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Fitness Landscape
706
Fitness Landscape
parasites and epidemics; on the other hand, a population depleted of individuals may suffer collapse and extinction. I have argued (Krimbas, 1984) that according to the `Red Queen hypothesis' of Van Valen, all populations (at least of the same species) seem to have, a priori, the same probability of extinction, and thus possess, a priori, the same long-term population fitness. In addition, it is not clear enough how we should consider a group: a group is not an organism that survives and reproduces. Although individuals of the group interact in complex ways and thus provide some image of cohesion, the `individuality' of the groups seems most of the time to be quite a loose subject. Should we consider group extinction per unit of time to determine group fitness? What about group multiplication? In order to achieve a model in group selection cases, one may resort to different population selective coefficients, or population adaptive coefficients (something related to the population fitness). In these cases, the search for the nature of population fitness becomes even more elusive. As a result, population fitness is a parameter useful exclusively for its expediency; no search for its hidden nature is justified.
References
Brandon RN (1990) Adaptation and Environment. Princeton, NJ: Princeton University Press. Gillois M (1996) Fitness. In Tort P (ed.) Dictionnaire du Darwinisme et de l'Evolution, vol. 2, 1676±1688. Paris: Presses Universitaires de France. Hartl DL and Clark AG (1989) Principles of Population Genetics, 2nd edn. Sunderland, MA: Sinauer Associates. Krimbas CB (1984) On adaptation, neo-Darwinian tautology, and population fitness. Evolutionary Biology 17: 1± 57. Lewontin RC (1965) Selection for colonizing ability. In: Baker HG and Stebbins GL (eds) The Genetics of Colonizing Species, 77±94. New York: Columbia University Press. Paul D (1992) Fitness: historical perspectives. In: Fox Keller E and Lloyd EA (eds) Keywords in Evolutionary Biology, 112±114. Cambridge, MA: Harvard University Press.
are gene (or sometimes genotype) frequencies. It is usually pictured in three dimensions, but conceptually can involve a larger number. In some models it has an exact mathematical meaning, in others it is employed as a metaphor. The idea of an adaptive surface was introduced by Sewall Wright. He thought of a surface on which each point on the surface corresponded to a combination of allele frequencies on the abscissae. Figure 1 shows a simple two-locus example. Random mating proportions and linkage equilibrium are assumed. The two abscissae are the frequencies of the dominant A and B alleles. The relative genotype fitnesses of aa bb, A bb, aa B , and A B are 1, 1 s, 1 s, and 1 t, where s and t are both positive and A (or B ) indicates that the second allele can be either A or a (or B or b). The ordinate represents the average fitness of a population with particular allele frequencies. There are two peaks, one when the genotype AA BB is fixed, the other a lower peak for the genotype aa bb. Genotypes AA bb and aa BB are at the other two corners and are least fit. Ordinarily a population, located at a point on the surface, climbs the nearest peak, but not necessarily in a straight line. The complications of mutation, linkage, and epistasis may cause the path upward to be circuitous. And, as these complications are introduced, along with more loci, the mathematics becomes more difficult. This is the situation envisioned by Sewall Wright. A population cannot change from the lower peak to the higher one, because it has to pass through a less fit region. It was this dilemma that led Wright to propose his shifting-balance theory whereby a combination of random drift and differential migration make it possible to cross the valley and reach a higher peak. Wright regarded the fitness surface more as a 1+t
1
Fitness Landscape
fitness
See also: Adaptive Landscapes; Darwin, Charles; Fitness Landscape; Natural Selection
J F Crow AA bb
Copyright ß 2001 Academic Press doi: 10.1006/rwgn.2001.0461
AA BB
1−s aa bb
A fitness landscape, or adaptive surface, is a geometrical construct in which the fitness or adaptive value of a genotype is the ordinate and the two abscissae
%A %B
Figure 1
aa BB
Example of a fitness landscape, with two loci.
Fix Ge n es 707 metaphor than as a mathematical model. As a result his papers present different, often confusing concepts. Sometimes the abscissae are allele frequencies, sometimes they are genotype frequencies, and sometimes phenotypes. How rugged the fitness surface is has been a matter of continual discussion since Wright first introduced his ideas in the 1930s. Wright thought of the multidimensional surface as quite rugged, with numerous peaks and valleys. Others, R. A. Fisher in particular, have suggested that the surface is more like an ocean with undulating wave patterns. Furthermore, as the number of dimensions increases, only a small fraction of the stationary points are maxima. A population is much more likely to be on a ridge than on a peak. The debate was not settled while Wright was alive and still continues. Wright summarized his lifetime view of the subject in a paper entitled ``Surfaces of selective value revisited,'' published in 1988, shortly before his death (Wright, 1988). Although Wright, more than anyone else, was responsible for introducing random processes into population genetic theory, he never attempted to model the whole shifting-balance process stochastically. Recently there has been considerable mathematical work in this area, partly as a way of developing and testing Wright's theory. The entire process has been treated stochastically, something that was missing in Wright's formulations. The landscape idea has been extended to concepts other than fitness, such as developmental morphology and protein structure. The ruggedness of the landscape determines whether orderly change is possible or whether alternatives, such as stasis or chaos, emerge. In evolution, the lower the peaks and the higher the valleys, the more likely it is that selection can carry a population, if not to the highest peak, at least to one that has a respectable fitness. Similar considerations apply to the study of morphological development in the presence of various constraints. The ruggedness of the landscape can be deduced from parameters, such as the number of factors involved, and especially the degree to which they are coupled, or in genetic terms, the degree of epistasis.
Further Reading
Kaufmann SA (1993) The Origins of Order. Oxford: Oxford University Press. Provine WB (1986) Sewall Wright and Evolutionary Biology. Chicago, IL: University of Chicago Press.
Reference
Wright S (1988) Surfaces of selective value revisited. American Naturalist 131: 115±123.
See also: Fisher, R.A.; Fitness; Wright, Sewall
Fix Genes J Vanderleyden, A Van Dommelen, and J Michiels Copyright ß 2001 Academic Press doi: 10.1006/rwgn.2001.1637
The process of biological nitrogen fixation is an extremely energy-demanding process requiring, under ideal conditions, approximately 16 moles of ATP per mole of N2 fixed. The property of reducing atmospheric dinitrogen to ammonia is found among a wide variety of free-living, associative, and strictly symbiotic bacteria. The genetics of nitrogen fixation were initiated in the free-living diazotroph Klebsiella pneumoniae. This analysis led to the identification of 20 nif (for nitrogen fixation) genes. The identification of these nif genes has substantially facilitated the study of nitrogen fixation in other prokaryotes such as Sinorhizobium meliloti (formerly Rhizobium meliloti) and Bradyrhizobium japonicum in identifying genes that are both structurally and functionally equivalent to K. pneumoniae nif genes, including nifHDK, nifA, nifB, nifE, nifN, nifS, nifW, and nifX. In addition, in these organisms, genes essential for nitrogen fixation were identified for which no homologs are present in K. pneumoniae. These were named fix genes and are often clustered with nif genes or regulated coordinately. Table 1 summarizes the properties and functions of fix genes.
Regulation of Nitrogen Fixation Owing to the extreme oxygen sensitivity of the nitrogenase enzyme, a major trigger for nif and fix gene expression in all systems studied so far is low oxygen tension. For instance, in the legume nodule, the dissolved oxygen concentration is 10±30 mmol l 1, creating a hypoxic environment. Conversely, all nitrogen-fixing bacteria deploy a complex regulatory cascade preventing aerobic expression of nif and fix genes. In addition, the deprivation of fixed nitrogen also controls the process of nitrogen fixation in freeliving fixers but not in symbiotic bacteria (except Azorhizobium caulinodans). Many, but not all, nif and fix genes including the nitrogenase structural genes and accessory functions are preceded by a characteristic type of promoter, the 24/ 12 promoter, recognized by the alternative sigma factor s54 (or RpoN). Activation of this promoter requires the presence of an activator protein, i.e., the nitrogen regulatory protein NtrC or the nitrogen fixation regulatory protein NifA. While NtrC regulates gene expression in response to the nitrogen status, NifA
Fitness Landscape
parasites and epidemics; on the other hand, a population depleted of individuals may suffer collapse and extinction. I have argued (Krimbas, 1984) that according to the `Red Queen hypothesis' of Van Valen, all populations (at least of the same species) seem to have, a priori, the same probability of extinction, and thus possess, a priori, the same long-term population fitness. In addition, it is not clear enough how we should consider a group: a group is not an organism that survives and reproduces. Although individuals of the group interact in complex ways and thus provide some image of cohesion, the `individuality' of the groups seems most of the time to be quite a loose subject. Should we consider group extinction per unit of time to determine group fitness? What about group multiplication? In order to achieve a model in group selection cases, one may resort to different population selective coefficients, or population adaptive coefficients (something related to the population fitness). In these cases, the search for the nature of population fitness becomes even more elusive. As a result, population fitness is a parameter useful exclusively for its expediency; no search for its hidden nature is justified.
References
Brandon RN (1990) Adaptation and Environment. Princeton, NJ: Princeton University Press. Gillois M (1996) Fitness. In Tort P (ed.) Dictionnaire du Darwinisme et de l'Evolution, vol. 2, 1676±1688. Paris: Presses Universitaires de France. Hartl DL and Clark AG (1989) Principles of Population Genetics, 2nd edn. Sunderland, MA: Sinauer Associates. Krimbas CB (1984) On adaptation, neo-Darwinian tautology, and population fitness. Evolutionary Biology 17: 1± 57. Lewontin RC (1965) Selection for colonizing ability. In: Baker HG and Stebbins GL (eds) The Genetics of Colonizing Species, 77±94. New York: Columbia University Press. Paul D (1992) Fitness: historical perspectives. In: Fox Keller E and Lloyd EA (eds) Keywords in Evolutionary Biology, 112±114. Cambridge, MA: Harvard University Press.
are gene (or sometimes genotype) frequencies. It is usually pictured in three dimensions, but conceptually can involve a larger number. In some models it has an exact mathematical meaning, in others it is employed as a metaphor. The idea of an adaptive surface was introduced by Sewall Wright. He thought of a surface on which each point on the surface corresponded to a combination of allele frequencies on the abscissae. Figure 1 shows a simple two-locus example. Random mating proportions and linkage equilibrium are assumed. The two abscissae are the frequencies of the dominant A and B alleles. The relative genotype fitnesses of aa bb, A bb, aa B , and A B are 1, 1 s, 1 s, and 1 t, where s and t are both positive and A (or B ) indicates that the second allele can be either A or a (or B or b). The ordinate represents the average fitness of a population with particular allele frequencies. There are two peaks, one when the genotype AA BB is fixed, the other a lower peak for the genotype aa bb. Genotypes AA bb and aa BB are at the other two corners and are least fit. Ordinarily a population, located at a point on the surface, climbs the nearest peak, but not necessarily in a straight line. The complications of mutation, linkage, and epistasis may cause the path upward to be circuitous. And, as these complications are introduced, along with more loci, the mathematics becomes more difficult. This is the situation envisioned by Sewall Wright. A population cannot change from the lower peak to the higher one, because it has to pass through a less fit region. It was this dilemma that led Wright to propose his shifting-balance theory whereby a combination of random drift and differential migration make it possible to cross the valley and reach a higher peak. Wright regarded the fitness surface more as a 1+t
1
Fitness Landscape
fitness
See also: Adaptive Landscapes; Darwin, Charles; Fitness Landscape; Natural Selection
J F Crow AA bb
Copyright ß 2001 Academic Press doi: 10.1006/rwgn.2001.0461
AA BB
1−s aa bb
A fitness landscape, or adaptive surface, is a geometrical construct in which the fitness or adaptive value of a genotype is the ordinate and the two abscissae
%A %B
Figure 1
aa BB
Example of a fitness landscape, with two loci.
Fix Ge n es 707 metaphor than as a mathematical model. As a result his papers present different, often confusing concepts. Sometimes the abscissae are allele frequencies, sometimes they are genotype frequencies, and sometimes phenotypes. How rugged the fitness surface is has been a matter of continual discussion since Wright first introduced his ideas in the 1930s. Wright thought of the multidimensional surface as quite rugged, with numerous peaks and valleys. Others, R. A. Fisher in particular, have suggested that the surface is more like an ocean with undulating wave patterns. Furthermore, as the number of dimensions increases, only a small fraction of the stationary points are maxima. A population is much more likely to be on a ridge than on a peak. The debate was not settled while Wright was alive and still continues. Wright summarized his lifetime view of the subject in a paper entitled ``Surfaces of selective value revisited,'' published in 1988, shortly before his death (Wright, 1988). Although Wright, more than anyone else, was responsible for introducing random processes into population genetic theory, he never attempted to model the whole shifting-balance process stochastically. Recently there has been considerable mathematical work in this area, partly as a way of developing and testing Wright's theory. The entire process has been treated stochastically, something that was missing in Wright's formulations. The landscape idea has been extended to concepts other than fitness, such as developmental morphology and protein structure. The ruggedness of the landscape determines whether orderly change is possible or whether alternatives, such as stasis or chaos, emerge. In evolution, the lower the peaks and the higher the valleys, the more likely it is that selection can carry a population, if not to the highest peak, at least to one that has a respectable fitness. Similar considerations apply to the study of morphological development in the presence of various constraints. The ruggedness of the landscape can be deduced from parameters, such as the number of factors involved, and especially the degree to which they are coupled, or in genetic terms, the degree of epistasis.
Further Reading
Kaufmann SA (1993) The Origins of Order. Oxford: Oxford University Press. Provine WB (1986) Sewall Wright and Evolutionary Biology. Chicago, IL: University of Chicago Press.
Reference
Wright S (1988) Surfaces of selective value revisited. American Naturalist 131: 115±123.
See also: Fisher, R.A.; Fitness; Wright, Sewall
Fix Genes J Vanderleyden, A Van Dommelen, and J Michiels Copyright ß 2001 Academic Press doi: 10.1006/rwgn.2001.1637
The process of biological nitrogen fixation is an extremely energy-demanding process requiring, under ideal conditions, approximately 16 moles of ATP per mole of N2 fixed. The property of reducing atmospheric dinitrogen to ammonia is found among a wide variety of free-living, associative, and strictly symbiotic bacteria. The genetics of nitrogen fixation were initiated in the free-living diazotroph Klebsiella pneumoniae. This analysis led to the identification of 20 nif (for nitrogen fixation) genes. The identification of these nif genes has substantially facilitated the study of nitrogen fixation in other prokaryotes such as Sinorhizobium meliloti (formerly Rhizobium meliloti) and Bradyrhizobium japonicum in identifying genes that are both structurally and functionally equivalent to K. pneumoniae nif genes, including nifHDK, nifA, nifB, nifE, nifN, nifS, nifW, and nifX. In addition, in these organisms, genes essential for nitrogen fixation were identified for which no homologs are present in K. pneumoniae. These were named fix genes and are often clustered with nif genes or regulated coordinately. Table 1 summarizes the properties and functions of fix genes.
Regulation of Nitrogen Fixation Owing to the extreme oxygen sensitivity of the nitrogenase enzyme, a major trigger for nif and fix gene expression in all systems studied so far is low oxygen tension. For instance, in the legume nodule, the dissolved oxygen concentration is 10±30 mmol l 1, creating a hypoxic environment. Conversely, all nitrogen-fixing bacteria deploy a complex regulatory cascade preventing aerobic expression of nif and fix genes. In addition, the deprivation of fixed nitrogen also controls the process of nitrogen fixation in freeliving fixers but not in symbiotic bacteria (except Azorhizobium caulinodans). Many, but not all, nif and fix genes including the nitrogenase structural genes and accessory functions are preceded by a characteristic type of promoter, the 24/ 12 promoter, recognized by the alternative sigma factor s54 (or RpoN). Activation of this promoter requires the presence of an activator protein, i.e., the nitrogen regulatory protein NtrC or the nitrogen fixation regulatory protein NifA. While NtrC regulates gene expression in response to the nitrogen status, NifA