as products of a single zygote. Clonality is a common strategy in angiosperms because it confers a potential two-fold fitness benefit—especially in relatively small species—by promoting longevity of the zygote product, while at the same time providing a fecundity supplement (through asexual multiplication of rooted units), thereby allowing offspring production economically, i.e. without requiring large adult size, and without even requiring the fertilization of ovules. The primary fitness benefit from clonality, therefore, is that the somatic product of a zygote can effectively avoid an intrinsic limitation predicted for all non-clonal plants: the trade-off between longevity and the potential rate of offspring/descendant production. These major fitness benefits of clonality are explored in considering why clonality is less common in larger species, why the largest species (trees) generally do not have the longest-lived zygote product, and in re-assessing traditional and recent views concerning the loss of sex in clonal plants, the predicted trade-off between the size and number of clonal offspring, and the predicted trade-off between sexual and asexual reproduction.     

Evolutionary responses to harvesting in ungulates

1. We investigate the evolutionary responses to harvesting in ungulates using a state-dependent, stochastic, density-dependent individual-based model of red deer Cervus elaphus (L.) females subject to different harvesting regimes. 2. The population's mean weight at first reproduction shifts towards light weights as harvesting increases, and its distribution changes from a single peak distribution under very low or high harvest rates, to a bimodal distribution under intermediate harvest rates. 3. These results suggest that, consistent with previous studies on aquatic species, harvesting-induced mortality may drive adaptive responses in ungulates by reducing the fitness benefits from adult survival and growth in favour of early and lightweight reproduction. 4. Selective harvesting for heavy animals has no additional effect on the evolutionarily stable strategy, suggesting that harvest rate is more important than the degree of selectivity in driving adaptive responses. However, selective harvesting of light females is positively associated with maturation weights even higher than those of a nonharvested population, probably due to the reduction in the fitness value of the offspring. 5. The average number of weight at maturation strategies in the population declines but the total number of strategies across all simulations increases with harvest rate, suggesting that harvesting-induced selection on weight at maturity overcomes the increase in strategy diversity expected from density-dependent release. 6. Yield initially increases with harvesting due to enhanced productivity of light females experiencing density-dependent release. However, it crashes under intense harvesting resulting in a population skewed to light, young and, therefore, less reproductive animals.     

Increased body size confers greater fitness at lower experimental temperature in male Drosophila melanogaster

Genetic variation of body size along latitudinal clines is found globally in Drosophila melanogaster, with larger individuals encountered at higher latitudes. Temperature has been implicated as a selective agent for these clines, because the body size of laboratory populations allowed to evolve in culture at lower temperatures is larger. In this study, we investigated the hypothesis that larger size is favoured at lower temperature through natural selection on adult males. We measured life‐span and age‐specific fertility of males from lines of flies artificially selected for body size at two different experimental temperatures. There was an interaction between experimental temperature and body size selection for male fitness; large‐line males were fitter than controls at both temperatures, but the difference in fitness was greater at the lower experimental temperature. Smaller males did not perform significantly differently from control males at either experimental temperature. The results imply that thermal selection for larger adult males is at least in part responsible for the evolution of larger body size at lower temperatures in this species. The responsible mechanisms require further investigation.     

Evolution of variance in offspring number: The effects of population size and migration

It was shown by Gillespie [1974. Am. Nat. 108, 145–151], that if two genotypes produce the same average number of offspring on but have a different variance associated within each generation, the genotype with a lower variance will have a higher effective fitness. Specifically, the effective fitness is {ei65-1}, where w is the mean fitness, {ei65-2} is the variance in offspring number, and N is the total population size. The model also predicts that if a strategy has a higher arithmetic mean fitness and a higher variance than the competitor, the outcome of selection will depend on the population size (with larger population sizes favoring the highvariance, high-mean genotype). This suggests that for metapopulation sizes favoring the high-variance, high-mean genotype). This suggests that for metapopulations with large numbers of (relatively) small demes, a strategy with lower variance and lower mean may be favored if the migration rate is low while higher migration rates (consistent with a larger effective population size) favor the opposite strategy. Individual-based simulation confirms that this is indeed the case for an island model of migration, though the effect of migration differs greatly depending on whether migration precedes or follows selection. It is noted in the appendix that while Gillespie [1974. Am. Nat. 108, 145–151] does seem to be heuristically accurate, it is not clear that the definition of effective fitness follows from his derivation.     

Florivory affects pollinator visitation and female fitness in <Emphasis Type="Italic">Nemophila menziesii</Emphasis>

While herbivory has traditionally been studied as damage to leaves, florivory – herbivory to flowers prior to seed set – can also have large effects on plant fitness. Florivory can decrease fitness directly, either through the destruction of gametes or through alterations to plant physiology during fruit set, and can also change the appearance of a flower, deterring pollinators and reducing seed set. In order to distinguish between these hypotheses, it is necessary to both damage flowers and add pollen in excess to study the effects of damage on pollen limitation. Very few studies have used this technique over the lifetime of a plant. Here I describe a series of experiments showing the effects of natural and artificial damage on reproductive success in the annual plant Nemophila menziesii (Hydrophyllaceae, sensu lato). I show that natural and artificial petal damage decreased radial symmetry relative to controls and that both types of damage deterred pollinator activity. Both naturally damaged flowers and artificially damaged flowers in the field set fewer fruit or seed relative to undamaged control flowers. Finally, in an experiment crossing artificial petal damage with pollen addition, petal damage alone over the lifetime of this plant decreased female fitness, but only after a threshold of damage was reached. The fitness effect appeared to be direct because there was no detectable effect of pollen addition on the relationship between florivory and fitness. This result implies that both damaged and undamaged plants show similar amounts of pollen limitation and suggests that pollinator-mediated effects contributed little to the negative effects of florivory on female fitness. Florivores may thus be an under-appreciated agent of selection in certain plants, although more experimental manipulation of florivory is needed to determine if it is important over a range of taxa.     

A Panax-centric view of invasive species

Plant-centric sampling provides a novel approach to quantifying the potential impact of invasive species on native plant species. The aim of this study was to determine the level of exposure of individuals and populations of Panax quinquefolius to invasive plant species using this approach in thirty natural ginseng populations. A high level of invasion was found with 63–70% of ginseng populations containing at least one invasive species. Approximately one-third of all individuals were found in close proximity to invasive plants. The most prevalent invasive species were Rosa multiflora and Berberis thunbergii. The exposure to invasives of plants in different size classes varied among populations. Invasive species presence increased with greater ginseng population sizes and presence of harvest. The abundance of invasives plants within forest interiors near this valuable medicinal herb suggests that the economic and ecological costs of competitive interactions with native species could be high.     

Natural selection on gall size: variable contributions of individual host plants to population-wide patterns

Studies that provide estimates of the form and magnitude of selection on herbivore traits at the level of individual plants in natural populations represent a vital step in understanding the interaction of selection and gene flow among host-affiliated insect populations when individual plants equate to differing selective regimes. We analyzed phenotypic selection on the trait gall size for a host-specific gall former at both the individual host plant and population level (across host plants) in each of two years. Linear and nonlinear selection and the fitness function relating gall size to the probability of survivorship in the absence of natural enemies were estimated for each level and year. Selection imposed by the host plant was observed in 19 of the 22 subpopulations monitored. At the population level, linear and nonlinear selection were evident each year. However, population-level estimates masked the significant heterogeneity in the form and direction of selection evident among plants each year. Heterogeneity among gall-former subpopulations is emphasized by our findings that selection varied from directional to stabilizing among plants and the majority of selection gradients estimated for individual plants did not fall within the 95% CIs of the population-level estimates.     

Hunting Bambi—evaluating the basis for selective harvesting of juveniles

Human harvesting is often a major mortality factor and, hence, an important proximate factor driving the population dynamics of large mammals. Several selective harvesting regimes focus on removing animals with low reproductive value, such as “antlered” harvests in North America and juvenile harvesting in many European countries. Despite its widespread use and assumed impact, the scientific basis of juvenile harvesting is scattered in the literature and not empirically well-documented. We give the first overview of demographic, evolutionary and practical management arguments for selective harvesting of juveniles. Furthermore, we empirically test two demographic arguments based on harvest statistics of Red Deer (Cervus elaphus) in seven European countries. P₁: Harvesting juveniles has little influence on harvest growth compared with harvesting adult females due to the lower reproductive value of juveniles than adult females; P₂: Harvesting of juveniles dampens variance in harvest due to lower and more variable natural survival rates of juveniles compared with adults. We found that harvesting juveniles has little effect on harvest growth rate, while harvesting adult females has a significant negative effect (consistent with P₁), but that increasing the proportion of juveniles in the harvest did not decrease the variability in harvest between years (P₂ not supported). Based on our empirical findings and overview of arguments, we discuss how the merits of juvenile harvesting may vary over time as populations move from a low density to a very high density state.     

Natural selection on body size is mediated by multiple interacting factors: a comparison of beetle populations varying naturally and experimentally in body size

Body size varies considerably among species and among populations within species, exhibiting many repeatable patterns. However, which sources of selection generate geographic patterns, and which components of fitness mediate evolution of body size, are not well understood. For many animals, resource quality and intraspecific competition may mediate selection on body size producing large-scale geographic patterns. In two sequential experiments, we examine how variation in larval competition and resource quality (seed size) affects the fitness consequences of variation in body size in a scramble-competing seed-feeding beetle, Stator limbatus. Specifically, we compared fitness components among three natural populations of S. limbatus that vary in body size, and then among three lineages of beetles derived from a single base population artificially selected to vary in size, all reared on three sizes of seeds at variable larval density. The effects of larval competition and seed size on larval survival and development time were similar for larger versus smaller beetles. However, larger-bodied beetles suffered a greater reduction in adult body mass with decreasing seed size and increasing larval density; the relative advantage of being large decreased with decreasing seed size and increasing larval density. There were highly significant interactions between the effects of seed size and larval density on body size, and a significant three-way interaction (population-by-density-by-seed size), indicating that environmental effects on the fitness consequences of being large are nonadditive. Our study demonstrates how multiple ecological variables (resource availability and resource competition) interact to affect organismal fitness components, and that such interactions can mediate natural selection on body size. Studying individual factors influencing selection on body size may lead to misleading results given the potential for nonlinear interactions among selective agents.     

Possible Secondary Population-Level Effects of Selective Harvest of Adult Male Muskoxen

Selective harvest regimes are often focused on males resulting in skewed sex-ratios, and for many ungulate species this strategy is sustainable. However, muskoxen (Ovibos moschatus) are very social and mature bulls (≥4 years old), particularly prime-age bulls (6–10 years old), play important roles in predator defense and recruitment. A year-round social structure incorporating large males into mixed-sex groups could make this species more susceptible to the effects of selective harvest if population composition and sex-ratios influence overall survival and reproductive success. Using detailed data collected on the muskox population occupying the Seward Peninsula, Alaska during 2002–2012, we formulated the hypothesis that the selective harvest of mature bulls may be related to documented changes in population composition and growth rates in this species. In addition, we reviewed existing published information from two other populations in Alaska, the Cape Thompson and Northeastern populations, to compare population growth rates among the three areas under differential harvest rates relative to our hypothesis. We found that on the Seward Peninsula, mature bull:adult cow ratios declined 4–12%/year and short-yearling:adult cow ratios (i.e., recruitment) declined 8–9%/year in the most heavily harvested areas. Growth rates in all 3 populations decreased disproportionately after increases in the number of bulls harvested, and calf:cow ratios declined in the Northeastern population as harvest increased. While lack of appropriate data prevented us from excluding other potential causes such as density dependent effects and changes in predator densities, our results did align with our hypothesis, suggesting that in the interest of conservation, harvest of mature males should be restricted until causal factors can be more definitively identified. If confirmed by additional research, our findings would have important implications for harvest management and conservation of muskoxen and other ungulate species with similar life-histories.     

Mutators, population size, adaptive landscape and the adaptation of asexual populations of bacteria.

Selection of mutator alleles, increasing the mutation rate up to 10, 000-fold, has been observed during in vitro experimental evolution. This spread is ascribed to the hitchhiking of mutator alleles with favorable mutations, as demonstrated by a theoretical model using selective parameters corresponding to such experiments. Observations of unexpectedly high frequencies of mutators in natural isolates suggest that the same phenomenon could occur in the wild. But it remains questionable whether realistic in natura parameter values could also result in selection of mutators. In particular, the main parameters of adaptation, the size of the adapting population and the height and steepness of the adaptive peak characterizing adaptation, are very variable in nature. By simulation approach, we studied the effect of these parameters on the selection of mutators in asexual populations, assuming additive fitness. We show that the larger the population size, the more likely the fixation of mutator alleles. At a large population size, at least four adaptive mutations are needed for mutator fixation; moreover, under stronger selection stronger mutators are selected. We propose a model based on multiple mutations to illustrate how second-order selection can optimize population fitness when few favorable mutations are required for adaptation.