Inheritance of size and shape in a natural population of collared flycatchers,Ficedula albicollis

Four external skeletal and three feather dimensions were measured on adult collared flycatchers (Ficedula albicollis) and their adult offspring. By using mid-offspring-midparent regressions, all traits were found to be heritable with an arithmetic mean heritability of 0.46. Heritability estimates from full-sib analyses were about 1.5 times higher (mean 0.67), indicating that variation in traits was affected by shared nest environment among full-sibs. The overall body size as measured by principal component one (PC1) was found to be heritable (h² = 0.40). However, this multivariate measure of heritability was not significant in offspring-father comparison, while highly so in offspring-mother comparison (h² = 0.60). Low offspring-father resemblance was evident also in univariate estimates of heritability. Possible causes of this (extra-pair copulations, maternal effects, sex-linked variance) are discussed. Genetic correlations among seven traits were estimated to be low (mean 0.22), and of similar magnitude or higher than phenotypic correlations (mean 0.18). All genetic correlations were positive. Genetic and phenotypic correlations as well as covariances were fairly similar to each other (r = 0.85 and r = 0.87, respectively). Environmental correlations did not follow the pattern of genetic correlations (r = 0.11), but were more similar to phenotypic correlations (r = 0.60). Given the low genetic correlations and moderate heritabilities, the overall conclusion is that the external morphology of collared flycatchers is largely under additive genetic control and that there is a strong potential for evolutionary change in morphology even under complex multivariate selection.     

GENETIC AND ENVIRONMENTAL VARIATION IN LIFE-HISTORY TRAITS OF A MONOCARPIC PERENNIAL: A DECADE-LONG FIELD EXPERIMENT

Directional and stabilizing selection tend to deplete additive genetic variance. On the other hand, genetic variance in traits related to fitness could be retained through polygenic mutation, spatially varying selection, genotype-environment interaction, or antagonistic pleiotropy. Most estimates of genetic variance in fitness-related traits have come from laboratory studies, with few estimates of heritability made under natural conditions, particularly for longer lived organisms. Here I estimated additive genetic variance in life-history characters of a monocarpic herb, Ipomopsis aggregata, that lives for up to a decade. Experimental crosses yielded 229 full-sibships nested within 32 paternal half-sibships. More than 5000 offspring were planted as seeds into natural field sites and were followed in most cases through their entire life cycle. Survival showed substantial additive genetic variance (genetic coefficient of variation ≈ 54%). Small differences at seedling emergence were magnified over time, such that the genetic variability in survival was only detectable by tracking the success of offspring for several years starting from seed. In contrast to survival, reproductive traits such as flower number, seeds per flower, and age at flowering showed little or no genetic variability. Despite relatively high levels of additive genetic variation for some life-history characters, high environmental variance in survival resulted in very low heritabilities (0–9%) for all of these characters. Maternal effects were evident in seed mass and remained strong throughout the lengthy vegetative period. No negative genetic correlations between major components of female fitness were detected. Mean corolla width for a paternal family was, however, negatively correlated with the finite rate of increase based on female fitness. That negative correlation could help to maintain additive genetic variance in the face of strong selection through male function for wide corollas.     

Selection,structure and the heritability of behaviour

Characters which are closely linked to fitness often have low heritabilities (V_A/V_P). Low heritabilities could be because of low additive genetic variation (V_A), that had been depleted by directional selection. Alternatively, low heritabilities may be caused by large residual variation (V_R=V_P – V_A) compounded at a disproportionately higher rate than V_A across integrated characters. Both hypotheses assume that each component of quantitative variation has an independent effect on heritability. However, V_A and V_R may also covary, in which case differences in heritability cannot be fully explained by the independent effects of elimination‐selection or compounded residual variation. We compared the central tendency of published behavioural heritabilities (mean=0.31, median=0.23) with morphological and life history data collected by 26 ). Average behavioural heritability was not significantly different from average life history heritability, but both were smaller than average morphological heritability. We cross‐classified behavioural traits to test whether variation in heritability was related to selection (dominance, domestic/wild) or variance compounding (integration level). There was a significant three‐way interaction between indices of selection and variance compounding, related to the absence of either effect at the highest integration level. At lower integration levels, high dominance variance indicated effects of selection. It was also indicated by the low CV_A of domestic species. At the same time CV_R increased disproportionately faster than CV_A across integration levels, demonstrating variance compounding. However, neither CV_R nor CV_A had a predominant effect on heritability. The partial regression coefficients of CV_R and CV_A on heritability were similar and a path analysis indicated that their (positive) correlation was also necessary to explain variation in heritability. These results suggest that relationships between additive genetic and residual components of quantitative genetic variation can constrain their independent direct effects on behavioural heritability.     

Estimating variance components and heritabilities in the wild: a case study using the ‘animal model’ approach

Using a genealogy containing over 1800 dams and nearly 400 sires (estimated by genetic paternity techniques), combined with maximum likelihood procedures and an ‘animal model’, we have estimated the heritabilities, genetic correlations and variance components of three morphometric traits in the Soay sheep (Ovis aries) on St Kilda, Scotland. This approach allows heritabilities to be estimated in natural populations that violate the assumptions of offspring–parent regression methods. Maternal (or paternal) effects can also be estimated under natural conditions. We demonstrate that all the traits, body weight, hind leg length and incisor arcade breadth, have low but significant heritabilities. Body weight, the trait that experiences the strongest selection, had the lowest heritability but the highest additive genetic coefficient of variation. An evolutionary response to selection is predicted. When maternal effects were not taken into consideration heritabilities were over‐estimated, although this effect was only significant in female offspring.     

GENOTYPE-BY-ENVIRONMENT INTERACTIONS IN THE DETERMINATION OF THE SIZE OF A SECONDARY SEXUAL CHARACTER IN THE COLLARED FLYCATCHER (FICEDULA ALBICOLLIS)

Although genetic variation in characters closely related to fitness is expected to either become depleted by selection or masked by environmental variation, “good gene” models of sexual selection require moderate to high heritabilities of secondary sexual characters to explain the occurrence of costly female mate preferences. In this study, I investigated whether the estimated heritability of a condition-dependent secondary sexual character (i.e., the white forehead badge) in the collared flycatcher varied depending on environmental conditions experienced during offspring growth. The data were collected over a period of 14 years making it possible to exploit natural variation in natal conditions. In addition, natal conditions were experimentally altered through brood size manipulations. During unfavorable conditions caused by generally poor weather or experimentally enlarged brood size, no significant heritability based on father-sons regressions could be demonstrated (0.19 ? h² ? 0.27). In contrast, sons reared during years with favorable weather or in experimentally reduced broods significantly resembled their fathers (0.44 ? h² ? 0.65). In addition, the heritability estimates declined with increasing maternal age. The strong effect of natal environmental condition on the estimated heritability of forehead badge size suggests that the potential genetic benefit from mate choice vary according to environmental conditions (e.g., the benefit is reduced during unfavorable rearing conditions). Because sons reared during poor conditions have probably experienced a natal environment different from that experienced by their fathers, the low heritability estimates obtained under poor conditions seem to be caused by low additive genetic variation expressed in such environments and/or a low genetic correlation between the expression of the trait in the two different environments (i.e., good vs. bad). Both of these explanations imply the presence of genotype-by-environment interactions. If such interactions frequently affect the expression of secondary sexual characters, this may offer an explanation of the high heritabilites sometimes reported for such traits, despite their exposure to long-term directional selection.     

Comparing Evolvability and Variability of Quantitative Traits

There are two distinct reasons for making comparisons of genetic variation for quantitative characters. The first is to compare evolvabilities, or ability to respond to selection, and the second is to make inferences about the forces that maintain genetic variability. Measures of variation that are standardized by the trait mean, such as the additive genetic coefficient of variation, are appropriate for both purposes. Variation has usually been compared as narrow sense heritabilities, but this is almost always an inappropriate comparative measure of evolvability and variability. Coefficients of variation were calculated from 842 estimates of trait means, variances and heritabilities in the literature. Traits closely related to fitness have higher additive genetic and nongenetic variability by the coefficient of variation criterion than characters under weak selection. This is the reverse of the accepted conclusion based on comparisons of heritability. The low heritability of fitness components is best explained by their high residual variation. The high additive genetic and residual variability of fitness traits might be explained by the great number of genetic and environmental events they are affected by, or by a lack of stabilizing selection to reduce their phenotypic variance. Over one-third of the quantitative genetics papers reviewed did not report trait means or variances. Researchers should always report these statistics, so that measures of variation appropriate to a variety of situations may be calculated.     

EVOLUTION OF FLORAL TRAITS IN A HERMAPHRODITIC PLANT: FIELD MEASUREMENTS OF HERITABILITIES AND GENETIC CORRELATIONS

Genetic variances, heritabilities, and genetic correlations of floral traits were measured in the monocarpic perennial Ipomopsis aggregata (Polemoniaceae). A paternal half-sib design was employed to generate seeds in each of four years, and seeds were planted back in the field near the parental site. The progeny were followed for up to eight years to estimate quantitative genetic parameters subject to natural levels of environmental variation over the entire life cycle. Narrow-sense heritabilities of 0.2–0.8 were detected for the morphometric traits of corolla length, corolla width, stigma position, and anther position. The proportion of time spent by the protandrous flowers in the pistillate phase (“proportion pistillate”) also exhibited detectable heritability of near 0.3. In contrast, heritability estimates for nectar reward traits were low and not significantly different from zero, due to high environmental variance between and within flowering years. The estimates of genetic parameters were combined with phenotypic selection gradients to predict evolutionary responses to selection mediated by the hummingbird pollinators. One trait, corolla width, showed the potential for a rapid response to ongoing selection through male function, as it experienced both direct selection, by influencing pollen export, and relatively high heritability. Predicted responses were lower for proportion pistillate and corolla length, even though these traits also experienced direct selection. Stigma position was expected to respond positively to indirect selection of proportion pistillate but negatively to selection of corolla length, with the net effect sensitive to variation in the selection estimates. Anther position also was not directly selected but could respond to indirect selection of genetically correlated traits.     

Molecular phylogeny and intraspecific structure of loaches (genera <Emphasis Type="Italic">Cobitis</Emphasis> and <Emphasis Type="Italic">Misgurnus</Emphasis>) from the Far East region of Russia and some conclusions on their systematics

Russian Far East loaches of the genera Cobitis and Misgurnus are among members of the family Cobitidae with poorly understood systematics. In this study we present phylogenetic hypotheses based on mitochondrial (cytochrome b) and nuclear (RAG-1) sequences. All analyses recovered comparable topological phylogenies, and all data sets supported the non-monophyly of the genera Cobitis and Misgurnus. Both genera are represented by multiple lineages that in some cases do not correspond to the species described. We found some phylogenetic incongruities for the genus Misgurnus (M. mohoity and M. anguillicaudatus) that are explained by ancient hybridization, as was suggested previously for M. anguillicaudatus. The revealed phylogenetic relationships suggest that Paramisgurnus should be treated as a synonym of Misgurnus and M. bipartitus as a synonym of M. mohoity. All analyses recovered C. choii as a member of the genus Cobitis, confirming previous taxonomic conclusions. Most of the molecular lineages found follow currently recognized taxa with some exceptions, such as M. anguillicaudatus and C. lutheri. Phylogenetic relationships recover several unrelated lineages of M. anguillicaudatus and suggest additional studies to solve current taxonomic uncertainty. We found that C. lutheri is a non-natural group that contains two unrelated lineages: specimens of C. lutheri from the Far East of Russia collected close to the type locality and a second lineage with specimens of C. lutheri from Korea, the identification of which must be revised. The study provides evidence of the presence of the Far East species M. nikolskyi in Sakhalin Island, but simultaneously shows conspicuous genetic distinctiveness between the island and the mainland populations.     

Genetic parameters for growth, wood density and pulp yield in Eucalyptus globulus

Genetic variation and co-variation among the key pulpwood selection traits for Eucalyptus globulus were estimated for a range of sites in Portugal, with the aim of improving genetic parameters used to predict breeding values and correlated response to selection. The trials comprised clonally replicated full-sib families (eight trials) and unrelated clones (17 trials), and exhibited varying levels of pedigree connectivity. The traits studied were stem diameter at breast height, Pilodyn penetration (an indirect measure of wood basic density) and near infrared reflectance predicted pulp yield. Univariate and multivariate linear mixed models were fitted within and across sites, and estimates of additive genetic, total genetic, environmental and phenotypic variances and covariances were obtained. All traits studied exhibited significant levels of additive genetic variation. The average estimated within-site narrow-sense heritability was 0.19 ± 0.03 for diameter and 0.29 ± 0.03 for Pilodyn penetration, and the pooled estimate for predicted pulp yield was 0.42 ± 0.14. When they could be tested, dominance and epistatic effects were generally not statistically significant, although broad-sense heritability estimates were slightly higher than narrow-sense heritability estimates. Averaged across trials, positive additive (0.64 ± 0.08), total genetic (0.58 ± 0.04), environmental (0.38 ± 0.03) and phenotypic (0.43 ± 0.02) correlation estimates were consistently obtained between diameter and Pilodyn penetration. This data argues for at least some form of pleiotropic relationship between these two traits and that selection for fast growth will adversely affect wood density in this population. Estimates of the across-site genetic correlations for diameter and Pilodyn penetration were high, indicating that the genotype by environment interaction is low across the range of sites tested. This result supports the use of single aggregated selection criteria for growth and wood density across planting environments in Portugal, as opposed to having to select for performance in different environments.     

Variation in the peacock’s train shows a genetic component

Female peafowl (Pavo cristatus) show a strong mating preference for males with elaborate trains. This, however, poses something of a paradox because intense directional selection should erode genetic variation in the males’ trains, so that females will no longer benefit by discriminating among males on the basis of these traits. This situation is known as the ‘lek paradox’, and leads to the theoretical expectation of low heritability in the peacock’s train. We used two independent breeding experiments, involving a total of 42 sires and 86 of their male offspring, to estimate the narrow sense heritabilities of male ornaments and other morphometric traits. Contrary to expectation, we found significant levels of heritability in a trait known to be used by females during mate choice (train length), while no significant heritabilities were evident for other, non-fitness related morphological traits (tarsus length, body weight or spur length). This study adds to the building body of evidence that high levels of additive genetic variance can exist in secondary sexual traits under directional selection, but further emphasizes the main problem of what maintains this variation.     

Sex differences in the genetic architecture of aggressiveness in a sexually dimorphic spider

Sex differences in the genetic architecture of behavioral traits can offer critical insight into the processes of sex‐specific selection and sexual conflict dynamics. Here, we assess genetic variances and cross‐sex genetic correlations of two personality traits, aggression and activity, in a sexually size‐dimorphic spider, Nuctenea umbratica. Using a quantitative genetic approach, we show that both traits are heritable. Males have higher heritability estimates for aggressiveness compared to females, whereas the coefficient of additive genetic variation and evolvability did not differ between the sexes. Furthermore, we found sex differences in the coefficient of residual variance in aggressiveness with females exhibiting higher estimates. In contrast, the quantitative genetic estimates for activity suggest no significant differentiation between males and females. We interpret these results with caution as the estimates of additive genetic variances may be inflated by nonadditive genetic effects. The mean cross‐sex genetic correlations for aggression and activity were 0.5 and 0.6, respectively. Nonetheless, credible intervals of both estimates were broad, implying high uncertainty for these estimates. Future work using larger sample sizes would be needed to draw firmer conclusions on how sexual selection shapes sex differences in the genetic architecture of behavioral traits.     

Variability and covariability for plant height,heading date,and seed weight in wheat crosses

Summary Variability, covariability, heritability, and expected genetic gains from selection for heading date, plant height, and kernel weight were estimated in progenies derived from six wheat crosses. The crosses differed in the magnitude of the genetic variabilities of their progenies, but all crosses had significant variabilities for all traits. Heritability estimates were calculated by the variance components method. The estimates of heritability were relatively high for all three traits and averaged 86% for heading date, 77% for plant height, and 70% for kernel weight. The presence of significant genetic variabilities and high heritability estimates indicated that selection would be effective for the three traits.The segregates derived from crosses between medium tall parents showed transgressive segregation that would permit isolation of short-statured types. Transgressive segregation also occurred for heading date and kernel weight.Heading date and plant height were positively and highly significantly correlated in four crosses out of six. But both plant height and heading date had, in general, low negative correlations with kernel weight which would not preclude the development of short wheats with high kernel weight from these crosses. The association between characters was mostly genetic in cause.     

Evolvability and genetic constraint in Dalechampia blossoms: components of variance and measures of evolvability

Many evolutionary arguments are based on the assumption that quantitative characters are highly evolvable entities that can be rapidly moulded by changing selection pressures. The empirical evaluation of this assumption depends on having an operational measure of evolvability that reflects the ability of a trait to respond to a given external selection pressure. We suggest short-term evolvability be measured as expected proportional response in a trait to a unit strength of directional selection, where strength of selection is defined independently of character variation and in units of the strength of selection on fitness itself. We show that the additive genetic variance scaled by the square of the trait mean, IA, is such a measure. The heritability, h2, does not measure evolvability in this sense. Based on a diallel analysis, we use IA to assess the evolvability of floral characters in a population of the neotropical vine Dalechampia scandens (Euphorbiaceae). Although we are able to demonstrate that there is additive genetic variation in a number of floral traits, we also find that most of the traits are not expected to change by more than a fraction of a percent per generation. We provide evidence that the degree of among-population divergence of traits is related to their predicted evolvabilities, but not to their heritabilities.     

The effect of trait type and strength of selection on heritability and evolvability in an island bird population

The heritability (h²) of fitness traits is often low. Although this has been attributed to directional selection having eroded genetic variation in direct proportion to the strength of selection, heritability does not necessarily reflect a trait's additive genetic variance and evolutionary potential (“evolvability”). Recent studies suggest that the low h² of fitness traits in wild populations is caused not by a paucity of additive genetic variance (V_A) but by greater environmental or nonadditive genetic variance (V_R). We examined the relationship between h² and variance‐standardized selection intensities (i or β_σ), and between evolvability (I_A:V_A divided by squared phenotypic trait mean) and mean‐standardized selection gradients (β_μ). Using 24 years of data from an island population of Savannah sparrows, we show that, across diverse traits, h² declines with the strength of selection, whereas I_A and I_R (V_R divided by squared trait mean) are independent of the strength of selection. Within trait types (morphological, reproductive, life‐history), h², I_A, and I_R are all independent of the strength of selection. This indicates that certain traits have low heritability because of increased residual variance due to the age at which they are expressed or the multiple factors influencing their expression, rather than their association with fitness.     

Heritability and genetic correlations of personality traits in a wild population of yellow‐bellied marmots (Marmota flaviventris)

Describing and quantifying animal personality is now an integral part of behavioural studies because individually distinctive behaviours have ecological and evolutionary consequences. Yet, to fully understand how personality traits may respond to selection, one must understand the underlying heritability and genetic correlations between traits. Previous studies have reported a moderate degree of heritability of personality traits, but few of these studies have either been conducted in the wild or estimated the genetic correlations between personality traits. Estimating the additive genetic variance and covariance in the wild is crucial to understand the evolutionary potential of behavioural traits. Enhanced environmental variation could reduce heritability and genetic correlations, thus leading to different evolutionary predictions. We estimated the additive genetic variance and covariance of docility in the trap, sociability (mirror image stimulation), and exploration and activity in two different contexts (open‐field and mirror image simulation experiments) in a wild population of yellow‐bellied marmots (Marmota flaviventris). We estimated both heritability of behaviours and of personality traits and found nonzero additive genetic variance in these traits. We also found nonzero maternal, permanent environment and year effects. Finally, we found four phenotypic correlations between traits, and one positive genetic correlation between activity in the open‐field test and sociability. We also found permanent environment correlations between activity in both tests and docility and exploration in the MIS test. This is one of a handful of studies to adopt a quantitative genetic approach to explain variation in personality traits in the wild and, thus, provides important insights into the potential variance available for selection.     

THE EVOLUTIONARY GENETICS OF MALE LIFE-HISTORY CHARACTERS IN DROSOPHILA MELANOGASTER

Alternative models of the maintenance of genetic variability, theories of life-history evolution, and theories of sexual selection and mate choice can be tested by measuring additive and nonadditive genetic variances of components of fitness. A quantitative genetic breeding design was used to produce estimates of genetic variances for male life-history traits in Drosophila melanogaster. Additive genetic covariances and correlations between traits were also estimated. Flies from a large, outbred, laboratory population were assayed for age-specific competitive mating ability, age-specific survivorship, body mass, and fertility. Variance-component analysis then allowed the decomposition of phenotypic variation into components associated with additive genetic, nonadditive genetic, and environmental variability. A comparison of dominance and additive components of genetic variation provides little support for an important role for balancing selection in maintaining genetic variance in this suite of traits. The results provide support for the mutation-accumulation theory, but not the antagonistic-pleiotropy theory of senescence. No evidence is found for the positive genetic correlations between mating success and offspring quality or quantity that are predicted by “good genes” models of sexual selection. Additive genetic coefficients of variation for life-history characters are larger than those for body weight. Finally, this set of male life-history characters exhibits a very low correspondence between estimates of genetic and phenotypic correlations.     

Environmental variation and quantitative genetic prameters in the feral pigeon, Columba livia

The estimation of quantitative genetic parameters and modes of selection in natural populations can provide critical information concerning both past and current evolution of mean phenotypes. We examine the influence of environmental variation on the genetic variance-covariance matrix ( G ) of external morphological traits in feral pigeons, and the degree of correspondence between phenotypic (r_p) and genetic correlations (r_g) of these characters. Our results suggest that adverse environmental conditions affect heritability, and that the correspondence between seasonal estimates of G based on midparent scores is low. There is, however, a strong correspondence between r_p and r_g. We suggest that, if environmental variation is relatively common, estimates of quantitative genetic parameters for prospective selection studies must be undertaken at each selection episode.     

Selection and genetic (co)variance in bighorn sheep

Genetic theory predicts that directional selection should deplete additive genetic variance for traits closely related to fitness, and may favor the maintenance of alleles with antagonistically pleiotropic effects on fitness-related traits. Trait heritability is therefore expected to decline with the degree of association with fitness, and some genetic correlations between selected traits are expected to be negative. Here we demonstrate a negative relationship between trait heritability and association with lifetime reproductive success in a wild population of bighorn sheep (Ovis canadensis) at Ram Mountain, Alberta, Canada. Lower heritability for fitness-related traits, however, was not wholly a consequence of declining genetic variance, because those traits showed high levels of residual variance. Genetic correlations estimated between pairs of traits with significant heritability were positive. Principal component analyses suggest that positive relationships between morphometric traits constitute the main axis of genetic variation. Trade-offs in the form of negative genetic or phenotypic correlations among the traits we have measured do not appear to constrain the potential for evolution in this population.     

Effect of various parameter combinations on genetic gain in computer simulated two-character selection

Summary In a simulation study, the effect of various parameter combinations such as linkage, dominance, heritability, and economic weights on the individual trait means was investigated using additive genetic, genotypic and the phenotypic index of Elston (1963). The characters responded differently to these indices under various parameter combinations, indicating favourable and unfavourable effects of the mentioned parameters. Linkage was found to reduce the rate of progress through selection. Depression of genetic gain was greater where the genes governing a character showed dominance and/or heritability coefficients were low. It was, however, noticed that depression of genetic gain due to low heritability of a character could be avoided by assigning higher economic weight to that character. This suggests that desirable changes in the means of characters available for selection can be manipulated by choosing appropriate economic weights. The additive genetic index, where only the additive genetic variances and covariances go into its construction, does not seem to be affected by intra-allelic interactions since they add to variances and covariances due to dominance deviations and these have nothing to do with the additive genetic variances and covariances. It seems that from such studies, if conducted extensively incorporating still more parameters, conclusions may be drawn on the most suitable selection model for simultaneous selection under a given set of parameters available in real biological systems.     

A meta-analysis of the heritability of developmental stability

The existence of additive genetic variance in developmental stability has important implications for our understanding of morphological variation. The heritability of individual fluctuating asymmetry and other measures of developmental stability have frequently been estimated from parent-offspring regressions, sib analyses, or from selection experiments. Here we review by meta-analysis published estimates of the heritability of developmental stability, mainly the degree of individual fluctuating asymmetry in morphological characters. The overall mean effect size of heritabilities of individual fluctuating asymmetry was 0.19 from 34 studies of 17 species differing highly significantly from zero (P < 0.0001). The mean heritability for 14 species was 0.27. This indicates that there is a significant additive genetic component to developmental stability. Effect size was larger for selection experiments than for studies based on parent-offspring regression or sib analyses, implying that genetic estimates were unbiased by maternal or common environment effects. Additive genetic coefficients of variation for individual fluctuating asymmetry were considerably higher than those for character size per se. Developmental stability may be significantly heritable either because of strong directional selection, or fluctuating selection regimes which prevent populations from achieving a high degree of developmental stability to current environmental and genetic conditions.