An integrated approach to oilseed rape cultivar selection using phenotypic stability

Summary Various methods of evaluating phenotypic stability have been proposed; however, no single method can adequately describe cultivar performance. The objectives of this study were to integrate a number of methods of evaluating stability and to use this approach for cultivar selection. These objectives were considered in the context of the broad-based oilseed rape cultivar (Brassica napus spp. oleifera) evaluation system currently used in western Canada. Regression analysis was used to assess cultivar response to environments. Cluster analysis was used to assemble cultivars into groups with similar regression coefficients (b _i ) and mean yield. Three parametric stability parameters, years within locations mean square (MS; Y/L), Shukla's stability variance ( _i ² ), and Francis and Kannenberg's coefficient of variability (CV _i ), were compared to determine which method would be most suitable for selection of oilseed rape cultivars from within clustered groups. Yield data from three cultivars and six breeding lines that had been tested for 2 years at 26 locations in the Western Canola Cooperative Test A were used for all calculations. The cluster analysis was successful in identifying commercially acceptable breeding lines. The parameter MS _i Y/L was considered to be more appropriate than either CV _i or _i ² , because it measured only the unpredictable portion of the genotype x environment interaction and was independent of the other cultivars in the test. The use of cluster analysis to group entries with similar b _i values and mean yields, followed by selection for stability within groups, was advocated.Contribution No. 846 of the Plant Science Department, University of Manitoba     

Regression analysis of yield stability is strongly affected by companion test varieties and locations — examples from a study of Nordic barley lines

The suitability of regression analysis for studying the phenotypic stability of grain yield was investigated using a collection of 220 Nordic barley lines. Linear regression explained 26–52% of the genotype x environment (GE) interactions in different groupings of the material. The regression coefficient, b _i , measures the yield response of the i-th genotype to improved environmental conditions. Deviations from regression, S _di ² , have been used to estimate Tai's stability parameter, _i , which is a measure of the phenotypic yield stability in the agronomic sense. Repeatability of b _i , _i , and grain yield was studied by means of correlations between estimates obtained in each experimental year. Yield had the highest repeatability, with correlations between years ranging from 0.57 to 0.85. In this study, regression coefficients and _i -values were not repeatable, i.e. genotypes reacted differentially to the yearly climatic variations. Six-rowed (6r) barleys had higher responsiveness, but lower mean yields, than two-rowed (2r) barleys. This is partly due to the history of selection of 6r-barleys, which mainly originate from regions with low potential yield levels, i.e. Finland and Norway. In general, responsiveness and stability were not correlated with yield. The highest-yielding lines had b _i 1. The response pattern of the different types of barleys used in this study show that responsiveness can be changed by recombination.     

Genetic substructure and admixture as important factors in linkage disequilibrium‐based estimation of effective number of breeders in recovering wildlife populations

The number of effective breeders (N_b) and effective population size (N_e) are population parameters reflective of evolutionary potential, susceptibility to stochasticity, and viability. We have estimated these parameters using the linkage disequilibrium‐based approach with LDNE through the latest phase of population recovery of the brown bears (Ursus arctos) in Finland (1993–2010; N = 621). This phase of the recovery was recently documented to be associated with major changes in genetic composition. In particular, differentiation between the northern and the southern genetic cluster declined rapidly within 1.5 generations. Based on this, we have studied effects of the changing genetic structure on N_b and N_e, by comparing estimates for whole Finland with the estimates for the two genetic clusters. We expected a potentially strong relationship between estimate sizes and genetic differentiation, which should disappear as the population recovers and clusters merge. Consistent with this, our estimates for whole Finland were lower than the sum of the estimates of the two genetic clusters and both approaches produced similar estimates in the end. Notably, we also found that admixed genotypes strongly increased the estimates. In all analyses, our estimates for N_e were larger than N_b and likely reflective for brown bears of the larger region of Finland and northwestern Russia. Conclusively, we find that neglecting genetic substructure may lead to a massive underestimation of N_b and N_e. Our results also suggest the need for further empirical analysis focusing on individuals with admixed genotypes and their potential high influence on N_b and N_e.     

A comparison of results obtained with two methods for assessing yield stability

Summary A major objective of the CIMMYT Maize Program is to develop open-pollinated varieties of maize (Zea mays L.) that are well adapted to a wide range of environments. To achieve this breeding goal, it is essential that the program use a stability technique that will identify high-yielding, stable genotypes accurately in international trials conducted under different environmental conditions. The objective of this study was to compare a spatial method with a modified conventional regression analysis method to determine the yield stability of 27 CIMMYT maize varieties evaluated at 37 locations. The methods also were compared on the basis of their consistency in assessing the stability of varieties when certain locations were omitted, and when subsets of varieties were analyzed. The varieties found to be stable by the spatial method with all sites included in the analysis were also stable (1) when the lowest and highest yielding sites were excluded from the analyses, and (2) when the varieties were considered, along with others, as a subset of the original group of materials. Stability parameters determined by regression analysis, however, varied for some varieties when (1) extreme sites were excluded, and (2) a subset of entries was considered in isolation. Because the spatial method was more consistent in identifying high-yielding stable varieties, it was considered the more useful of the two methods.     

Kinematics of nonstationary locomotion in the centipede <Emphasis Type="Italic">Scolopendra cingulata</Emphasis>: A single instant change of speed

The spatiotemporal parameters of leg movement in Scolopendra instantly changing the locomotion speed from V ₁ to V ₂ ≠ V ₁ are investigated. It is shown that (i) the principle of “in trail” leg placement is kept upon a change of speed; (ii) the continuity of the metachronal coordination is not disturbed; but (iii) for some time after changing speed the set of ipsilateral legs comprises (a) head-proximal legs creating a new trackway of steps with pace ℓ₂, and (b) distal legs still using the old trackway with pace ℓ₁. The two groups differ in kinematic parameters. Group (a) works in the stationary mode corresponding to speed V ₂, while group (b) works in a transitory mode. Consecutively, with a metachronal wave propagating backwards along the body but immobile relative to the ground, more and more legs from group (b) switch to the new stationary mode.     

干旱胁迫下油橄榄品种光合特性研究

为揭示油橄榄(Olea europaea L.)耐旱性与光合特性之间的关系,以筛选出的适宜于半干旱川西南地区种植的7个引进油橄榄品种为供试材料,采用盆栽模拟干旱胁迫的方法,研究持续干旱胁迫对其光合特性的影响。结果表明:(1)随着干旱胁迫程度加剧,7个油橄榄品种叶片相对含水量均显著降低,至干旱胁迫后期(25d),各品种叶片均出现大幅失水,其中品种‘科拉蒂’失水率最高(45.79%),而品种‘小苹果’失水率最低(25.52%),说明‘小苹果’叶片在干旱胁迫下较其他油橄榄品种具有更高保水能力。(2)随着干旱胁迫程度加剧,7个油橄榄品种叶片光合色素含量均不同程度降低,表明光合色素分解量大于合成量;干旱胁迫持续25d时,品种‘豆果’的叶绿素a和叶绿素b含量下降幅度最大(P0.05),品种‘皮削利’类胡萝卜素含量下降幅度最大(P0.05),而品种‘小苹果’叶绿素a含量下降幅度最小。(3)随着干旱胁迫的持续进行,各油橄榄品种叶片净光合速率(Pn)、蒸腾速率(Tr)、气孔导度(Gs)和胞间CO2浓度(Ci)均不同程度降低,而水分利用效率(WUE)则呈上升趋势;干旱胁迫期间,品种‘佛奥’的Pn、Tr和Ci以及‘皮削利’的Gs降幅均高于其他品种,而‘小苹果’的Pn、Gs和Ci降幅均为最小且WUE上升幅度最大。研究发现,在持续干旱胁迫条件下,油橄榄幼苗叶片均大幅失水,光合色素结构被破坏、色素分解、含量降低,同时气孔关闭蒸发减少,光合作用减弱,而供试油橄榄品种中‘小苹果’对干旱胁迫的适应性最强,适宜于在半干旱的川西地区种植。     

ALGORITHM FOR APPLICATION OF FOURIER ANALYSIS FOR BIORHYTHMIC BASELINES OF PHARMACODYNAMIC INDIRECT RESPONSE MODELS

The change of an indirect pharmacological response R(t) can be described by a periodic time-dependent production rate k_in (t) and a first-order loss constant k_out. If k_in(t) follows some biological rhythm (e.g., circadian), then the response R(t) also displays a periodic behavior. A new approach for describing the input function in indirect response models with biorhythmic baselines of physiologic substances is introduced. The present approach uses the baseline (placebo) response R_b(t) to recover the equation for k_in(t). Fourier analysis provides an approximate equation for R_b(t) that consists of terms (usually two or three) of the Fourier series (harmonics) that contribute most to the overall sum. The model differential equation is solved backward for k_in(t), yielding the equation involving R_b(t). A computer program was developed to perform the square L²-norm approximation technique. Fourier analysis was also performed based on nonlinear regression. Cortisol suppression after inhalation of fluticasone propionate (FP) was modeled based on the inhibition of the secretion rate k_in(t) using ADAPT II. The pharmacodynamic parameters k_out and IC₅₀ were estimated from the model equation with k_in(t) derived by the new approach. The proposed method of describing the input function needs no assumption about the behavior of k_in(t), is as efficient as methods used previously, and is more flexible in describing the baseline data than the nonlinear regression method. (Chronobiology International, 17(1), 77–93, 2000)     

Molecular and morphological differences between two geographic populations of Salanx ariakensis (Salangidae) from Korea and Japan

Geographic variations of a salangid, Salanx ariakensis, from Korea and Japan, based on partial mtDNA cyt b gene sequences and morphometric data, are presented and compared with Salanx cuvieri from China. Analyses of molecular variance (AMOVA) suggested that the two populations of S. ariakensis differed significantly from each other in pairwise fixation index (F _ST = 0.43), although their reciprocal monophyly was not constructed in the phylogenetic analysis. The phylogenetic analysis, however, supported the reciprocal monophyly of S. ariakensis (Korean population + Japanese population) and S. cuvieri. Differences in genetic structure between the two populations of S. ariakensis were suggested by diversity indices, mismatch distribution shape, and minimum spanning network. In particular, diversity indices indicated that the Korean population was historically larger and more stable than the Japanese population. In addition, both the principal component analysis (PCA) and canonical discriminant analysis (CDA) for morphometric characters, and the Kruskal–Wallis test for some meristic characters, showed that the two populations of S. ariakensis differed from each other, although morphological differences between the two populations of S. ariakensis were smaller than those between S. ariakensis and S. cuvieri. Such morphological differences were consistent with the differences in mtDNA.     

Sensitivity of Patterns of Molecular Evolution to Alterations in Methodology: A Critique of Hughes and Yeager

Employing a set of 43 othologous mouse and rat genes, Hughes and Yeager (J. Mol. Evol. 45:125–130, 1997) reported (1) no correlation between synonymous and nonsynonymous rates of nucleotide substitution, (2) a positive correlation between intronic GC contents (GC _i) and intronic substitution rates (K _i), (3) that the average K _i value was very similar to the average K _s value, and (4) that the compositional correlation between the rat and the mouse genes is stronger at the third codon position (GC₃) than at the first and second codon positions (GC₁₂). We have examined the robustness of these results to alterations in substitution rate estimation protocol, alignment protocol, and statistical procedure. We find that a significant correlation between K _a and K _s is observed either if a rank correlation statistic is used instead of regression analysis, if one outlier is excluded from the analysis, or if a regression weighted by gene size is employed. The correlation between K _i and GC _i we find to be sensitive to changes in alignment protocol and disappears on the use of weighted means. The finding that K _s and K _i are approximately the same is dependent on the method for estimating K _s values. Finally, the variance around the regression line of rat GC₃ versus mouse GC₃ we find to be significantly higher than that in GC₁₂. The source of the discrepancy between this and Hughes and Yeager's result is unclear. The variance around the line for GC₄ is higher still, as might be expected. Using a methodology that may be considered preferable to that of Hughes and Yeager, we find that all four of their results are contradicted. More importantly this analysis reinforces the need for caution in assembling and analyzing data sets, as the degree of sensitivity to what many might consider minor methodological alterations is unexpected. Received: 2 February 1998 / Accepted: 23 March 1998     

Accuracy of Optimized Chemical-exchange Parameters Derived by Fitting CPMG R 2 Dispersion Profiles when R 2 0a ≠ R 2 0b

The transverse relaxation rate, R₂, measured as a function of the effective field (R₂ dispersion) using a Carr-Purcell-Meiboom-Gill (CPMG) pulse train, is well suited to detect conformational exchange in proteins. The dispersion data are commonly fitted by a two-site (sites a and b) exchange model with four parameters: the relative population, p_a, the difference in chemical shifts of the two sites, δω, the correlation time for exchange, τ_ex, and the intrinsic relaxation rate (i.e., transverse relaxation rate in the absence of chemical exchange), R₂⁰. Although the intrinsic relaxation rates of the two sites, R₂^0a and R₂^0b, can differ, they are normally assumed to be the same (i.e., R₂^0a = R₂^0b = R₂⁰) when fitting dispersion data. The purpose of this investigation is to determine the magnitudes of the errors in the optimized exchange parameters that are introduced by the assumption that R₂^0a = R₂^0b. In order to accomplish this goal, we first generated synthetic constant-time CPMG R₂ dispersion data assuming two-site exchange with R₂^0a ≠ R₂^0b, and then fitted the synthetic data assuming two-site exchange with R₂⁰ = R₂^0a = R₂^0b. Although all the synthetic data generated assuming R₂^0a ≠ R₂^0b were well fitted (assuming R₂^0a = R₂^0b), the optimized values of p_a and τ _ex differed from their true values, whereas the optimized values of δω values did not. A theoretical analysis using the Carver–Richards equation explains these results, and yields simple, general equations for estimating the magnitudes of the errors in the optimized parameters, as a function of ( R₂^0a − R₂^0b).     

Evaluating thermal resource partitioning

Summary The field thermal biology of sympatric Anolis cooki and A. cristatellus were evaluated in January and in August in desert scrub forest at Playa de Tamarindo near Guanica, Puerto Rico. Data on randomly positioned copper models of lizards, each equipped with a built-in thermocouple, established null hypotheses about basking frequency and operative temperatures (T _e) against which the behavior and body temperatures (T _b) of live lizards were evaluated. Both species exhibited non-random hourly basking rates (more marked in cristatellus than in cooki), and cristatellus was virtually inactive during the warm mid-day hours. The relationship between lizards' T _b and randomly sampled T _e differed between the species: cristatellus's mean T _b was 2° to 3° C lower than randomly sampled mean T _e in both months, whereas cooki's mean T _b was slightly higher than mean T _e in January and slightly lower in August. Although cooki's mean T _b was higher than that of cristatellus in both months, the T _b's of the two species overlapped substantially over an annual cycle. Given the similarities in their field active T _b and the low thermal heterogeneity among microsites at Playa de Tamarindo, these species appear not to partition the thermal environment there in a coarse-grained way. Instead, the relatively small differences in their field active T _b probably result from small differences in their use of similar microhabitats within their mutually exclusive territories. Thermal resource partitioning by territorial animals is unlikely unless thermal heterogeneity is coarse-grained in relation to territory size.     

Gas Exchange of Spring Barley and Wheat Grown under Mild Water Shortage

During mild water stress (decrease of full water capacity from 60 to 35 %) net photosynthetic rate (P _N) of four spring barley and wheat genotypes was about twice lower than that for unstressed plants and was mainly limited by non-stomatal factors. Availability of CO₂ from intercellular spaces did not change significantly when stomatal conductance (g _s) decreased from 0.25-0.35 to 0.15-0.20 mol(H₂O) m⁻² s⁻¹. There may be two main processes leading to similar intercellular CO₂ concentration (c _i) in stressed and unstressed seedlings despite of twice lower P _N under mild water stress: (a) lower diffusion of CO₂ through stomata represented by lower g _s, (b) lower consumption of CO₂ by photosynthetic apparatus of stressed plants. Last factor is partially pronounced by lower response of P _N to c _i observed for stressed than for control plants. This revised version was published online in August 2006 with corrections to the Cover Date.     

The area under the function: an index for selecting desirable genotypes

The linear regression approach has been widely used for selecting high-yielding and stable genotypes targeted to several environments. The genotype mean yield and the regression coefficient of a genotype's performance on an index of environmental productivity are the two main stability parameters. Using both can often complicate the breeder's decision when comparing high-yielding, less-stable genotypes with low-yielding, stable genotypes. This study proposes to combine the mean yield and regression coefficient into a unified desirability index (D _i). Thus, D _i is defined as the area under the linear regression function divided by the difference between the two extreme environmental indexes. D _i is equal to the mean of the i ^th genotype across all environments plus its slope multiplied by the mean of the environmental indexes of the two extreme environments (symmetry). Desirable genotypes are those with a large D _i. For symmetric trials the desirability index depends largely on the mean yield of the genotype and for asymmetric trials the slope has an important influence on the desirability index. The use of D _i was illustrated by a 20-environments maize yield trial and a 25-environments wheat yield trial. Three maize genotypes out of nine showed values of D _i 's that were significantly larger than a hypothetical, stable genotype. These were considered desirable, even though two of them had slopes significantly greater than 1.0. The results obtained from ranking wheat genotypes on mean yield differ from a ranking based on D _i .     

Photosynthesis Parameters in Two Cultivars of Mulberry Differing in Salt Tolerance

Three-month-old mulberry (Morus alba L.) cultivars (salt tolerant cv. S1 and salt sensitive cv. ATP) were subjected to different concentrations of NaCl for 12 d. Leaf area, dry mass accumulation, total chlorophyll (Chl) content, net CO₂ assimilation rate (P _N), stomatal conductance (g _s), and transpiration rate (E) declined, and intercellular CO₂ concentration (C _i) increased. The changes in these parameters were dependent on stress severity and duration, and differed between the two cultivars. The tolerant cultivar showed a lesser reduction in P _N and g _s coupled with a better C _i and water use efficiency (WUE) than the sensitive cultivar. This revised version was published online in June 2006 with corrections to the Cover Date.     

高寒草甸种间性状差异和物种均匀度对物种多样性与功能多样性关系的影响

物种多样性(SD)与功能多样性(FD)之间存在多种关系,但由于生态系统功能主要由物种的功能属性决定,因而功能多样性对生态系统功能的影响大于物种多样性的影响。但在种间性状差异和物种均匀度这两个构成功能多样性的基本成分中,何者对功能多样性影响更大,并进而决定SD-FD关系尚不明确。通过在高寒矮嵩草(Kobresia humilis)草甸为期6a的刈割(留茬1 cm、3 cm及不刈割)和施肥(尿素7.5 g m~(-2)a~(-1)+磷酸二胺1.8 g m~(-2)a~(-1)、不施肥)控制实验,研究了种间性状差异(33个物种13个性状)和物种均匀度(所有物种)对物种多样性(所有物种)与功能多样性(33个物种13个性状)之间关系的影响。研究结果显示:(1)物种多样性与功能多样性正相关,它们与多性状种间差异负相关,而与物种均匀度正相关。物种均匀度是导致功能多样性变化的主要因素,也是导致SD-FD正相关的原因,这是因为随着物种多样性增加,物种均匀度的增加程度大于多性状种间差异的减少程度,因而功能多样性增加,SD-FD正相关;(2)功能多样性指数(FD_(Rao)和FDis)随物种多样性指数(H')减速递增,表明群落存在一定的功能冗余,且功能冗余随物种多样性的增大而增大,但尚未达到产生SD-FD无相关性的极限H'值;(3)功能多样性对高寒草甸生态系统地上净初级生产力(ANPP)的影响大于物种多样性的影响,二元线性回归显示在同时考虑二者对ANPP的影响时,可排除物种多样性的作用。但由于物种多样性下降或物种丧失引起的物种功能性状丢失或性状空间维度减小将导致功能多样性降低,表明它们之间存在一定互补性,在研究生物多样性与生态系统功能关系时,同时考虑物种多样性和功能多样性的影响仍十分必要。     

Ecological determinants of mating system within and between three Fagus sylvatica populations along an elevational gradient

Studies addressing the variation of mating system between plant populations rarely account for the variability of these parameters between individuals within populations, although this variability is often non‐negligible. Here, we propose a new direct method based on paternity analyses (Mixed Effect Mating Model) to estimate individual migration (m_i) and selfing rates (s_i) together with the pollen dispersal kernel. Using this method and the KINDIST approach, we investigated the variation of mating system parameters within and between three populations of Fagus sylvatica along an elevational gradient. Among the mother trees, s_i varied from 0% to 48%, m_i varied from 12% to 86% and the effective number of pollen donors (Nep_i) varied from 2 to 364. The mating patterns differed along the gradient, the top population showing higher m and lower s, and a trend to higher Nep than the bottom populations. The phenological lag shaped long‐distance pollen flow both within population (by increasing m_i at mother‐tree level) and between populations (by increasing m at high elevation). Rather than the mate density, the canopy density was detected as a major mating system determinant within population; it acted as a barrier to pollen flow, decreasing the proportion of long‐distance pollen flow and increasing s_i. Overall, the effects of ecological factors on mating system were not the same within vs. between populations across the gradient, and these factors also differed from those traditionally found to shape variation at range‐wide scale, highlighting the interest of multiscale approaches.     

Quantitative trait loci controlling water use efficiency and related traits in Quercus robur L.

Genetic variation for intrinsic water use efficiency (W _i) and related traits was estimated in a full-sib family of Quercus robur L. over 3 years. The genetic linkage map available for this F1 family was used to locate quantitative trait loci (QTL) for W _i, as estimated by leaf carbon stable isotope composition (δ ¹³C) or the ratio of net CO₂ assimilation rate (A) to stomatal conductance to water vapour (g _w) and related leaf traits. Gas exchange measurements were used to standardize estimates of A and g _w and to model the sensitivity of g _w to leaf-to-air vapour pressure deficit (sg^VPD). δ ¹³C varied by more than 3‰ among the siblings, which is equivalent to 40% variation of W _i. Most of the studied traits exhibited high clonal mean repeatabilities (>50%; proportion of clonal mean variability in global variance). Repeatabilities for δ ¹³C, leaf mass per area (LMA) and leaf nitrogen content were higher than 70%. For δ ¹³C, ten QTLs were detected, one of which was detected repeatedly for all 3 years and consistently explained more than 20% of measured variance. Four genomic regions were found in which co-localizing traits linked variation in W _i to variations in leaf chlorophyll and nitrogen content, LMA and sg^VPD. A positive correlation using clonal means between δ ¹³C and A/g _w, as well as a co-localisation of QTL detected for both traits, can be seen as validation of the theoretical model linking the genetic architecture of these two traits.     

Daily rhythmicity and hibernation in the Anatolian ground squirrel under natural and laboratory conditions

We studied daily rhythmicity of body temperature (T _b) before and during hibernation in Anatolian ground squirrels (Spermophilus xanthoprymnus) under natural and laboratory conditions using surgically implanted temperature loggers. Under both conditions, robust daily T _b rhythmicity with parameters comparable to those of other ground squirrel species was observed before but not during hibernation. Euthermic animals had robust daily T _b rhythms with a mean of 37.0°C and a range of excursion of approximately 4°C. No T _b rhythm was detected during torpor bouts, either because T _b rhythmicity was absent or because the daily range of excursion was smaller than 0.2°C. The general patterns of hibernation that we observed in Anatolian ground squirrels were similar to those previously observed by other investigators in other species of ground squirrels.     

Some Simple Statistics to Test Against Ordered Alternatives in Complete Block Designs

Consider testing the hypothesis of no treatment effects against a postulated ranking of the m treatments, given data from n Complete Blocks. A suitable test statistic is the weighted average rank correlation w = σb_QiC_i where C_i is the correlation between the postulated ranking and the ranking observed within the ith block, Q_i is the rank of the ith block with respect to credibility, and the b_i's are weights such that 0 ≦ b¹ ≦ … ≦ bn. In this paper we introduce some simple statistics: the first extends the signed-rank statistic to m ≦ 3, the second uses a simple measure of correlation based on the antirank, and the third a statistic based on Spearman's footrule. Tables for critical values are provided and the normal approximation is investigated.     

The size distribution of insertions and deletions in human and rodent pseudogenes suggests the logarithmic gap penalty for sequence alignment

The size distributions of deletions, insertions, and indels (i.e., insertions or deletions) were studied, using 78 human processed pseudogenes and other published data sets. The following results were obtained: (1) Deletions occur more frequently than do insertions in sequence evolution; none of the pseudogenes studied shows significantly more insertions than deletions. (2) Empirically, the size distributions of deletions, insertions, and indels can be described well by a power law, i.e., f _k = Ck ^–b , where f _k is the frequency of deletion, insertion, or indel with gap length k, b is the power parameter, and C is the normalization factor. (3) The estimates of b for deletions and insertions from the same data set are approximately equal to each other, indicating that the size distributions for deletions and insertions are approximately identical. (4) The variation in the estimates of b among various data sets is small, indicating that the effect of local structure exists but only plays a secondary role in the size distribution of deletions and insertions. (5) The linear gap penalty, which is most commonly used in sequence alignment, is not supported by our analysis; rather, the power law for the size distribution of indels suggests that an appropriate gap penalty is w _k = a + b ln k, where a is the gap creation cost and blnk is the gap extension cost. (6) The higher frequency of deletion over insertion suggests that the gap creation cost of insertion (a _i ) should be larger than that of deletion (a _d ); that is, a _i – a _d = In R, where R is the frequency ratio of deletions to insertions. Correspondence to: W.-H. Li