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In
evolutionary biology Evolutionary biology is the subfield of biology Biology is the natural science that studies life and living organisms, including their anatomy, physical structure, Biochemistry, chemical processes, Molecular biology, molecular interacti ...
, fitness landscapes or adaptive landscapes (types of
evolutionary landscape An evolutionary landscape is a metaphorWright, Sewall (1932) The Roles of Mutation, Inbreeding, Crossbreeding, and Selection in Evolution. ''Proceedings of the Sixth International Congress of Genetics'' 1: 356–366 or a construct used to think abou ...
s) are used to visualize the relationship between
genotype The genotype of an organism is its complete set of genetic material. Genotype can also be used to refer to the or variants an individual carries in a particular gene or genetic location. The number of alleles an individual can have in a specific ...
s and
reproductive success Reproductive success is an individual's production of offspring per breeding event or lifetime. This is not limited by the number of offspring produced by one individual, but also the reproductive success of these offspring themselves. Reproductive ...
. It is assumed that every
genotype The genotype of an organism is its complete set of genetic material. Genotype can also be used to refer to the or variants an individual carries in a particular gene or genetic location. The number of alleles an individual can have in a specific ...
has a well-defined replication rate (often referred to as fitness). This fitness is the "height" of the landscape. Genotypes which are similar are said to be "close" to each other, while those that are very different are "far" from each other. The set of all possible genotypes, their degree of similarity, and their related fitness values is then called a fitness landscape. The idea of a fitness landscape is a metaphor to help explain flawed forms in evolution by
natural selection Natural selection is the differential survival and reproduction of individuals due to differences in phenotype right , Here the relation between genotype and phenotype is illustrated, using a Punnett square, for the character of peta ...
, including exploits and glitches in animals like their reactions to supernormal stimuli. The idea of studying evolution by visualizing the distribution of fitness values as a kind of landscape was first introduced by
Sewall Wright Sewall Green Wright FRS(For) H FRSE (December 21, 1889March 3, 1988) was an American geneticist known for his influential work on evolutionary theory Evolutionary thought, the recognition that species change over time and the perceived unde ...

Sewall Wright
in 1932. In
evolutionary optimization
evolutionary optimization
problems, fitness landscapes are evaluations of a
fitness function{{no footnotes, date=May 2015 A fitness function is a particular type of objective function that is used to summarise, as a single figure of merit, how close a given design solution is to achieving the set aims. Fitness functions are used in genetic ...
for all candidate solutions (see below).


In biology

In all fitness landscapes, height represents and is a visual metaphor for fitness. There are three distinct ways of characterizing the other dimensions, though in each case distance represents and is a metaphor for degree of dissimilarity. Fitness landscapes are often conceived of as ranges of mountains. There exist local peaks (points from which all paths are downhill, i.e. to lower fitness) and valleys (regions from which many paths lead uphill). A fitness landscape with many local peaks surrounded by deep valleys is called rugged. If all
genotype The genotype of an organism is its complete set of genetic material. Genotype can also be used to refer to the or variants an individual carries in a particular gene or genetic location. The number of alleles an individual can have in a specific ...
s have the same replication rate, on the other hand, a fitness landscape is said to be flat. An evolving
population Population typically refers the number of people in a single area whether it be a city or town, region, country, or the world. Governments typically quantify the size of the resident population within their jurisdiction by a process called a ...

population
typically climbs uphill in the fitness landscape, by a series of small genetic changes, until – in the infinite time limit – a local optimum is reached. Note that a local optimum cannot always be found even in evolutionary time: if the local optimum can be found in a reasonable amount of time then the fitness landscape is called "easy" and if the time required is exponential then the fitness landscape is called "hard". Hard landscapes are characterized by the maze-like property by which an allele that was once beneficial becomes deleterious, forcing evolution to backtrack. However, the presence of the maze-like property in biophysically inspired fitness landscapes may not be sufficient to generate a hard landscape.


Genotype to fitness landscapes

Wright visualized a genotype space as a
hypercube In geometry Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position of ...

hypercube
. No continuous genotype "dimension" is defined. Instead, a network of genotypes are connected via mutational paths.
Stuart Kauffman Stuart Alan Kauffman (born September 28, 1939) is an American medical doctor, theoretical biologist Mathematical and theoretical biology or, Biomathematics, is a branch of biology Biology is the natural science that studies life and livin ...

Stuart Kauffman
's
NK model The NK model is a mathematical model A mathematical model is a description of a system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surround ...
falls into this category of fitness landscape. Newer network analysis techniques such as selection-weighted attraction graphing (SWAG) also use a dimensionless genotype space.


Allele frequency to fitness landscapes

Wright's mathematical work described fitness as a function of allele frequencies. Here, each dimension describes an allele frequency at a different gene, and goes between 0 and 1.


Phenotype to fitness landscapes

In the third kind of fitness landscape, each dimension represents a different phenotypic trait. Under the assumptions of quantitative genetics, these phenotypic dimensions can be mapped onto genotypes. See the visualizations below for examples of phenotype to fitness landscapes.


In evolutionary optimization

Apart from the field of evolutionary biology, the concept of a fitness landscape has also gained importance in methods such as
genetic algorithm In computer science Computer science deals with the theoretical foundations of information, algorithms and the architectures of its computation as well as practical techniques for their application. Computer science is the study of c ...

genetic algorithm
s or
evolution strategies In computer science, an evolution strategy (ES) is an optimization (mathematics), optimization technique based on ideas of evolution. It belongs to the general class of evolutionary computation or artificial evolution methodologies. History The 'ev ...
. In evolutionary optimization, one tries to solve real-world problems (e.g.,
engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more speciali ...

engineering
or
logistics Logistics is generally the detailed organization and implementation of a complex operation. In a general business sense, logistics is the management of the flow of things between the point of origin and the point of consumption to meet the requ ...

logistics
problems) by imitating the dynamics of biological evolution. For example, a delivery truck with a number of destination addresses can take a large variety of different routes, but only very few will result in a short driving time. In order to use many common forms of evolutionary optimization, one has to define for every possible
solution Solution may refer to: * Solution (chemistry) In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, prope ...
''s'' to the problem of interest (i.e., every possible route in the case of the delivery truck) how 'good' it is. This is done by introducing a
scalar Scalar may refer to: *Scalar (mathematics), an element of a field, which is used to define a vector space, usually the field of real numbers *Scalar (physics), a physical quantity that can be described by a single element of a number field such as ...
-valued
function Function or functionality may refer to: Computing * Function key A function key is a key on a computer A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations automatically. Modern comp ...
''f(s)'' (scalar valued means that ''f(s)'' is a simple number, such as 0.3, while ''s'' can be a more complicated object, for example a list of destination addresses in the case of the delivery truck), which is called the
fitness function{{no footnotes, date=May 2015 A fitness function is a particular type of objective function that is used to summarise, as a single figure of merit, how close a given design solution is to achieving the set aims. Fitness functions are used in genetic ...
. A high ''f(s)'' implies that ''s'' is a good solution. In the case of the delivery truck, ''f(s)'' could be the number of deliveries per hour on route ''s''. The best, or at least a very good, solution is then found in the following way: initially, a population of random solutions is created. Then, the solutions are mutated and selected for those with higher fitness, until a satisfying solution has been found. Evolutionary optimization techniques are particularly useful in situations in which it is easy to determine the quality of a single solution, but hard to go through all possible solutions one by one (it is easy to determine the driving time for a particular route of the delivery truck, but it is almost impossible to check all possible routes once the number of destinations grows to more than a handful). Even in cases where a fitness function is hard to define, the concept of a fitness landscape can be useful. For example, if fitness evaluation is by stochastic sampling, then sampling is from a (usually unknown) distribution at each point; nevertheless is can be useful to reason about the landscape formed by the expected fitness at each point. If fitness changes with time (dynamic optimisation) or with other species in the environment (co-evolution), it can still be useful to reason about the trajectories of the instantaneous fitness landscape. However in some cases (for example, preference-based interactive evolutionary computation) the relevance is more limited, because there is no guarantee that human preferences are consistent with a single fitness assignment. The concept of a scalar valued fitness function ''f(s)'' also corresponds to the concept of a potential or
energy function Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. Optimization problems of sorts arise i ...
in
physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical scie ...

physics
. The two concepts only differ in that
physicists A physicist is a scientist A scientist is a person who conducts scientific research The scientific method is an Empirical evidence, empirical method of acquiring knowledge that has characterized the development of science since at lea ...

physicists
traditionally think in terms of minimizing the potential function, while
biologists File:Francesco Redi.jpg, Francesco Redi, the founder of biology, is recognized to be one of the greatest biologists of all time A biologist is a professional who has specialized knowledge in the field of biology, understanding the underlying mech ...

biologists
prefer the notion that fitness is being maximized. Therefore, taking the inverse of a potential function turns it into a fitness function, and vice versa .


Caveats and limitations

Several important caveats exist. Since the human mind struggles to think in greater than three dimensions, 3D topologies can mislead when discussing highly multi-dimensional fitness landscapes. In particular it is not clear whether peaks in natural biological fitness landscapes are ever truly separated by fitness valleys in such multidimensional landscapes, or whether they are connected by vastly long neutral ridges. Additionally, the fitness landscape is not static in time but dependent on the changing environment and evolution of other genes. It is hence more of a seascape, further affecting how separated adaptive peaks can actually be. Additionally, it is relevant to take into account that a landscape is in general not an absolute but a relative function. Finally, since it is common to use function as a proxy for fitness when discussing enzymes, any promiscuous activities exist as overlapping landscapes that together will determine the ultimate fitness of the organism, implying a gap between different coexisting relative landscapes. With these limitations in mind, fitness landscapes can still be an instructive way of thinking about evolution. It is fundamentally possible to measure (even if not to visualise) some of the parameters of landscape ruggedness and of peak number, height, separation, and clustering. Simplified 3D landscapes can then be used relative to each other to visually represent the relevant features. Additionally, fitness landscapes of small subsets of evolutionary pathways may be experimentally constructed and visualized, potentially revealing features such as fitness peaks and valleys. Fitness landscapes of evolutionary pathways indicate the probable evolutionary steps and endpoints among sets of individual mutations.


See also

*
Fitness approximation Fitness approximation Y. JinA comprehensive survey of fitness approximation in evolutionary computation Soft Computing, 9:3–12, 2005 aims to approximate the objective or fitness functions in evolutionary optimization by building up machine learn ...
*
Fitness function{{no footnotes, date=May 2015 A fitness function is a particular type of objective function that is used to summarise, as a single figure of merit, how close a given design solution is to achieving the set aims. Fitness functions are used in genetic ...
*
Evolution Evolution is change in the heritable Heredity, also called inheritance or biological inheritance, is the passing on of Phenotypic trait, traits from parents to their offspring; either through asexual reproduction or sexual reproduction, ...

Evolution
*
Genetic algorithm In computer science Computer science deals with the theoretical foundations of information, algorithms and the architectures of its computation as well as practical techniques for their application. Computer science is the study of c ...

Genetic algorithm
*
Habitat (ecology) In ecology Ecology (from el, οἶκος, "house" and el, -λογία, label=none, "study of") is the study of the relationships between living organisms, including humans, and their physical environment. Ecology considers organism ...
*
Hill climbing In numerical analysis, hill climbing is a Optimization (mathematics), mathematical optimization technique which belongs to the family of Local search (optimization), local search. It is an iterative algorithm that starts with an arbitrary solu ...
*
NK model The NK model is a mathematical model A mathematical model is a description of a system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surround ...
* Potential function *
Self-organized criticality Self-organized criticality (SOC) is a property of dynamical system In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in a Manifold, geometrica ...
*
Teleology in biology Teleology in biology is the use of the language of goal-directedness in accounts of evolution Evolution is change in the heritable Heredity, also called inheritance or biological inheritance, is the passing on of Phenotypic trait, t ...


References


External links

;Examples of visualized fitness landscapes
Video: Using fitness landscapes to visualize evolution in action

BEACON Blog—Evolution 101: Fitness Landscapes


* ttp://news.ucdavis.edu/search/news_detail.lasso?id=10451 Pup Fish Evolution—UC Davis
Evolution 101—Shifting Balance Theory (Figure at bottom of page)

Superimposing evolutionary trajectories onto fitness landscapes in virtual reality
;Further reading

* ttp://msutoday.msu.edu/news/2013/no-peak-in-sight-for-evolving-bacteria/ Example of the use of Evolutionary Landscapes in thinking & speaking about evolution* * * * * * * * * {{DEFAULTSORT:Fitness Landscape Modern synthesis (20th century) Population genetics Selection