Convergence to equilibrium in a genetic model with differential viability between the sexes

A single locus, diallelic selection model with female and male viability differences is studied. If the variables are ratios of allele frequencies in each sex, a 2-dimensional difference equation describes the model. Because of the strong monotonicity of the resulting map, every initial genotypic structure converges to an equilibrium structure assuming that no equilibrium has eigenvalues on the unit circle.Partially supported by funds provided by a Science and Education Grant to the USDA-Forest Service, Southeastern Forest Experiment Station, Population Genetics of Forest Trees Research Unit, Raleigh, USASupported by a grant from the Max Kade Foundation, New York, USA     

To identify impacts in variable systems using anomalous changes: a salt marsh example

A method is proposed to identify impacts of habitat modification in cases where it is difficult to site experimental and control samples. This problem occurs especially in heterogeneous systems, but may pose difficulties in any field experimental situation. The method is relevant to the situation where treated (modified) and untreated sites are spread over a range of habitat types. Types of change are identified and compared to treatments. If a specific change type is associated with a particular treatment then it is likely that the change is causally related to the treatment. There are five stages in the analysis. First, the classes or states of the sample sites, over a period of time, are identified (by numerical classification). Second, for each sample site, the sequence of states is listed. Third, transition matrices are made for each sample site to show the changes which have occurred. Fourth, the transition matrices are classified, to identify types of change. Finally, we use the Chisquared test to indicate whether the treated and untreated sites are associated with particular types of change. As an example, we refer to habitat modification to manage salt-marsh mosquitoes and we evaluate impacts on the environment mainly through changes to the vegetation. We consider that the method has potential to identify changes in heterogeneous systems even though little change was identified in the particular salt marsh studied.     

鳗鲡幼鱼耳石日轮的研究

本文报道采自辽东半岛沿岸鳗鲡(Anguilla japonica)的白仔鳗和经人工培育的当年幼鳗耳石日轮生长的观察结果。白仔鳗和幼鳗耳石平均直径均与体全长成直线相关。12尾白仔鳗耳石的平均日轮数146.3,据此推测其产卵期为11—12月。观察证实从咸淡水转人到淡水生活的幼鳗耳石的环纹有过渡带存在。     

Vegetation succession on the dunes near Oostvoorne,The Netherlands,since 1934, interpreted from air photographs and vegetation maps

The vegetation succession on the dunes near Oostvoorne, The Netherlands has been followed by means of a novel combination of repeated large-scale vegetation mapping and air photograph interpretation. Vegetation units have been discerned on the formation level because these could be distinguished fairly easily on the photographs and because the rates of change are appropriate to the time interval chosen. Nineteen formations were distinguished. Five 1:6250 maps were constructed, reflecting the formation pattern in 1934, 1943, 1959, 1972 and 1980. An overlay with 2736 grid points at 25 m field distance was used to quantify changes in the formation pattern.The results suggest a pronounced multiple pathway succession with nevertheless three principal trajectories of succession from pioneer to woodland vegetation. The outer dunes, which have originated since 1910, are distinct in successional characteristics from the inner dunes, which already existed but were released from heavy grazing pressure in 1910. The rate of change in the outer dunes was high in the beginning and is slowly decreasing eversince. In the inner dunes it went the other way around. Through visual extrapolation the likely formation patterns in 1910 and in 2000 were estimated.Transition frequencies proved highly variable for most formations. Moreover, strong spatial dependence was found. Limitations in the use of Markov models in cases of long-term succession in heterogeneous environments are discussed.Nomenclature follows the same sources as in van der Maarel et al. (1984).Field work carried out 1980–1981 when the authors were at the Division of Geobotany, University of Nijmegen. We thank Jos Rijntjes, Nijmegen, for his cooperation in the field. Vegetation maps were prepared and calculations performed at Uppsala. We thank the Foundation Het Zuid-Hollands Landschap, Rotterdam, for providing facilities and a grant for fieldwork as well as additional means to reproduce the vegetation maps. Two reviewers gave useful comments.     

A method for studying vegetation dynamics when there are no obvious individuals: Virtual-population analysis applied to the tundra shrub Betula nana L.

A method is presented to study dynamics of plants that cannot be separated into individuals such as many grassland, salt marsh and tundra species. A virtual population is created by using a permanent transect line through the vegetation and individuals are defined as the branch segments distal to the intercept with the transect line. Addition and loss of individuals together with growth or shrinkage form the basis for constructing a size-structured transition matrix. A discrete-event simulation demonstrates that: 1) a virtual population of individuals grows at the same rate as the parent population; and, 2) size-structured transition matrices for a virtual population and parent vegetation have similar dominant and subdominant eigenvalues so a virtual population can be used to describe the dynamics of a parent vegetation.Dwarf birch, Betula nana L., was studied in the northern foothills of the Brooks Range, Alaska, by using photography to record branch intercepts along permanent transect lines. The distal branch segments constitute a virtual population of the parent vegetation. Transects were photographed in 1985 and again in 1986 and changes of branch segments were used to construct two transition matrices for shrubs with and without elevated fertilizer treatment. Analysis of the virtual populations suggests that although Betula nana may show increased branch growth with increased fertilizer, in the long run this shrub may decline in the tundra in response to such treatment.     

水稻伸长生长的数学模型

水稻地上部诸器官的伸长生长,可以分为3个阶段和两个过渡期．器官在前期的凹型曲线生长为加速生长（定为第1阶段）,中期的直线生长为等速生长（第2阶段）,后期的凸型曲线生长为减速生长（第3阶段）;每两个阶段临界处均存在特殊的生长过程,前面的定为第1过渡期,做变加速生长,后面的定为第2过渡期,做变减速生长.组成器官的各个细胞的伸长生长,也可以分为前期凹型曲线阶段、中期的直线阶段以及这两个阶段临界处的过渡期.运用类比原理推断;细胞在凹型曲线阶段,其原生质的膨压大于壁压,而且这两个压差始终维持稳定,这就使细胞做等加速生长;细胞经过过渡期的变加速生长过渡到直线生长阶段,在这个阶段中,膨压大小与壁压相等,这就使细胞以过渡期最末的生长速度做等速生长;最后壁压大于膨压,而且这两个相差压会阻止细胞的“惯性”生长直至停止生长,其结果产生减速生长．     

Unbiased estimation of the rates of synonymous and nonsynonymous substitution

Summary The current convention in estimating the number of substitutions per synonymous site (K _S ) and per nonsynonymous site (K _A ) between two protein-coding genes is to count each twofold degenerate site as one-third synonymous and two-thirds nonsynonymous because one of the three possible changes at such a site is synonymous and the other two are nonsynonymous. This counting rule can considerably overestimate theK _S value because transitional mutations tend to occur more often than transversional mutations and because most transitional mutations at twofold degenerate sites are synonymous. A new method that gives unbiased estimates is proposed. An application of the new and the old method to 14 pairs of mouse and rat genes shows that the new method gives aK _S value very close to the number of substitutions per fourfold degenerate site whereas the old method gives a value 30% higher. Both methods give aK _A value close to the number of substitutions per nondegenerate site.     

Formation of dioxygen complexes of transition metal chelates in oxygen saturated aprotic solvents. Cyclic voltammetric evidence at a micro glassy carbon disk electrode

Cyclic voltammetry at a micro electrode of Co(II) salen, Fe(II) salen, electrode generated Fe(II)(acac)₂, Fe(II) (salicylaldehyde)₂, Fe(II) (salicylaldoxime)₂, Fe(II) (bipy)₃, Fe(II) (bipy)₂, Co(II) (bipy)₃, Co(II) (benzacac)₂, and electrode generated Co(acac)₂ in oxygen saturated aprotic solvents show positive shift of the O₂ sigmoidal wave, as well as enhancement of the limiting current in the case of the first five compounds. In the case of Co(II) (bipy)₃ the slope of the sigmoidal wave due to O₂ becomes more positive, while for the other two Co(II) complexes there is no change except a small decrease in the wave height. The data are used to correlate and predict the O₂ binding properties of the chelates in solution. The data for the diketone complexes of Co(II) indicate absence of any direct association, which is in line with the interpretation offered in the literature on the mechanism of their catalytic role in the O₂ oxidation of substrates. The mechanism of the autoxidation of dimethylformamide in the presence of Fe(III) (bipy)₃ and Cu(II) (bipy)₂ is elucidated by the observation that these higher valent compounds are reduced to their next lower oxidation state by DMF.     

Synonymous substitution rates in Drosophila: Mitochondrial versus nuclear genes

Synonymous substitution rates in mitochondrial and nuclear genes of Drosophila were compared. To make accurate comparisons, we considered the following: (1) relative synonymous rates, which do not require divergence time estimates, should be used; (2) methods estimating divergence should take into account base composition; (3) only very closely related species should be used to avoid effects of saturation; (4) the heterogeneity of rates should be examined. We modified the methods estimating synonymous substitution numbers to account for base composition bias. By using these methods, we found that mitochondrial genes have 1.7–3.4 times higher synonymous substitution rates than the fastest nuclear genes or 4.5–9.0 times higher rates than the average nuclear genes. The average rate of synonymous transversions was 2.7 (estimated from the melanogaster species subgroup) or 2.9 (estimated from the obscura group) times higher in mitochondrial genes than in nuclear genes. Synonymous transversions in mitochondrial genes occurred at an approximately equivalent rate to those in the fastest nuclear genes. This last result is not consistent with the hypothesis that the difference in turnover rates between mitochondrial and nuclear genomes is the major factor determining higher synonymous substitution rates in mtDNA. We conclude that the difference in synonymous substitution rates is due to a combination of two factors: a higher transitional mutation rate in mtDNA and constraints on nuclear genes due to selection for codon usage. Received: 27 November 1996 / Accepted: 8 May 1997     

Temperature response of the cell cycle of Haplopappus gracilis in suspension culture and its significance to the G1 transition probability model

The effects of temperature on the cell cycle of Haplopappus gracilis suspension cultures were analysed by the fraction of labelled mitoses method. Sphase in these cultures shows a different temperature optimum as compared to optima derived for G₂ and mitosis. G₁ phase has a much lower Q₁₀ than the other cell cycle phases and shows no temperature optimum between 22 and 34° C. These results are discussed in relation to a transition probability model of the cell cycle proposed by Smith and Martin (Proc. Natl. Acad. Sci. USA 70, 1263–1267, 1973), in which each cell has a time independent probability of initiating the transition into another round of DNA replication and division. The implications of such a model for cell cycle analysis are discussed and a tentative model for a probabilistic transition trigger is advanced.Abbreviations FLM Fraction of labelled mitoses - T_B Total B-phase