Disease resistance is an extremely valuable control measure of rusts in cereal crops and is based, almost entirely, on simple procedures of identification and incorporation of major genes for resistance into economic varieties. Usually, several loci that carry these genes are known in each plant species. Frequently, several alleles at a locus can be distinguished on the basis of their reaction to various races of the pathogen. In spite of the vast array of resistance genes now known, their use has been sharply limited by the restricted number of loci in each species. The result has been a never-ending cycle of (1) releasing a variety resistant to prevalent races, (2) finding it susceptible to new races of the pathogen appearing a few years later, (3) breeding resistance to the new races, and (4) releasing the new variety only to find it susceptible, a few years later, to yet new races of the pathogen. Thus, breeding for rust resistance in cereals has been so repetitious that the value and use in disease control of genes that condition resistance to only a portion of the possible rust races is now widely questioned.' Although major genes for rust resistance have been used extensively, little is known about their fine structure. This is probably due to the fact that in crops, where resistance genes have been of maximum importance, genetic analyses requiring large test-cross progenies are not feasible. Economic and biological considerations, however, provide compelling reasons why studies on the structure of genes for rust resistance should be made. The system of genetic resistance to rust, Puccinia sorghi Schw., in maize, Zea mays L., is apparently parallel to that found in other cereal crops. In maize, there are at least five loci (Rpl, Rp3, Rp4, Rp5, and Rp6) at which dominant genes for rust resistance occur.2-6 Rp, is located in the short arm of chromosome 10 and was considered to occupy the terminal position on the genetic map.3'7 Recently, Rpi has been shown to be located between Rp5 and Rpe which are 1.1 and 2.1 map units, respectively, from it.' Orientation of these genes with respect to the centromere is not known. Rp3 and Rp4 are independent of Rpi. On the basis of genetic studies and disease reaction, 14 alleles, Rpia, Rp b... to
In maize (Zea mays L.) Rp3 expresses itself as a dominant gene for resistance to Puccinia sorghi Schw. culture 90laba and as a recessive gene for resistance to culture 933a. Suspecting that Rp3 is a complex locus consisting of two closely linked genes, efforts were made to separate the two putative genes by crossing over. Maize lines heterozygous for resistance and glossy leaf genes (Rp3 - Gl6/rp3 - gl6) were crossed with inbreds homozygous for susceptibility and glossy leaves (rp3 - gl6/rp3 - gl6). The testcross progeny, consisting of 4802 seedlings, was tested with culture 90laba. Fifty-seven recombinant seedlings, resistant to culture 90laba and glossy, were isolated and grown to maturity. These were selfed and their progeny tested to identify those that may have arisen from crossing over within region Rp3. No recombinants of this nature were found. If Rp3 is a complex locus, the two genes comprising it could not be more than 0.06 map units apart.
1577which differs from the linear solution found by LR [their Eq. (C19)] in that the exponential streaming operator contains the full, field-dependent Hamilton operator 8+ (E/M) &/&V instead of the fieldfree operator. Note also that we have not used the scaled velocity variable Vy ' here as we are not interested in a y expansion, but rather an exact result for the model. For the full streaming operator we find that where f'(") ., &v E) 0 1 y2m4 Q)g 2 1+ (~~)'The second equation above follows from the first and (5) after an integration by parts (or change of variable). Rearranging terms in (7) we then find that + y~m*E(S= sin~s), (6)where the reduced mass m~, and are identical to thequantities defined in LR [note (C22) has a, mis-printt], m*= (1+ y')-'~=~, (1+ y')'" Since the full streaming operator which appears in (5) does not commute with po the integral equation for f becomes considerably less tractable than the corresponding linear equation, and it is no longer practical to attempt to solve directly for this quantity. However, the steady-state current can be calculated fairly directly j= dVdHdv'dr Vp,d VdRdvd r x dt exp t H+ ----V which is identical to the linear result which one obtains from the results of LB when these are expressed in terms of the physical velocity V [cf.(C24)].The result that there is no nonlinear, response in the quasistochastic model is instructive in that it indicates that the transport coefficients associated with this current cannot be expressed solely in terms of functions of the linear-transport coefficient, i. e. , the friction coefficient, but depend on higher-order correlation functions, which vanish for this model. This conclusion could not have been made on the basis of the linear results found previously from the dynamical theory.Finally, it is interesting to note that the same "solution technique" used in this paper can be used to obtain exact solutions for some other nonequilibrium problems, e. g. , the nonlinear heat flow in a linear harmonic chain. We are currently carrying out the computations for this problem.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.