Computer simulation

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Computer_simulation 

A 48-hour computer simulation of Typhoon Mawar using the Weather Research and Forecasting model

 

Process of building a computer model, and the interplay between experiment, simulation, and theory.

Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determined by comparing their results to the real-world outcomes they aim to predict. Computer simulations have become a useful tool for the mathematical modeling of many natural systems in physics (computational physics), astrophysics, climatology, chemistry, biology and manufacturing, as well as human systems in economics, psychology, social science, health care and engineering. Simulation of a system is represented as the running of the system's model. It can be used to explore and gain new insights into new technology and to estimate the performance of systems too complex for analytical solutions.

Computer simulations are realized by running computer programs that can be either small, running almost instantly on small devices, or large-scale programs that run for hours or days on network-based groups of computers. The scale of events being simulated by computer simulations has far exceeded anything possible (or perhaps even imaginable) using traditional paper-and-pencil mathematical modeling. In 1997, a desert-battle simulation of one force invading another involved the modeling of 66,239 tanks, trucks and other vehicles on simulated terrain around Kuwait, using multiple supercomputers in the DoD High Performance Computer Modernization Program. Other examples include a 1-billion-atom model of material deformation; a 2.64-million-atom model of the complex protein-producing organelle of all living organisms, the ribosome, in 2005; a complete simulation of the life cycle of Mycoplasma genitalium in 2012; and the Blue Brain project at EPFL (Switzerland), begun in May 2005 to create the first computer simulation of the entire human brain, right down to the molecular level.

Because of the computational cost of simulation, computer experiments are used to perform inference such as uncertainty quantification.

Simulation versus model

A computer model is the algorithms and equations used to capture the behavior of the system being modeled. By contrast, computer simulation is the actual running of the program that contains these equations or algorithms. Simulation, therefore, is the process of running a model. Thus one would not "build a simulation"; instead, one would "build a model(or a simulator)", and then either "run the model" or equivalently "run a simulation".

History

Computer simulation developed hand-in-hand with the rapid growth of the computer, following its first large-scale deployment during the Manhattan Project in World War II to model the process of nuclear detonation. It was a simulation of 12 hard spheres using a Monte Carlo algorithm. Computer simulation is often used as an adjunct to, or substitute for, modeling systems for which simple closed form analytic solutions are not possible. There are many types of computer simulations; their common feature is the attempt to generate a sample of representative scenarios for a model in which a complete enumeration of all possible states of the model would be prohibitive or impossible.

Data preparation

The external data requirements of simulations and models vary widely. For some, the input might be just a few numbers (for example, simulation of a waveform of AC electricity on a wire), while others might require terabytes of information (such as weather and climate models).

Input sources also vary widely:

• Sensors and other physical devices connected to the model;
• Control surfaces used to direct the progress of the simulation in some way;
• Current or historical data entered by hand;
• Values extracted as a by-product from other processes;
• Values output for the purpose by other simulations, models, or processes.

Lastly, the time at which data is available varies:

• "invariant" data is often built into the model code, either because the value is truly invariant (e.g., the value of π) or because the designers consider the value to be invariant for all cases of interest;
• data can be entered into the simulation when it starts up, for example by reading one or more files, or by reading data from a preprocessor;
• data can be provided during the simulation run, for example by a sensor network.

Because of this variety, and because diverse simulation systems have many common elements, there are a large number of specialized simulation languages. The best-known may be Simula. There are now many others.

Systems that accept data from external sources must be very careful in knowing what they are receiving. While it is easy for computers to read in values from text or binary files, what is much harder is knowing what the accuracy (compared to measurement resolution and precision) of the values are. Often they are expressed as "error bars", a minimum and maximum deviation from the value range within which the true value (is expected to) lie. Because digital computer mathematics is not perfect, rounding and truncation errors multiply this error, so it is useful to perform an "error analysis"^[8] to confirm that values output by the simulation will still be usefully accurate.

Types

Computer models can be classified according to several independent pairs of attributes, including:

• Stochastic or deterministic (and as a special case of deterministic, chaotic) – see external links below for examples of stochastic vs. deterministic simulations
• Steady-state or dynamic
• Continuous or discrete (and as an important special case of discrete, discrete event or DE models)
• Dynamic system simulation, e.g. electric systems, hydraulic systems or multi-body mechanical systems (described primarily by DAE:s) or dynamics simulation of field problems, e.g. CFD of FEM simulations (described by PDE:s).
• Local or distributed.

Another way of categorizing models is to look at the underlying data structures. For time-stepped simulations, there are two main classes:

• Simulations which store their data in regular grids and require only next-neighbor access are called stencil codes. Many CFD applications belong to this category.
• If the underlying graph is not a regular grid, the model may belong to the meshfree method class.

Equations define the relationships between elements of the modeled system and attempt to find a state in which the system is in equilibrium. Such models are often used in simulating physical systems, as a simpler modeling case before dynamic simulation is attempted.

• Dynamic simulations model changes in a system in response to (usually changing) input signals.
• Stochastic models use random number generators to model chance or random events;
• A discrete event simulation (DES) manages events in time. Most computer, logic-test and fault-tree simulations are of this type. In this type of simulation, the simulator maintains a queue of events sorted by the simulated time they should occur. The simulator reads the queue and triggers new events as each event is processed. It is not important to execute the simulation in real time. It is often more important to be able to access the data produced by the simulation and to discover logic defects in the design or the sequence of events.
• A continuous dynamic simulation performs numerical solution of differential-algebraic equations or differential equations (either partial or ordinary). Periodically, the simulation program solves all the equations and uses the numbers to change the state and output of the simulation. Applications include flight simulators, construction and management simulation games, chemical process modeling, and simulations of electrical circuits. Originally, these kinds of simulations were actually implemented on analog computers, where the differential equations could be represented directly by various electrical components such as op-amps. By the late 1980s, however, most "analog" simulations were run on conventional digital computers that emulate the behavior of an analog computer.
• A special type of discrete simulation that does not rely on a model with an underlying equation, but can nonetheless be represented formally, is agent-based simulation. In agent-based simulation, the individual entities (such as molecules, cells, trees or consumers) in the model are represented directly (rather than by their density or concentration) and possess an internal state and set of behaviors or rules that determine how the agent's state is updated from one time-step to the next.
• Distributed models run on a network of interconnected computers, possibly through the Internet. Simulations dispersed across multiple host computers like this are often referred to as "distributed simulations". There are several standards for distributed simulation, including Aggregate Level Simulation Protocol (ALSP), Distributed Interactive Simulation (DIS), the High Level Architecture (simulation) (HLA) and the Test and Training Enabling Architecture (TENA).

Visualization

Formerly, the output data from a computer simulation was sometimes presented in a table or a matrix showing how data were affected by numerous changes in the simulation parameters. The use of the matrix format was related to traditional use of the matrix concept in mathematical models. However, psychologists and others noted that humans could quickly perceive trends by looking at graphs or even moving-images or motion-pictures generated from the data, as displayed by computer-generated-imagery (CGI) animation. Although observers could not necessarily read out numbers or quote math formulas, from observing a moving weather chart they might be able to predict events (and "see that rain was headed their way") much faster than by scanning tables of rain-cloud coordinates. Such intense graphical displays, which transcended the world of numbers and formulae, sometimes also led to output that lacked a coordinate grid or omitted timestamps, as if straying too far from numeric data displays. Today, weather forecasting models tend to balance the view of moving rain/snow clouds against a map that uses numeric coordinates and numeric timestamps of events.

Similarly, CGI computer simulations of CAT scans can simulate how a tumor might shrink or change during an extended period of medical treatment, presenting the passage of time as a spinning view of the visible human head, as the tumor changes.

Other applications of CGI computer simulations are being developed to graphically display large amounts of data, in motion, as changes occur during a simulation run.

Computer simulation in science

Computer simulation of the process of osmosis

Generic examples of types of computer simulations in science, which are derived from an underlying mathematical description:

• a numerical simulation of differential equations that cannot be solved analytically, theories that involve continuous systems such as phenomena in physical cosmology, fluid dynamics (e.g., climate models, roadway noise models, roadway air dispersion models), continuum mechanics and chemical kinetics fall into this category.
• a stochastic simulation, typically used for discrete systems where events occur probabilistically and which cannot be described directly with differential equations (this is a discrete simulation in the above sense). Phenomena in this category include genetic drift, biochemical or gene regulatory networks with small numbers of molecules. (see also: Monte Carlo method).
• multiparticle simulation of the response of nanomaterials at multiple scales to an applied force for the purpose of modeling their thermoelastic and thermodynamic properties. Techniques used for such simulations are Molecular dynamics, Molecular mechanics, Monte Carlo method, and Multiscale Green's function.

Specific examples of computer simulations follow:

• statistical simulations based upon an agglomeration of a large number of input profiles, such as the forecasting of equilibrium temperature of receiving waters, allowing the gamut of meteorological data to be input for a specific locale. This technique was developed for thermal pollution forecasting.
• agent based simulation has been used effectively in ecology, where it is often called "individual based modeling" and is used in situations for which individual variability in the agents cannot be neglected, such as population dynamics of salmon and trout (most purely mathematical models assume all trout behave identically).
• time stepped dynamic model. In hydrology there are several such hydrology transport models such as the SWMM and DSSAM Models developed by the U.S. Environmental Protection Agency for river water quality forecasting.
• computer simulations have also been used to formally model theories of human cognition and performance, e.g., ACT-R.
• computer simulation using molecular modeling for drug discovery.
• computer simulation to model viral infection in mammalian cells.
• computer simulation for studying the selective sensitivity of bonds by mechanochemistry during grinding of organic molecules.
• Computational fluid dynamics simulations are used to simulate the behaviour of flowing air, water and other fluids. One-, two- and three-dimensional models are used. A one-dimensional model might simulate the effects of water hammer in a pipe. A two-dimensional model might be used to simulate the drag forces on the cross-section of an aeroplane wing. A three-dimensional simulation might estimate the heating and cooling requirements of a large building.
• An understanding of statistical thermodynamic molecular theory is fundamental to the appreciation of molecular solutions. Development of the Potential Distribution Theorem (PDT) allows this complex subject to be simplified to down-to-earth presentations of molecular theory.

Notable, and sometimes controversial, computer simulations used in science include: Donella Meadows' World3 used in the Limits to Growth, James Lovelock's Daisyworld and Thomas Ray's Tierra.

In social sciences, computer simulation is an integral component of the five angles of analysis fostered by the data percolation methodology, which also includes qualitative and quantitative methods, reviews of the literature (including scholarly), and interviews with experts, and which forms an extension of data triangulation. Of course, similar to any other scientific method, replication is an important part of computational modeling 

Computer simulation in practical contexts

Computer simulations are used in a wide variety of practical contexts, such as:

• analysis of air pollutant dispersion using atmospheric dispersion modeling
• design of complex systems such as aircraft and also logistics systems.
• design of noise barriers to effect roadway noise mitigation
• modeling of application performance
• flight simulators to train pilots
• weather forecasting
• forecasting of risk
• simulation of electrical circuits
• Power system simulation
• simulation of other computers is emulation.
• forecasting of prices on financial markets (for example Adaptive Modeler)
• behavior of structures (such as buildings and industrial parts) under stress and other conditions
• design of industrial processes, such as chemical processing plants
• strategic management and organizational studies
• reservoir simulation for the petroleum engineering to model the subsurface reservoir
• process engineering simulation tools.
• robot simulators for the design of robots and robot control algorithms
• urban simulation models that simulate dynamic patterns of urban development and responses to urban land use and transportation policies.
• traffic engineering to plan or redesign parts of the street network from single junctions over cities to a national highway network to transportation system planning, design and operations. See a more detailed article on Simulation in Transportation.
• modeling car crashes to test safety mechanisms in new vehicle models.
• crop-soil systems in agriculture, via dedicated software frameworks (e.g. BioMA, OMS3, APSIM)

The reliability and the trust people put in computer simulations depends on the validity of the simulation model, therefore verification and validation are of crucial importance in the development of computer simulations. Another important aspect of computer simulations is that of reproducibility of the results, meaning that a simulation model should not provide a different answer for each execution. Although this might seem obvious, this is a special point of attention in stochastic simulations, where random numbers should actually be semi-random numbers. An exception to reproducibility are human-in-the-loop simulations such as flight simulations and computer games. Here a human is part of the simulation and thus influences the outcome in a way that is hard, if not impossible, to reproduce exactly.

Vehicle manufacturers make use of computer simulation to test safety features in new designs. By building a copy of the car in a physics simulation environment, they can save the hundreds of thousands of dollars that would otherwise be required to build and test a unique prototype. Engineers can step through the simulation milliseconds at a time to determine the exact stresses being put upon each section of the prototype.

Computer graphics can be used to display the results of a computer simulation. Animations can be used to experience a simulation in real-time, e.g., in training simulations. In some cases animations may also be useful in faster than real-time or even slower than real-time modes. For example, faster than real-time animations can be useful in visualizing the buildup of queues in the simulation of humans evacuating a building. Furthermore, simulation results are often aggregated into static images using various ways of scientific visualization.

In debugging, simulating a program execution under test (rather than executing natively) can detect far more errors than the hardware itself can detect and, at the same time, log useful debugging information such as instruction trace, memory alterations and instruction counts. This technique can also detect buffer overflow and similar "hard to detect" errors as well as produce performance information and tuning data.

Pitfalls

Although sometimes ignored in computer simulations, it is very important to perform a sensitivity analysis to ensure that the accuracy of the results is properly understood. For example, the probabilistic risk analysis of factors determining the success of an oilfield exploration program involves combining samples from a variety of statistical distributions using the Monte Carlo method. If, for instance, one of the key parameters (e.g., the net ratio of oil-bearing strata) is known to only one significant figure, then the result of the simulation might not be more precise than one significant figure, although it might (misleadingly) be presented as having four significant figures.

Model calibration techniques

The following three steps should be used to produce accurate simulation models: calibration, verification, and validation. Computer simulations are good at portraying and comparing theoretical scenarios, but in order to accurately model actual case studies they have to match what is actually happening today. A base model should be created and calibrated so that it matches the area being studied. The calibrated model should then be verified to ensure that the model is operating as expected based on the inputs. Once the model has been verified, the final step is to validate the model by comparing the outputs to historical data from the study area. This can be done by using statistical techniques and ensuring an adequate R-squared value. Unless these techniques are employed, the simulation model created will produce inaccurate results and not be a useful prediction tool.

Model calibration is achieved by adjusting any available parameters in order to adjust how the model operates and simulates the process. For example, in traffic simulation, typical parameters include look-ahead distance, car-following sensitivity, discharge headway, and start-up lost time. These parameters influence driver behavior such as when and how long it takes a driver to change lanes, how much distance a driver leaves between his car and the car in front of it, and how quickly a driver starts to accelerate through an intersection. Adjusting these parameters has a direct effect on the amount of traffic volume that can traverse through the modeled roadway network by making the drivers more or less aggressive. These are examples of calibration parameters that can be fine-tuned to match characteristics observed in the field at the study location. Most traffic models have typical default values but they may need to be adjusted to better match the driver behavior at the specific location being studied.

Model verification is achieved by obtaining output data from the model and comparing them to what is expected from the input data. For example, in traffic simulation, traffic volume can be verified to ensure that actual volume throughput in the model is reasonably close to traffic volumes input into the model. Ten percent is a typical threshold used in traffic simulation to determine if output volumes are reasonably close to input volumes. Simulation models handle model inputs in different ways so traffic that enters the network, for example, may or may not reach its desired destination. Additionally, traffic that wants to enter the network may not be able to, if congestion exists. This is why model verification is a very important part of the modeling process.

The final step is to validate the model by comparing the results with what is expected based on historical data from the study area. Ideally, the model should produce similar results to what has happened historically. This is typically verified by nothing more than quoting the R-squared statistic from the fit. This statistic measures the fraction of variability that is accounted for by the model. A high R-squared value does not necessarily mean the model fits the data well. Another tool used to validate models is graphical residual analysis. If model output values drastically differ from historical values, it probably means there is an error in the model. Before using the model as a base to produce additional models, it is important to verify it for different scenarios to ensure that each one is accurate. If the outputs do not reasonably match historic values during the validation process, the model should be reviewed and updated to produce results more in line with expectations. It is an iterative process that helps to produce more realistic models.

Validating traffic simulation models requires comparing traffic estimated by the model to observed traffic on the roadway and transit systems. Initial comparisons are for trip interchanges between quadrants, sectors, or other large areas of interest. The next step is to compare traffic estimated by the models to traffic counts, including transit ridership, crossing contrived barriers in the study area. These are typically called screenlines, cutlines, and cordon lines and may be imaginary or actual physical barriers. Cordon lines surround particular areas such as a city's central business district or other major activity centers. Transit ridership estimates are commonly validated by comparing them to actual patronage crossing cordon lines around the central business district.

Three sources of error can cause weak correlation during calibration: input error, model error, and parameter error. In general, input error and parameter error can be adjusted easily by the user. Model error however is caused by the methodology used in the model and may not be as easy to fix. Simulation models are typically built using several different modeling theories that can produce conflicting results. Some models are more generalized while others are more detailed. If model error occurs as a result, in may be necessary to adjust the model methodology to make results more consistent.

In order to produce good models that can be used to produce realistic results, these are the necessary steps that need to be taken in order to ensure that simulation models are functioning properly. Simulation models can be used as a tool to verify engineering theories, but they are only valid if calibrated properly. Once satisfactory estimates of the parameters for all models have been obtained, the models must be checked to assure that they adequately perform the intended functions. The validation process establishes the credibility of the model by demonstrating its ability to replicate reality. The importance of model validation underscores the need for careful planning, thoroughness and accuracy of the input data collection program that has this purpose. Efforts should be made to ensure collected data is consistent with expected values. For example, in traffic analysis it is typical for a traffic engineer to perform a site visit to verify traffic counts and become familiar with traffic patterns in the area. The resulting models and forecasts will be no better than the data used for model estimation and validation.

 

The Blind Watchmaker

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/The_Blind_Watchmaker 

The Blind Watchmaker

First edition cover
Author	Richard Dawkins
Country	United Kingdom
Language	English
Subject	Evolutionary biology
Publisher	Norton & Company, Inc
Publication date	1986
Media type	Print
ISBN	0-393-31570-3
OCLC	35648431
Dewey Decimal	576.8/2 21
LC Class	QH366.2 .D37 1996
Preceded by	The Extended Phenotype
Followed by	River Out of Eden

The Blind Watchmaker: Why the Evidence of Evolution Reveals a Universe without Design is a 1986 book by Richard Dawkins, in which the author presents an explanation of, and argument for, the theory of evolution by means of natural selection. He also presents arguments to refute certain criticisms made on his first book, The Selfish Gene. (Both books espouse the gene-centric view of evolution.) An unabridged audiobook edition was released in 2011, narrated by Richard Dawkins and Lalla Ward.

Overview

In his choice of the title for this book, Dawkins refers to the watchmaker analogy made famous by William Paley in his 1802 book Natural Theology. Paley, writing long before Charles Darwin published On the Origin of Species in 1859, held that the complexity of living organisms was evidence of the existence of a divine creator by drawing a parallel with the way in which the existence of a watch compels belief in an intelligent watchmaker. Dawkins, in contrasting the differences between human design and its potential for planning with the workings of natural selection, therefore dubbed evolutionary processes as analogous to a blind watchmaker.

To dispel the idea that complexity cannot arise without the intervention of a "creator", Dawkins uses the example of the eye. Beginning with a simple organism, capable only of distinguishing between light and dark, in only the crudest fashion, he takes the reader through a series of minor modifications, which build in sophistication until we arrive at the elegant and complex mammalian eye. In making this journey, he points to several creatures whose various seeing apparatus are, whilst still useful, living examples of intermediate levels of complexity.

In developing his argument that natural selection can explain the complex adaptations of organisms, Dawkins' first concern is to illustrate the difference between the potential for the development of complexity as a result of pure randomness, as opposed to that of randomness coupled with cumulative selection. He demonstrates this by the example of the weasel program. Dawkins then describes his experiences with a more sophisticated computer model of artificial selection implemented in a program also called The Blind Watchmaker, which was sold separately as a teaching aid.

The program displayed a two-dimensional shape (a "biomorph") made up of straight black lines, the length, position, and angle of which were defined by a simple set of rules and instructions (analogous to a genome). Adding new lines (or removing them) based on these rules offered a discrete set of possible new shapes (mutations), which were displayed on screen so that the user could choose between them. The chosen mutation would then be the basis for another generation of biomorph mutants to be chosen from, and so on. Thus, the user, by selection, could steer the evolution of biomorphs. This process often produced images which were reminiscent of real organisms for instance beetles, bats, or trees. Dawkins speculated that the unnatural selection role played by the user in this program could be replaced by a more natural agent if, for example, colourful biomorphs could be selected by butterflies or other insects, via a touch-sensitive display set up in a garden.

"Biomorph" that randomly evolves following changes of several numeric "genes", determining its shape. The gene values are given as bars on the top.

In an appendix to a later edition of the book (1996), Dawkins explains how his experiences with computer models led him to a greater appreciation of the role of embryological constraints on natural selection. In particular, he recognised that certain patterns of embryological development could lead to the success of a related group of species in filling varied ecological niches, though he emphasised that this should not be confused with group selection. He dubbed this insight the evolution of evolvability.

After arguing that evolution is capable of explaining the origin of complexity, near the end of the book Dawkins uses this to argue against the existence of God: "a deity capable of engineering all the organized complexity in the world, either instantaneously or by guiding evolution ... must already have been vastly complex in the first place ..." He calls this "postulating organized complexity without offering an explanation."

In the preface, Dawkins states that he wrote the book "to persuade the reader, not just that the Darwinian world-view happens to be true, but that it is the only known theory that could, in principle, solve the mystery of our existence."

Reception

Tim Radford, writing in The Guardian, noted that despite Dawkins's "combative secular humanism", he had written "a patient, often beautiful book from 1986 that begins in a generous mood and sustains its generosity to the end." 30 years on, people still read the book, Radford argues, because it is "one of the best books ever to address, patiently and persuasively, the question that has baffled bishops and disconcerted dissenters alike: how did nature achieve its astonishing complexity and variety?"^[1]

The philosopher and historian of biology, Michael T. Ghiselin, writing in The New York Times, comments that Dawkins "succeeds admirably in showing how natural selection allows biologists to dispense with such notions as purpose and design". He notes that analogies with computer programs have their limitations, but are still useful. Ghiselin observes that Dawkins is "not content with rebutting creationists" but goes on to press home his arguments against alternative theories to neo-Darwinism. He thinks the book fills the need to know more about evolution "that others [creationists] would conceal from them." He concludes that "Readers who are not outraged will be delighted."

The American philosopher of religion Dallas Willard, reflecting on the book, denies the connection of evolution to the validity of arguments from design to God: whereas, he asserts, Dawkins seems to consider the arguments to rest entirely on that basis. Willard argues that Chapter 6, "Origins and Miracles", attempts the "hard task" of making not just a blind watchmaker but "a blind watchmaker watchmaker", which he comments would have made an "honest" title for the book. He notes that Dawkins demolishes several "weak" arguments, such as the argument from personal incredulity. He denies that Dawkins's computer "exercises" and arguments from gradual change show that complex forms of life could have evolved. Willard concludes by arguing that in writing this book, Dawkins is not functioning as a scientist "in the line of Darwin", but as "just a naturalist metaphysician".

Influence

The engineer Theo Jansen read the book in 1986 and became fascinated by evolution and natural selection. Since 1990 he has been building kinetic sculptures, the Strandbeest, capable of walking when impelled by the wind.

The journalist Dick Pountain described Sean B. Carroll's 2005 account of evolutionary developmental biology, Endless Forms Most Beautiful, as the most important popular science book since The Blind Watchmaker, "and in effect a sequel [to it]."

 

Sexual selection

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Sexual_selection 

Sexual selection creates colourful differences between sexes (sexual dimorphism) in Goldie's bird-of-paradise. Male above; female below. Painting by John Gerrard Keulemans (d.1912)

Sexual selection is a mode of natural selection in which members of one biological sex choose mates of the other sex to mate with (intersexual selection), and compete with members of the same sex for access to members of the opposite sex (intrasexual selection). These two forms of selection mean that some individuals have greater reproductive success than others within a population, for example because they are more attractive or prefer more attractive partners to produce offspring. Successful males benefit from frequent mating and monopolizing access to one or more fertile females. Females can have a limited number of offspring and maximize the return on the energy they invest in reproduction.

The concept was first articulated by Charles Darwin who wrote of a "second agency" of selection, in which competition between mate candidates could lead to speciation. The theory was given a mathematical basis by Ronald Fisher in the early 20th century. Sexual selection can lead males to extreme efforts to demonstrate their fitness to be chosen by females, producing sexual dimorphism in secondary sexual characteristics, such as the ornate plumage of birds such as birds of paradise and peafowl, or the antlers of deer, or the manes of lions, caused by a positive feedback mechanism known as a Fisherian runaway, where the passing-on of the desire for a trait in one sex is as important as having the trait in the other sex in producing the runaway effect. Although the sexy son hypothesis indicates that females would prefer male offspring, Fisher's principle explains why the sex ratio is most often 1:1. Sexual selection is also found in plants and fungi.

History

Darwin

Sexual selection was first proposed by Charles Darwin in The Origin of Species (1859) and developed in The Descent of Man and Selection in Relation to Sex (1871), as he felt that natural selection alone was unable to account for certain types of non-survival adaptations. He once wrote to a colleague that "The sight of a feather in a peacock's tail, whenever I gaze at it, makes me sick!" His work divided sexual selection into male-male competition and female choice.

... depends, not on a struggle for existence, but on a struggle between the males for possession of the females; the result is not death to the unsuccessful competitor, but few or no offspring.

... when the males and females of any animal have the same general habits ... but differ in structure, colour, or ornament, such differences have been mainly caused by sexual selection.

These views were to some extent opposed by Alfred Russel Wallace, mostly after Darwin's death. He accepted that sexual selection could occur, but argued that it was a relatively weak form of selection. He argued that male-male competitions were forms of natural selection, but that the "drab" peahen's coloration is itself adaptive as camouflage. In his opinion, ascribing mate choice to females was attributing the ability to judge standards of beauty to animals (such as beetles) far too cognitively undeveloped to be capable of aesthetic feeling.

Ronald Fisher

Ronald Fisher, the English statistician and evolutionary biologist developed a number of ideas about sexual selection in his 1930 book The Genetical Theory of Natural Selection including the sexy son hypothesis and Fisher's principle. The Fisherian runaway describes how sexual selection accelerates the preference for a specific ornament, causing the preferred trait and female preference for it to increase together in a positive feedback runaway cycle. In a remark that was not widely understood for another 50 years he said:

... plumage development in the male, and sexual preference for such developments in the female, must thus advance together, and so long as the process is unchecked by severe counterselection, will advance with ever-increasing speed. In the total absence of such checks, it is easy to see that the speed of development will be proportional to the development already attained, which will therefore increase with time exponentially, or in geometric progression. —Ronald Fisher, 1930

Male long-tailed widowbird

This causes a dramatic increase in both the male's conspicuous feature and in female preference for it, resulting in marked sexual dimorphism, until practical physical constraints halt further exaggeration. A positive feedback loop is created, producing extravagant physical structures in the non-limiting sex. A classic example of female choice and potential runaway selection is the long-tailed widowbird. While males have long tails that are selected for by female choice, female tastes in tail length are still more extreme with females being attracted to tails longer than those that naturally occur. Fisher understood that female preference for long tails may be passed on genetically, in conjunction with genes for the long tail itself. Long-tailed widowbird offspring of both sexes inherit both sets of genes, with females expressing their genetic preference for long tails, and males showing off the coveted long tail itself.

Richard Dawkins presents a non-mathematical explanation of the runaway sexual selection process in his book The Blind Watchmaker. Females that prefer long tailed males tend to have mothers that chose long-tailed fathers. As a result, they carry both sets of genes in their bodies. That is, genes for long tails and for preferring long tails become linked. The taste for long tails and tail length itself may therefore become correlated, tending to increase together. The more tails lengthen, the more long tails are desired. Any slight initial imbalance between taste and tails may set off an explosion in tail lengths. Fisher wrote that:

The exponential element, which is the kernel of the thing, arises from the rate of change in hen taste being proportional to the absolute average degree of taste. —Ronald Fisher, 1932

The peacock tail in flight, the proposed classic example of a Fisherian runaway

The female widowbird chooses to mate with the most attractive long-tailed male so that her progeny, if male, will themselves be attractive to females of the next generation—thereby fathering many offspring that carry the female's genes. Since the rate of change in preference is proportional to the average taste amongst females, and as females desire to secure the services of the most sexually attractive males, an additive effect is created that, if unchecked, can yield exponential increases in a given taste and in the corresponding desired sexual attribute.

It is important to notice that the conditions of relative stability brought about by these or other means, will be far longer duration than the process in which the ornaments are evolved. In most existing species the runaway process must have been already checked, and we should expect that the more extraordinary developments of sexual plumage are not due like most characters to a long and even course of evolutionary progress, but to sudden spurts of change. —Ronald Fisher, 1930

After Fisher

Since Fisher's initial conceptual model of the 'runaway' process, Russell Lande and Peter O'Donald have provided detailed mathematical proofs that define the circumstances under which runaway sexual selection can take place. Alongside this, biologists have extended Darwin's formulation; Malte Andersson's widely-accepted 1994 definition is that "sexual selection is the differences in reproduction that arise from variation among individuals in traits that affect success in competition over mates and fertilizations". Despite some practical challenges for biologists, the concept of sexual selection is "straightforward".

Theory

Reproductive success

Extinct Irish elk (Megaloceros giganteus). These antlers span 2.7 metres (8.9 ft) and have a mass of 40 kg (88 lb).

The reproductive success of an organism is measured by the number of offspring left behind, and their quality or probable fitness.

Sexual preference creates a tendency towards assortative mating or homogamy. The general conditions of sexual discrimination appear to be (1) the acceptance of one mate precludes the effective acceptance of alternative mates, and (2) the rejection of an offer is followed by other offers, either certainly or at such high chance that the risk of non-occurrence is smaller than the chance advantage to be gained by selecting a mate. Bateman's principle states that the sex which invests the most in producing offspring becomes a limiting resource for which the other sex competes, illustrated by the greater nutritional investment of an egg in a zygote, and the limited capacity of females to reproduce; for example, in humans, a woman can only give birth every ten months, whereas a male can become a father numerous times in the same period. More recently, researchers have doubted whether Bateman was correct.

Modern interpretation

Darwin's ideas on sexual selection were met with scepticism by his contemporaries and not considered of great importance until in the 1930s biologists decided to include sexual selection as a mode of natural selection. Only in the 21st century have they become more important in biology; the theory is now seen as generally applicable and analogous to natural selection.

A ten-year study, experimentally varying sexual selection on flour beetles with other factors held constant, showed that sexual selection protected even an inbred population against extinction.

The handicap principle of Amotz Zahavi, Russell Lande and W. D. Hamilton, holds that the male's survival until and through the age of reproduction with seemingly maladaptive traits is taken by the female as a signal of his overall fitness. Such handicaps might prove he is either free of or resistant to disease, or that he possesses more speed or a greater physical strength that is used to combat the troubles brought on by the exaggerated trait. Zahavi's work spurred a re-examination of the field and several new theories. In 1984, Hamilton and Marlene Zuk introduced the "Bright Male" hypothesis, suggesting that male elaborations might serve as a marker of health, by exaggerating the effects of disease and deficiency.

In 1990, Michael Ryan and A.S. Rand, working with the Túngara frog, proposed the hypothesis of "Sensory Exploitation", where exaggerated male traits may provide a sensory stimulation that females find hard to resist. In the late 1970s, Janzen and Mary Willson, noting that male flowers are often larger than female flowers, expanded the field of sexual selection into plants.

More recently, the field has grown to include other areas of study, not all of which fit Darwin's definition of sexual selection. A "bewildering" range of models variously attempt to relate sexual selection not only to the fundamental questions of anisogamy and parental roles, but also to mechanisms such as sex ratios, parental care, having sexy sons, sexual conflict, and the "most-debated effect", namely mate choice.

Elaborated characteristics that might seem costly for their bearers (e.g., the tail of the swordfish Xiphophorus montezumae) do not always have an energetics, performance or even survival cost; this may be because "compensatory traits" have evolved in concert with the sexually selected traits.

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  Male mountain gorilla, a tournament species

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  Sexual selection protected flour beetles from extinction in a ten-year experiment.

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  Túngara frog exemplified theory of "Sensory Exploitation", where exaggerated male traits supposedly made males irresistible to females.

Toolkit of natural selection

Reconstruction of Protarchaeopteryx, an early proto-bird

Sexual selection may explain how characteristics such as feathers had survival value at an early stage in their evolution. Geoffrey Miller proposes that the feathers of proto-birds like Archaeopteryx were originally sexual ornaments. The earliest proto-birds such as Protarchaeopteryx had well-developed feathers but no sign of the top/bottom asymmetry that gives wings lift. One proposal is that the feathers served as insulation, helping females incubate their eggs. But if proto-bird courtship combined displays of forelimb feathers with energetic jumps, then the transition from display to aerodynamic functions could have been relatively smooth.

Sexual selection sometimes generates features that may help cause a species' extinction, as has been suggested for the giant antlers of the Irish elk (Megaloceros giganteus) that became extinct in Pleistocene Europe. Or it may do the opposite, driving species divergence—sometimes through elaborate changes in genitalia—such that new species emerge.

Sexual dimorphism

Main article: Sexual dimorphism

Sex differences directly related to reproduction and serving no direct purpose in courtship are called primary sexual characteristics. Traits amenable to sexual selection, which give an organism an advantage over its rivals (such as in courtship) without being directly involved in reproduction, are called secondary sex characteristics.

The rhinoceros beetle is a classic case of sexual dimorphism. Plate from Darwin's Descent of Man (male above)

In most sexual species the males and females have different equilibrium strategies, due to a difference in relative investment in producing offspring. As formulated in Bateman's principle, females have a greater initial investment in producing offspring (pregnancy in mammals or the production of the egg in birds and reptiles), and this difference in initial investment creates differences in variance in expected reproductive success and bootstraps the sexual selection processes. (Pipefish and Wilson's phalarope are classic examples of sex role reversal.) Also, unlike a female, a male (except in monogamous species) has some uncertainty about whether or not he is the true parent of a child, and so is less interested in spending his energy helping to raise offspring that may or may not be related to him. As a result of these factors, males can be expected to be more willing to mate than females, while females are expected to be the ones doing the choosing (except in cases of forced copulations, which has been observed in numerous species, including mammals, birds, insects and fish). The effects of sexual selection are thus often more pronounced in males than in females.

Differences in secondary sexual characteristics between males and females of a species are referred to as sexual dimorphisms. These can be as subtle as a size difference (sexual size dimorphism, often abbreviated as SSD) or as extreme as horns and colour patterns. Sexual dimorphisms abound in nature. Examples include the possession of antlers by only male deer, the brighter coloration of many male birds in comparison with females of the same species, or even more distinct differences in basic morphology, such as the drastically increased eye-span of the male stalk-eyed fly. The peacock, with its elaborate and colourful tail feathers, which the peahen lacks, is often referred to as perhaps the most extraordinary example of a dimorphism. Male and female black-throated blue warblers and Guianan cock-of-the-rocks also differ radically in their plumage. Early naturalists even believed the females to be a separate species. The largest sexual size dimorphism in vertebrates is the shell dwelling cichlid fish Neolamprologus callipterus in which males are up to 30 times the size of females. Many other fish such as guppies are sexually dimorphic. Extreme sexual size dimorphism, with females larger than males, is quite common in spiders and birds of prey.

The maintenance of sexual reproduction in a highly competitive world is one of the major puzzles in biology given that asexual reproduction can reproduce much more quickly as 50% of offspring are not males, unable to produce offspring themselves. Many non-exclusive hypotheses have been proposed, including the positive impact of an additional form of selection, sexual selection, on the probability of persistence of a species.

Male intrasexual competition

See also: Female intrasexual competition

Male-male competition occurs when two males of the same species compete for the opportunity to mate with a female. Sexually dimorphic traits, size, sex ratio, and the social situation may all play a role in the effects male-male competition has on the reproductive success of a male and the mate choice of a female. Larger males tend to win male-male conflicts due to their sheer strength and ability to ward off other males from taking over their females. For instance, in the fly Dryomyza anilis, size shows the strongest correlation to the outcome of male-male conflicts over resources like territory and females.

Influencing factors

Sex ratio

Japanese medaka, Oryzias latipes

There are multiple types of male-male competition that may occur in a population at different times depending on the conditions. Competition variation occurs based on the frequency of various mating behaviours present in the population. One factor that can influence the type of competition observed is the population density of males. When there is a high density of males present in the population, competition tends to be less aggressive and therefore sneak tactics and disruptions techniques are more often employed. These techniques often indicate a type of competition referred to as scramble competition. In Japanese medaka, Oryzias latipes, sneaking behaviours refer to when a male interrupts a mating pair during copulation by grasping on to either the male or the female and releasing their own sperm in the hopes of being the one to fertilize the female. Disruption is a technique which involves one male bumping the male that is copulating with the female away just before his sperm is released and the eggs are fertilized.

However, all techniques are not equally successful when in competition for reproductive success. Disruption results in a shorter copulation period and can therefore disrupt the fertilization of the eggs by the sperm, which frequently results in lower rates of fertilization and smaller clutch size.

Resource value and social ranking

Another factor that can influence male-male competition is the value of the resource to competitors. Male-male competition can pose many risks to a male's fitness, such as high energy expenditure, physical injury, lower sperm quality and lost paternity. The risk of competition must therefore be worth the value of the resource. A male is more likely to engage in competition for a resource that improves their reproductive success if the resource value is higher. While male-male competition can occur in the presence or absence of a female, competition occurs more frequently in the presence of a female. The presence of a female directly increases the resource value of a territory or shelter and so the males are more likely to accept the risk of competition when a female is present. The smaller males of a species are also more likely to engage in competition with larger males in the presence of a female. Due to the higher level of risk for subordinate males, they tend to engage in competition less frequently than larger, more dominant males and therefore breed less frequently than dominant males. This is seen in many species, such as the Omei treefrog, Rhacophorus omeimontis, where larger males obtain more mating opportunities and mate with larger females.

Winner–loser effects

A third factor that can impact the success of a male in competition is winner-loser effects. Burrowing crickets, Velarifictorus aspersus, compete for burrows to attract females using their large mandibles for fighting. Female burrowing crickets are more likely to choose winner of a competition in the 2 hours after the fight. The presence of a winning male suppresses mating behaviours of the losing males because the winning male tends to produce more frequent and enhanced mating calls in this period of time.

Effect on female fitness

Male-male competition can both positively and negatively affect female fitness. When there is a high density of males in a population and a large number of males attempting to mate with the female, she is more likely to resist mating attempts, resulting in lower fertilization rates. High levels of male-male competition can also result in a reduction in female investment in mating. Many forms of competition can also cause significant distress for the female negatively impacting her ability to reproduce. An increase in male-male competition can affect a female's ability to select the best mates, and therefore decrease the likelihood of successful reproduction.

However, group mating in Japanese medaka has been shown to positively affect the fitness of females due to an increase in genetic variation, a higher likelihood of paternal care and a higher likelihood of successful fertilization. Exposure to environmental estrogens, such as some herbicides, can confuse female choice of males.

In different taxa

See also: Major histocompatibility complex and sexual selection

SEM image of lateral view of a love dart of the land snail Monachoides vicinus. The scale bar is 500 μm (0.5 mm).

 

Human spermatozoa can reach 250 million in a single ejaculation

Sexual selection has been observed to occur in plants, animals and fungi. In certain hermaphroditic snail and slug species of molluscs the throwing of love darts is a form of sexual selection. Certain male insects of the order Lepidoptera cement the vaginal pores of their females.

A male bed bug (Cimex lectularius) traumatically inseminates a female bed bug (top). The female's ventral carapace is visibly cracked around the point of insemination.

Today, biologists say that certain evolutionary traits can be explained by intraspecific competition—competition between members of the same species—distinguishing between competition before or after sexual intercourse.

Illustration from The Descent of Man showing the tufted coquette Lophornis ornatus: female on left, ornamented male on right

Before copulation, intrasexual selection—usually between males—may take the form of male-to-male combat. Also, intersexual selection, or mate choice, occurs when females choose between male mates. Traits selected by male combat are called secondary sexual characteristics (including horns, antlers, etc.), which Darwin described as "weapons", while traits selected by mate (usually female) choice are called "ornaments". Due to their sometimes greatly exaggerated nature, secondary sexual characteristics can prove to be a hindrance to an animal, thereby lowering its chances of survival. For example, the large antlers of a moose are bulky and heavy and slow the creature's flight from predators; they also can become entangled in low-hanging tree branches and shrubs, and undoubtedly have led to the demise of many individuals. Bright colourations and showy ornamenations, such as those seen in many male birds, in addition to capturing the eyes of females, also attract the attention of predators. Some of these traits also represent energetically costly investments for the animals that bear them. However, one must also consider that intersexual selection can occur with an emphasis on resources that one sex possesses rather than morphological and physiological differences. For example, males of Euglossa imperialis, a non-social bee species, form aggregations of territories considered to be leks, to defend fragrant-rich primary territories. The purpose of these aggregations is only facultative, since the more suitable fragrant-rich sites there are, the more habitable territories there are to inhabit, giving females of this species a large selection of males with whom to potentially mate.

After copulation, male–male competition distinct from conventional aggression may take the form of sperm competition, as described by Parker in 1970. More recently, interest has arisen in cryptic female choice, a phenomenon of internally fertilised animals such as mammals and birds, where a female can get rid of a male's sperm without his knowledge.

Victorian cartoonists quickly picked up on Darwin's ideas about display in sexual selection. Here he is fascinated by the apparent steatopygia in the latest fashion.

Finally, sexual conflict is said to occur between breeding partners, sometimes leading to an evolutionary arms race between males and females. Sexual selection can also occur as a product of pheromone release, such as with the stingless bee, Trigona corvina.

Female mating preferences are widely recognized as being responsible for the rapid and divergent evolution of male secondary sexual traits. Females of many animal species prefer to mate with males with external ornaments—exaggerated features of morphology such as elaborate sex organs. These preferences may arise when an arbitrary female preference for some aspect of male morphology—initially, perhaps, a result of genetic drift—creates, in due course, selection for males with the appropriate ornament. One interpretation of this is known as the sexy son hypothesis. Alternatively, genes that enable males to develop impressive ornaments or fighting ability may simply show off greater disease resistance or a more efficient metabolism, features that also benefit females. This idea is known as the good genes hypothesis.

Bright colors that develop in animals during mating season function to attract partners. It has been suggested that there is a causal link between strength of display of ornaments involved in sexual selection and free radical biology. To test this idea, experiments were performed on male painted dragon lizards. Male lizards are brightly conspicuous in their breeding coloration, but their color declines with aging. Experiments involving administration of antioxidants to these males led to the conclusion that breeding coloration is a reflection of innate anti-oxidation capacity that protects against oxidative damage, including oxidative DNA damage. Thus color could act as a "health certificate" that allows females to visualize the underlying oxidative stress induced damage in potential mates.

Darwin conjectured that heritable traits such as beards and hairlessness in different human populations are results of sexual selection in humans. Geoffrey Miller has hypothesized that many human behaviours not clearly tied to survival benefits, such as humour, music, visual art, verbal creativity, and some forms of altruism, are courtship adaptations that have been favoured through sexual selection. In that view, many human artefacts could be considered subject to sexual selection as part of the extended phenotype, for instance clothing that enhances sexually selected traits. Some argue that the evolution of human intelligence is a sexually selected trait, as it would not confer enough fitness in itself relative to its high maintenance costs.

Fisherian runaway

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Fisherian_runaway 

 

The peacock tail in flight, the classic example of an ornament assumed to be a Fisherian runaway

Fisherian runaway or runaway selection is a sexual selection mechanism proposed by the mathematical biologist Ronald Fisher in the early 20th century, to account for the evolution of exaggerated male ornamentation by persistent, directional female choice. An example is the colourful and elaborate peacock plumage compared to the relatively subdued peahen plumage; the costly ornaments, notably the bird's extremely long tail, appear to be incompatible with natural selection. Fisherian runaway can be postulated to include sexually dimorphic phenotypic traits such as behavior expressed by a particular sex.

Extreme and apparently maladaptive sexual dimorphism represented a paradox for evolutionary biologists from Charles Darwin's time up to the modern synthesis. Darwin attempted to resolve the paradox by assuming heredity for both the preference and the ornament, and supposed an "aesthetic sense" in higher animals, leading to powerful selection of both characteristics in subsequent generations. Fisher developed the theory further by assuming genetic correlation between the preference and the ornament, that initially the ornament signalled greater potential fitness (the likelihood of leaving more descendants), so preference for the ornament had a selective advantage. Subsequently, if strong enough, female preference for exaggerated ornamentation in mate selection could be enough to undermine natural selection even when the ornament has become non-adaptive. Over subsequent generations this could lead to runaway selection by positive feedback, and the speed with which the trait and the preference increase could (until counter-selection interferes) increase exponentially.

Fisherian runaway has been difficult to demonstrate empirically, because it has been difficult to detect both an underlying genetic mechanism and a process by which it is initiated.

Female (left) and male (right) pheasant, a sexually dimorphic species

 

Peacock spider males perform courtship dances that display their boldly patterned mandibles, legs, and abdomens. Females are cryptic brown.

History

From Charles Darwin to Ronald Fisher

Charles Darwin published a book on sexual selection in 1871 called The Descent of Man, and Selection in Relation to Sex, which garnered interest upon its release but by the 1880s the ideas had been deemed too controversial and were largely neglected. Alfred Russel Wallace disagreed with Darwin, particularly after Darwin's death, that sexual selection was a real phenomenon.

Ronald Fisher was one of the few other biologists to engage with the question. When Wallace stated that animals show no sexual preference in his 1915 paper, The evolution of sexual preference, Fisher publicly disagreed:

The objection raised by Wallace ... that animals do not show any preference for their mates on account of their beauty, and in particular that female birds do not choose the males with the finest plumage, always seemed to the writer a weak one; partly from our necessary ignorance of the motives from which wild animals choose between a number of suitors; partly because there remains no satisfactory explanation either of the remarkable secondary sexual characters themselves, or of their careful display in love-dances, or of the evident interest aroused by these antics in the female; and partly also because this objection is apparently associated with the doctrine put forward by Sir Alfred Wallace in the same book, that the artistic faculties in man belong to his "spiritual nature," and therefore have come to him independently of his "animal nature" produced by natural selection.

— R.A. Fisher (1915)

Fisher, in the foundational 1930 book, The Genetical Theory of Natural Selection, first outlined a model by which runaway inter-sexual selection could lead to sexually dimorphic male ornamentation based upon female choice and a preference for "attractive" but otherwise non-adaptive traits in male mates. He suggested that selection for traits that increase fitness may be quite common:

Occasions may not be infrequent when a sexual preference of a particular kind may confer a selective advantage, and therefore become established in the species. Whenever appreciable differences exist in a species, which are in fact correlated with selective advantage, there will be a tendency to select also those individuals of the opposite sex which most clearly discriminate the difference to be observed, and which most decidedly prefer the more advantageous type. Sexual preference originated in this way may or may not confer any direct advantage upon the individuals selected, and so hasten the effect of the Natural Selection in progress. It may therefore be far more widespread than the occurrence of striking secondary sexual characters.

— R.A. Fisher (1930)

A strong female choice for the expression alone, as opposed to the function, of a male ornament can oppose and undermine the forces of natural selection and result in the runaway sexual selection that leads to the further exaggeration of the ornament (as well as the preference) until the costs (incurred by natural selection) of the expression become greater than the benefit (bestowed by sexual selection).

Peacocks and sexual dimorphism

The peacock, on the right, is courting the peahen, on the left.

The plumage dimorphism of the peacock and peahen of the species within the genus Pavo is a prime example of the ornamentation paradox that has long puzzled evolutionary biologists; Darwin wrote in 1860:

The sight of a feather in a peacock’s tail, whenever I gaze at it, makes me sick!

The peacock's colorful and elaborate tail requires a great deal of energy to grow and maintain. It also reduces the bird's agility, and may increase the animal's visibility to predators. The tail appears to lower the overall fitness of the individuals who possess it. Yet, it has evolved, indicating that peacocks who have longer and more colorfully elaborate tails have some advantage over peacocks who don't. Fisherian runaway posits that the evolution of the peacock tail is made possible if peahens have a preference to mate with peacocks that possess a longer and more colourful tail. Peahens that select males with these tails in turn have male offspring that are more likely to have long and colourful tails and thus are more likely to be sexually successful themselves. Equally importantly, the female offspring of these peahens are more likely to have a preference for peacocks with longer and more colourful tails. However, though the relative fitness of males with large tails is higher than those without, the absolute fitness levels of all the members of the population (both male and female) is less than it would be if none of the peahens (or only a small number) had a preference for a longer or more colorful tail.

Mechanism

Initiation

Fisher outlined two fundamental conditions that must be fulfilled for the Fisherian runaway mechanism to lead to the evolution of extreme ornamentation:

1. Sexual preference in at least one of the sexes
2. A corresponding reproductive advantage to the preference.

Fisher argued in his 1915 paper, "The evolution of sexual preference" that the type of female preference necessary for Fisherian runaway could be initiated without any understanding or appreciation for beauty. Fisher suggested that any visible features that indicate fitness, that are not themselves adaptive, that draw attention, and that vary in their appearance amongst the population of males so that the females can easily compare them, would be enough to initiate Fisherian runaway. This suggestion is compatible with his theory, and indicates that the choice of feature is essentially arbitrary, and could be different in different populations. Such arbitrariness is borne out by mathematical modelling, and by observation of isolated populations of sandgrouse, where the males can differ markedly from those in other populations.

Genetic basis

Fisherian runaway assumes that sexual preference in females and ornamentation in males are both genetically variable (heritable).

If instead of regarding the existence of sexual preference as a basic fact to be established only by direct observation, we consider that the tastes of organisms ... be regarded as the products of evolutionary change, governed by the relative advantage which such tastes may confer. Whenever appreciable differences exist in a species ... there will be a tendency to select also those individuals of the opposite sex which most clearly discriminate the difference to be observed, and which most decidedly prefer the more advantageous type.
— R. A. Fisher (1930)

Female choice

Fisher argued that the selection for exaggerated male ornamentation is driven by the coupled exaggeration of female sexual preference for the ornament.

Certain remarkable consequences do, however, follow ... in a species in which the preferences of ... the female, have a great influence on the number of offspring left by individual males. ... development will proceed, so long as the disadvantage is more than counterbalanced by the advantage in sexual selection ... there will also be a net advantage in favour of giving to it a more decided preference.
— R. A. Fisher (1930)

Positive feedback

Over time a positive feedback mechanism, one that involves a loop in which an increase in a quantity causes a further increase in the same quantity, will see more exaggerated sons and choosier daughters being produced with each successive generation; resulting in the runaway selection for the further exaggeration of both the ornament and the preference (until the costs for producing the ornament outweigh the reproductive benefit of possessing it).

The two characteristics affected by such a process, namely [ornamental] development in the male, and sexual preference for such development in the female, must thus advance together, and … will advance with ever increasing speed. [I]t is easy to see that the speed of development will be proportional to the development already attained, which will therefore increase with time exponentially, or in a geometric progression.
— R. A. Fisher (1930)

Such a process must soon run against some check. Two such are obvious. If carried far enough … counterselection in favour of less ornamented males will be encountered to balance the advantage of sexual preference; … elaboration and … female preference will be brought to a standstill, and a condition of relative stability will be attained. It will be more effective still if the disadvantage to the males of their sexual ornaments so diminishes their numbers surviving, relative to the females, as to cut at the root of the process, by demising the reproductive advantage to be conferred by female preference.
— R. A. Fisher (1930)

Alternative hypotheses

Several alternative hypotheses use the same genetic runaway (or positive feedback) mechanism but differ in the mechanisms of the initiation. The sexy son hypothesis (also proposed by Fisher) suggests that females that choose desirably ornamented males will have desirably ornamented (or sexy) sons, and that the effect of that behaviour on spreading the female's genes through subsequent generations may outweigh other factors such as the level of parental investment by the father. Indicator hypotheses suggest that females choose desirably ornamented males because the cost of producing the desirable ornaments is indicative of good genes by way of the individual's vigour; for instance, the handicap principle proposes that females distinguish the best males by the measurable cost of certain visible features which have no other purpose, by analogy with a handicap race, in which the best horses carry the largest weights.

The sensory exploitation hypothesis proposes that sexual preferences for exaggerated traits are the result of sensory biases, such as that for supernormal stimuli.