Drake equation

From Wikipedia, the free encyclopedia

Dr. Frank Drake

The Drake equation is a probabilistic argument used to estimate the number of active, communicative extraterrestrial civilizations in the Milky Way galaxy.

The equation was written in 1961 by Frank Drake, not for purposes of quantifying the number of civilizations, but as a way to stimulate scientific dialogue at the first scientific meeting on the search for extraterrestrial intelligence (SETI). The equation summarizes the main concepts which scientists must contemplate when considering the question of other radio-communicative life. It is more properly thought of as a Fermi problem rather than as a serious attempt to nail down a precise number.

Criticism related to the Drake equation focuses not on the equation itself, but on the fact that the estimated values for several of its factors are highly conjectural, the combined effect being that the uncertainty associated with any derived value is so large that the equation cannot be used to draw firm conclusions.

Equation

The Drake equation is:

${\displaystyle N=R_{*}\cdot f_{\mathrm {p} }\cdot n_{\mathrm {e} }\cdot f_{\mathrm {l} }\cdot f_{\mathrm {i} }\cdot f_{\mathrm {c} }\cdot L}$

where:

N = the number of civilizations in our galaxy with which communication might be possible (i.e. which are on our current past light cone);

and

R_∗ = the average rate of star formation in our galaxy

f_p = the fraction of those stars that have planets

n_e = the average number of planets that can potentially support life per star that has planets

f_l = the fraction of planets that could support life that actually develop life at some point

f_i = the fraction of planets with life that actually go on to develop intelligent life (civilizations)

f_c = the fraction of civilizations that develop a technology that releases detectable signs of their existence into space

L = the length of time for which such civilizations release detectable signals into space

History

In September 1959, physicists Giuseppe Cocconi and Philip Morrison published an article in the journal Nature with the provocative title "Searching for Interstellar Communications". Cocconi and Morrison argued that radio telescopes had become sensitive enough to pick up transmissions that might be broadcast into space by civilizations orbiting other stars. Such messages, they suggested, might be transmitted at a wavelength of 21 cm (1,420.4 MHz). This is the wavelength of radio emission by neutral hydrogen, the most common element in the universe, and they reasoned that other intelligences might see this as a logical landmark in the radio spectrum.

Two months later, Harvard University astronomy professor Harlow Shapley speculated on the number of inhabited planets in the universe, saying "The universe has 10 million, million, million suns (10 followed by 18 zeros) similar to our own. One in a million has planets around it. Only one in a million million has the right combination of chemicals, temperature, water, days and nights to support planetary life as we know it. This calculation arrives at the estimated figure of 100 million worlds where life has been forged by evolution."

Seven months after Cocconi and Morrison published their article, Drake made the first systematic search for signals from communicative extraterrestrial civilizations. Using the 25 m dish of the National Radio Astronomy Observatory in Green Bank, West Virginia, Drake monitored two nearby Sun-like stars: Epsilon Eridani and Tau Ceti. In this project, which he called Project Ozma, he slowly scanned frequencies close to the 21 cm wavelength for six hours per day from April to July 1960. The project was well designed, inexpensive, and simple by today's standards. It was also unsuccessful.
Soon thereafter, Drake hosted a "search for extraterrestrial intelligence" meeting on detecting their radio signals. The meeting was held at the Green Bank facility in 1961. The equation that bears Drake's name arose out of his preparations for the meeting.

As I planned the meeting, I realized a few day[s] ahead of time we needed an agenda. And so I wrote down all the things you needed to know to predict how hard it's going to be to detect extraterrestrial life. And looking at them it became pretty evident that if you multiplied all these together, you got a number, N, which is the number of detectable civilizations in our galaxy. This was aimed at the radio search, and not to search for primordial or primitive life forms.

—Frank Drake

The ten attendees were conference organizer J. Peter Pearman, Frank Drake, Philip Morrison, businessman and radio amateur Dana Atchley, chemist Melvin Calvin, astronomer Su-Shu Huang, neuroscientist John C. Lilly, inventor Barney Oliver, astronomer Carl Sagan and radio-astronomer Otto Struve. These participants dubbed themselves "The Order of the Dolphin" (because of Lilly's work on dolphin communication), and commemorated their first meeting with a plaque at the observatory hall.

Usefulness

The Allen Telescope Array for SETI

The Drake equation amounts to a summary of the factors affecting the likelihood that we might detect radio-communication from intelligent extraterrestrial life. The last four parameters, f_l, f_i, f_c, and L, are not known and are very difficult to estimate, with values ranging over many orders of magnitude (see criticism). Therefore, the usefulness of the Drake equation is not in the solving, but rather in the contemplation of all the various concepts which scientists must incorporate when considering the question of life elsewhere, and gives the question of life elsewhere a basis for scientific analysis. The Drake equation is a statement that stimulates intellectual curiosity about the universe around us, for helping us to understand that life as we know it is the end product of a natural, cosmic evolution, and for helping us realize how much we are a part of that universe. What the equation and the search for life has done is focus science on some of the other questions about life in the universe, specifically abiogenesis, the development of multi-cellular life and the development of intelligence itself.

Within the limits of our existing technology, any practical search for distant intelligent life must necessarily be a search for some manifestation of a distant technology. After about 50 years, the Drake equation is still of seminal importance because it is a 'road map' of what we need to learn in order to solve this fundamental existential question. It also formed the backbone of astrobiology as a science; although speculation is entertained to give context, astrobiology concerns itself primarily with hypotheses that fit firmly into existing scientific theories. Some 50 years of SETI have failed to find anything, even though radio telescopes, receiver techniques, and computational abilities have improved enormously since the early 1960s, but it has been discovered, at least, that our galaxy is not teeming with very powerful alien transmitters continuously broadcasting near the 21 cm hydrogen frequency. No one could say this in 1961.

Modifications

As many observers have pointed out, the Drake equation is a very simple model that does not include potentially relevant parameters,^[17] and many changes and modifications to the equation have been proposed. One line of modification, for example, attempts to account for the uncertainty inherent in many of the terms.

Others note that the Drake equation ignores many concepts that might be relevant to the odds of contacting other civilizations. For example, David Brin states: "The Drake equation merely speaks of the number of sites at which ETIs spontaneously arise. The equation says nothing directly about the contact cross-section between an ETIS and contemporary human society". Because it is the contact cross-section that is of interest to the SETI community, many additional factors and modifications of the Drake equation have been proposed.

Colonization 

It has been proposed to generalize the Drake equation to include additional effects of alien civilizations colonizing other star systems. Each original site expands with an expansion velocity v, and establishes additional sites that survive for a lifetime L. The result is a more complex set of 3 equations.

Reappearance factor 

The Drake equation may furthermore be multiplied by how many times an intelligent civilization may occur on planets where it has happened once. Even if an intelligent civilization reaches the end of its lifetime after, for example, 10,000 years, life may still prevail on the planet for billions of years, permitting the next civilization to evolve. Thus, several civilizations may come and go during the lifespan of one and the same planet. Thus, if n_r is the average number of times a new civilization reappears on the same planet where a previous civilization once has appeared and ended, then the total number of civilizations on such a planet would be 1 + n_r, which is the actual reappearance factor added to the equation.

The factor depends on what generally is the cause of civilization extinction. If it is generally by temporary uninhabitability, for example a nuclear winter, then n_r may be relatively high. On the other hand, if it is generally by permanent uninhabitability, such as stellar evolution, then n_r may be almost zero. In the case of total life extinction, a similar factor may be applicable for f_l, that is, how many times life may appear on a planet where it has appeared once.

METI factor 

Alexander Zaitsev said that to be in a communicative phase and emit dedicated messages are not the same. For example, humans, although being in a communicative phase, are not a communicative civilization; we do not practise such activities as the purposeful and regular transmission of interstellar messages. For this reason, he suggested introducing the METI factor (messaging to extraterrestrial intelligence) to the classical Drake equation.^[20] He defined the factor as "the fraction of communicative civilizations with clear and non-paranoid planetary consciousness", or alternatively expressed, the fraction of communicative civilizations that actually engage in deliberate interstellar transmission.

The METI factor is somewhat misleading since active, purposeful transmission of messages by a civilization is not required for them to receive a broadcast sent by another that is seeking first contact. It is merely required they have capable and compatible receiver systems operational; however, this is a variable humans cannot accurately estimate.

Biogenic gases 

Astronomer Sara Seager proposed a revised equation that focuses on the search for planets with biosignature gases. These gases are produced by living organisms that can accumulate in a planet atmosphere to levels that can be detected with remote space telescopes.

The Seager equation looks like this:

$${\displaystyle N=N_{*}\cdot F_{\mathrm {Q} }\cdot F_{\mathrm {HZ} }\cdot F_{\mathrm {O} }\cdot F_{\mathrm {L} }\cdot F_{\mathrm {S} }}$$

where:

N = the number of planets with detectable signs of life

N_∗ = the number of stars observed

F_Q = the fraction of stars that are quiet

F_HZ = the fraction of stars with rocky planets in the habitable zone

F_O = the fraction of those planets that can be observed

F_L = the fraction that have life

F_S = the fraction on which life produces a detectable signature gas

Seager stresses, “We’re not throwing out the Drake Equation, which is really a different topic,” explaining, “Since Drake came up with the equation, we have discovered thousands of exoplanets. We as a community have had our views revolutionized as to what could possibly be out there. And now we have a real question on our hands, one that’s not related to intelligent life: Can we detect any signs of life in any way in the very near future?”

Estimates

Original estimates

There is considerable disagreement on the values of these parameters, but the 'educated guesses' used by Drake and his colleagues in 1961 were:

• R_∗ = 1 yr⁻¹ (1 star formed per year, on the average over the life of the galaxy; this was regarded as conservative)
• f_p = 0.2 to 0.5 (one fifth to one half of all stars formed will have planets)
• n_e = 1 to 5 (stars with planets will have between 1 and 5 planets capable of developing life)
• f_l = 1 (100% of these planets will develop life)
• f_i = 1 (100% of which will develop intelligent life)
• f_c = 0.1 to 0.2 (10–20% of which will be able to communicate)
• L = 1000 to 100,000,000 years (which will last somewhere between 1000 and 100,000,000 years)

Inserting the above minimum numbers into the equation gives a minimum N of 20. Inserting the maximum numbers gives a maximum of 50,000,000. Drake states that given the uncertainties, the original meeting concluded that N ≈ L, and there were probably between 1000 and 100,000,000 civilizations in the Milky Way galaxy.

Current estimates

This section discusses and attempts to list the best current estimates for the parameters of the Drake equation.

Rate of star creation in our galaxy, R_∗

Latest calculations from NASA and the European Space Agency indicate that the current rate of star formation in our galaxy is about 0.68–1.45 M_☉ of material per year. To get the number of stars per year, this must account for the initial mass function (IMF) for stars, where the average new star mass is about 0.5 M_☉. This gives a star formation rate of about 1.5–3 stars per year.

Fraction of those stars that have planets, f_p

Recent analysis of microlensing surveys has found that f_p may approach 1—that is, stars are orbited by planets as a rule, rather than the exception; and that there are one or more bound planets per Milky Way star.

Average number of planets that might support life per star that has planets n_e

In November 2013, astronomers reported, based on Kepler space mission data, that there could be as many as 40 billion Earth-sized planets orbiting in the habitable zones of sun-like stars and red dwarf stars within the Milky Way Galaxy. 11 billion of these estimated planets may be orbiting sun-like stars. Since there are about 100 billion stars in the galaxy, this implies f_p · n_e is roughly 0.4. The nearest planet in the habitable zone is Proxima Centauri b, which is as close as about 4.2 light-years away.

The consensus at the Green Bank meeting was that n_e had a minimum value between 3 and 5. Dutch science journalist Govert Schilling has opined that this is optimistic. Even if planets are in the habitable zone, the number of planets with the right proportion of elements is difficult to estimate. Brad Gibson, Yeshe Fenner, and Charley Lineweaver determined that about 10% of star systems in the Milky Way galaxy are hospitable to life, by having heavy elements, being far from supernovae and being stable for a sufficient time.

The discovery of numerous gas giants in close orbit with their stars has introduced doubt that life-supporting planets commonly survive the formation of their stellar systems. So-called hot Jupiters may migrate from distant orbits to near orbits, in the process disrupting the orbits of habitable planets.

On the other hand, the variety of star systems that might have habitable zones is not just limited to solar-type stars and Earth-sized planets. It is now estimated that even tidally locked planets close to red dwarf stars might have habitable zones, although the flaring behavior of these stars might argue against this. The possibility of life on moons of gas giants (such as Jupiter's moon Europa, or Saturn's moon Titan) adds further uncertainty to this figure.

The authors of the rare Earth hypothesis propose a number of additional constraints on habitability for planets, including being in galactic zones with suitably low radiation, high star metallicity, and low enough density to avoid excessive asteroid bombardment. They also propose that it is necessary to have a planetary system with large gas giants which provide bombardment protection without a hot Jupiter; and a planet with plate tectonics, a large moon that creates tidal pools, and moderate axial tilt to generate seasonal variation.

Fraction of the above that actually go on to develop life, f_l

Geological evidence from the Earth suggests that f_l may be high; life on Earth appears to have begun around the same time as favorable conditions arose, suggesting that abiogenesis may be relatively common once conditions are right. However, this evidence only looks at the Earth (a single model planet), and contains anthropic bias, as the planet of study was not chosen randomly, but by the living organisms that already inhabit it (ourselves). From a classical hypothesis testing standpoint, there are zero degrees of freedom, permitting no valid estimates to be made. If life were to be found on Mars, Europa, Enceladus or Titan that developed independently from life on Earth it would imply a value for f_l close to 1. While this would raise the degrees of freedom from zero to one, there would remain a great deal of uncertainty on any estimate due to the small sample size, and the chance they are not really independent.

Countering this argument is that there is no evidence for abiogenesis occurring more than once on the Earth — that is, all terrestrial life stems from a common origin. If abiogenesis were more common it would be speculated to have occurred more than once on the Earth. Scientists have searched for this by looking for bacteria that are unrelated to other life on Earth, but none have been found yet. It is also possible that life arose more than once, but that other branches were out-competed, or died in mass extinctions, or were lost in other ways. Biochemists Francis Crick and Leslie Orgel laid special emphasis on this uncertainty: "At the moment we have no means at all of knowing" whether we are "likely to be alone in the galaxy (Universe)" or whether "the galaxy may be pullulating with life of many different forms." As an alternative to abiogenesis on Earth, they proposed the hypothesis of directed panspermia, which states that Earth life began with "microorganisms sent here deliberately by a technological society on another planet, by means of a special long-range unmanned spaceship".

Fraction of the above that develops intelligent life, f_i

This value remains particularly controversial. Those who favor a low value, such as the biologist Ernst Mayr, point out that of the billions of species that have existed on Earth, only one has become intelligent and from this, infer a tiny value for f_i. Likewise, the Rare Earth hypothesis, notwithstanding their low value for n_e above, also think a low value for f_i dominates the analysis. Those who favor higher values note the generally increasing complexity of life over time, concluding that the appearance of intelligence is almost inevitable, implying an f_i approaching 1. Skeptics point out that the large spread of values in this factor and others make all estimates unreliable.

In addition, while it appears that life developed soon after the formation of Earth, the Cambrian explosion, in which a large variety of multicellular life forms came into being, occurred a considerable amount of time after the formation of Earth, which suggests the possibility that special conditions were necessary. Some scenarios such as the snowball Earth or research into the extinction events have raised the possibility that life on Earth is relatively fragile. Research on any past life on Mars is relevant since a discovery that life did form on Mars but ceased to exist might raise our estimate of f_l but would indicate that in half the known cases, intelligent life did not develop.
Estimates of f_i have been affected by discoveries that the Solar System's orbit is circular in the galaxy, at such a distance that it remains out of the spiral arms for tens of millions of years (evading radiation from novae). Also, Earth's large moon may aid the evolution of life by stabilizing the planet's axis of rotation.

Fraction of the above revealing their existence via signal release into space, f_c

For deliberate communication, the one example we have (the Earth) does not do much explicit communication, though there are some efforts covering only a tiny fraction of the stars that might look for our presence. (See Arecibo message, for example). There is considerable speculation why an extraterrestrial civilization might exist but choose not to communicate. However, deliberate communication is not required, and calculations indicate that current or near-future Earth-level technology might well be detectable to civilizations not too much more advanced than our own. By this standard, the Earth is a communicating civilization.

Another question is what percentage of civilizations in the galaxy are close enough for us to detect, assuming that they send out signals. For example, existing Earth radio telescopes could only detect Earth radio transmissions from roughly a light year away.

Lifetime of such a civilization wherein it communicates its signals into space, L

Michael Shermer estimated L as 420 years, based on the duration of sixty historical Earthly civilizations. Using 28 civilizations more recent than the Roman Empire, he calculates a figure of 304 years for "modern" civilizations. It could also be argued from Michael Shermer's results that the fall of most of these civilizations was followed by later civilizations that carried on the technologies, so it is doubtful that they are separate civilizations in the context of the Drake equation. In the expanded version, including reappearance number, this lack of specificity in defining single civilizations does not matter for the end result, since such a civilization turnover could be described as an increase in the reappearance number rather than increase in L, stating that a civilization reappears in the form of the succeeding cultures. Furthermore, since none could communicate over interstellar space, the method of comparing with historical civilizations could be regarded as invalid.

David Grinspoon has argued that once a civilization has developed enough, it might overcome all threats to its survival. It will then last for an indefinite period of time, making the value for L potentially billions of years. If this is the case, then he proposes that the Milky Way galaxy may have been steadily accumulating advanced civilizations since it formed. He proposes that the last factor L be replaced with f_IC · T, where f_IC is the fraction of communicating civilizations become "immortal" (in the sense that they simply do not die out), and T representing the length of time during which this process has been going on. This has the advantage that T would be a relatively easy to discover number, as it would simply be some fraction of the age of the universe.

It has also been hypothesized that once a civilization has learned of a more advanced one, its longevity could increase because it can learn from the experiences of the other.

The astronomer Carl Sagan speculated that all of the terms, except for the lifetime of a civilization, are relatively high and the determining factor in whether there are large or small numbers of civilizations in the universe is the civilization lifetime, or in other words, the ability of technological civilizations to avoid self-destruction. In Sagan's case, the Drake equation was a strong motivating factor for his interest in environmental issues and his efforts to warn against the dangers of nuclear warfare.

Range of results

As many skeptics have pointed out, the Drake equation can give a very wide range of values, depending on the assumptions, and the values used in portions of the Drake equation are not well-established. In particular, the result can be N ≪ 1, meaning we are likely alone in the galaxy, or N ≫ 1, implying there are many civilizations we might contact. One of the few points of wide agreement is that the presence of humanity implies a probability of intelligence arising of greater than zero.
As an example of a low estimate, combining NASA's star formation rates, the rare Earth hypothesis value of f_p · n_e · f_l = 10⁻⁵, Mayr's view on intelligence arising, Drake's view of communication, and Shermer's estimate of lifetime:

R_∗ = 1.5–3 yr⁻¹, f_p · n_e · f_l = 10⁻⁵, f_i = 10⁻⁹, f_c = 0.2, and L = 304 years

gives:

N = 1.5 × 10⁻⁵ × 10⁻⁹ × 0.2 × 304 = 9.1 × 10⁻¹¹

i.e., suggesting that we are probably alone in this galaxy, and possibly in the observable universe.
On the other hand, with larger values for each of the parameters above, values of N can be derived that are greater than 1. The following higher values that have been proposed for each of the parameters:

R_∗ = 1.5–3 yr⁻¹, f_p = 1, n_e = 0.2, f_l = 0.13, f_i = 1, f_c = 0.2, and L = 10⁹ years

Use of these parameters gives:

N = 3 × 1 × 0.2 × 0.13 × 1 × 0.2 × 10⁹ = 15,600,000

Monte Carlo simulations of estimates of the Drake equation factors based on a stellar and planetary model of the Milky Way have resulted in the number of civilizations varying by a factor of 100.

Has intelligent life ever existed?

The Drake equation can be modified to determine just how unlikely intelligent life must be, to give the result that Earth has the only intelligent life that has ever arisen, either in our galaxy or the universe as a whole. This simplifies the calculation by removing the lifetime and communication constraints. Since star and planets counts are known, this leaves the only unknown as the odds that a habitable planet ever develops intelligent life. For Earth to have the only civilization that has ever occurred in the universe, then the odds of any habitable planet ever developing such a civilization must be less than 2.5×10⁻²⁴. Similarly, for Earth to host the only civilization in our galaxy for all time, the odds of a habitable zone planet ever hosting intelligent life must be less than 1.7×10⁻¹¹ (about 1 in 60 billion). The figure for the universe implies that it is highly unlikely that Earth hosts the only intelligent life that has ever occurred. The figure for our galaxy suggests that other civilizations may have occurred or will likely occur in our galaxy.

Criticism

Criticism of the Drake equation follows mostly from the observation that several terms in the equation are largely or entirely based on conjecture. Star formation rates are well-known, and the incidence of planets has a sound theoretical and observational basis, but the other terms in the equation become very speculative. The uncertainties revolve around our understanding of the evolution of life, intelligence, and civilization, not physics. No statistical estimates are possible for some of the parameters, where only one example is known. The net result is that the equation cannot be used to draw firm conclusions of any kind, and the resulting margin of error is huge, far beyond what some consider acceptable or meaningful.

One reply to such criticisms is that even though the Drake equation currently involves speculation about unmeasured parameters, it was intended as a way to stimulate dialogue on these topics. Then the focus becomes how to proceed experimentally. Indeed, Drake originally formulated the equation merely as an agenda for discussion at the Green Bank conference.

Fermi paradox

The pessimists' most telling argument in the SETI debate stems not from theory or conjecture but from an actual observation: the presumed lack of extraterrestrial contact. A civilization lasting for tens of millions of years might be able to travel anywhere in the galaxy, even at the slow speeds foreseeable with our own kind of technology. Furthermore, no confirmed signs of intelligence elsewhere have been recognized as such, either in our galaxy or in the observable universe of 2 trillion galaxies. According to this line of thinking, the tendency to fill up all available territory seems to be a universal trait of living things, so the Earth should have already been colonized, or at least visited, but no evidence of this exists. Hence Fermi's question "Where is everybody?".

A large number of explanations have been proposed to explain this lack of contact; a book published in 2015 elaborated on 75 different explanations. In terms of the Drake Equation, the explanations can be divided into three classes:

• Few intelligent civilizations ever arise. This is an argument that at least one of the first few terms, R_∗ · f_p · n_e · f_l · f_i, has a low value. The most common suspect is f_i, but explanations such as the rare Earth hypothesis argue that n_e is the small term.
• Intelligent civilizations exist, but we see no evidence, meaning f_c is small. Typical arguments include that civilizations are too far apart, it is too expensive to spread throughout the galaxy, civilizations broadcast signals for only a brief period of time, it is dangerous to communicate, and many others.
• The lifetime of intelligent, communicative civilizations is short, meaning the value of L is small. Drake suggested that a large number of extraterrestrial civilizations would form, and he further speculated that the lack of evidence of such civilizations may be because technological civilizations tend to disappear rather quickly. Typical explanations include it is the nature of intelligent life to destroy itself, it is the nature of intelligent life to destroy others, they tend to be destroyed by natural events, and others.

These lines of reasoning lead to the Great Filter hypothesis, which states that since there are no observed extraterrestrial civilizations, despite the vast number of stars, then some step in the process must be acting as a filter to reduce the final value. According to this view, either it is very difficult for intelligent life to arise, or the lifetime of such civilizations, or the period of time they reveal their existence, must be relatively short.

In fiction and popular culture

The equation was cited by Gene Roddenberry as supporting the multiplicity of inhabited planets shown on Star Trek, the television series he created. However, Roddenberry did not have the equation with him, and he was forced to "invent" it for his original proposal. The invented equation created by Roddenberry is:

${\displaystyle Ff^{2}(MgE)-C^{1}Ri^{1}\cdot M=L/So}$

However, a number raised to the first power is merely the number itself.

Group selection

From Wikipedia, the free encyclopedia

 

Early explanations of social behavior, such as the lekking of blackcock, spoke of "the good of the species". Blackcocks at the Lek watercolour and bodycolour by Archibald Thorburn, 1901.

Group selection is a proposed mechanism of evolution in which natural selection acts at the level of the group, instead of at the more conventional level of the individual.

Early authors such as V. C. Wynne-Edwards and Konrad Lorenz argued that the behavior of animals could affect their survival and reproduction as groups, speaking for instance of actions for the good of the species. From the mid 1960s, evolutionary biologists such as John Maynard Smith argued that natural selection acted primarily at the level of the individual. They argued on the basis of mathematical models that individuals would not altruistically sacrifice fitness for the sake of a group. They persuaded the majority of biologists that group selection did not occur, other than in special situations such as the haplodiploid social insects like honeybees (in the Hymenoptera), where kin selection was possible.

In 1994 David Sloan Wilson and Elliott Sober argued for multi-level selection, including group selection, on the grounds that groups, like individuals, could compete. In 2010 three authors including E. O. Wilson, known for his work on social insects especially ants, again revisited the arguments for group selection. They argued that group selection can occur when competition between two or more groups, some containing altruistic individuals who act cooperatively together, is more important for survival than competition between individuals within each group. Their proposals provoked a strong rebuttal from a large group of evolutionary biologists.

As of yet, there is no clear consensus among biologists regarding the importance of group selection.  Steven Pinker expressed his ambivalence with the theory: "Human beings live in groups, are affected by the fortunes of their groups, and sometimes make sacrifices that benefit their groups. Does this mean that the human brain has been shaped by natural selection to promote the welfare of the group in competition with other groups, even when it damages the welfare of the person and his or her kin?... I think that this reasonableness is an illusion. The more carefully you think about group selection, the less sense it makes, and the more poorly it fits the facts of human psychology and history." However, there is active debate among specialists in many fields of study. It is possible that a theory of group selection can be modified to provide valuable explanations. Group selection could be useful for understanding the evolution of human culture, since humans form groups that are unlike any other animal. Group selection may be used to understand human history. Some researchers have used the framework to understand the development of human morality.

Early Developments

Charles Darwin developed the theory of evolution in his book, Origin of Species. Darwin also made the first suggestion of group selection in The Descent of Man that the evolution of groups could affect the survival of individuals. He wrote, "If one man in a tribe... invented a new snare or weapon, the tribe would increase in number, spread, and supplant other tribes. In a tribe thus rendered more numerous there would always be a rather better chance of the birth of other superior and inventive members."

Once Darwinism had been accepted, animal behavior was glibly explained with unsubstantiated hypotheses about survival value, which was largely taken for granted. The naturalist Konrad Lorenz had argued loosely in books like On Aggression (1966) that animal behavior patterns were "for the good of the species", without actually studying survival value in the field; Richard Dawkins noted that Lorenz was a "'good of the species' man" so accustomed to group selection thinking that he did not realize his views "contravened orthodox Darwinian theory". The ethologist Niko Tinbergen praised Lorenz for his interest in the survival value of behavior, and naturalists enjoyed Lorenz's writings for the same reason. In 1962, group selection was used as a popular explanation for adaptation by the zoologist V. C. Wynne-Edwards. In 1976, Richard Dawkins wrote a well-known book on the importance of evolution at the level of the gene or the individual, The Selfish Gene.

Social behavior in honeybees is explained by kin selection: their haplodiploid inheritance system makes workers very closely related to their queen (centre).

From the mid 1960s, evolutionary biologists argued that natural selection acted primarily at the level of the individual. In 1964, John Maynard Smith, C. M. Perrins (1964), and George C. Williams in his 1966 book Adaptation and Natural Selection cast serious doubt on group selection as a major mechanism of evolution; Williams's 1971 book Group Selection assembled writings from many authors on the same theme.

It was at that time generally agreed that the primary exception of social group selection was in the social insects, and the explanation was limited to the unique inheritance system (involving haplodiploidy) of the eusocial Hymenoptera such as honeybees, which encourages kin selection, since workers are closely related.

Kin selection and inclusive fitness theory

Early group selection models assumed that genes acted independently, for example a gene that coded for cooperation or altruism. Genetically-based reproduction of individuals implies that, in group formation, the altruistic genes would need a way to act for the benefit of members in the group to enhance the fitness of many individuals with the same gene. But it is expected from this model that individuals of the same species would compete against each other for the same resources. This would put cooperating individuals at a disadvantage, making genes for cooperation tend to be eliminated. Group selection on the level of the species is flawed because it is difficult to see how selective pressures would be applied to competing/non-cooperating individuals.

Experiments from the late 1970s suggested that selection involving groups was possible. Kin selection between related individuals is accepted as an explanation of altruistic behavior. In this model, genetically related individuals cooperate because survival advantages to one individual also benefit kin who share some fraction of the same genes, giving a mechanism for favoring genetic selection.

Inclusive fitness theory, first proposed by W. D. Hamilton in the early 1960s, gives a selection criterion for evolution of social traits when social behavior is costly to an individual organism's survival and reproduction. This behavior could emerge under conditions such that the statistical likelihood that benefits accrue to the survival and reproduction of other organisms whom also carry the social trait. Inclusive fitness theory is a general treatment of the statistical probabilities of social traits accruing to any other organisms likely to propagate a copy of the same social trait. Kin selection theory treats the narrower but simpler case of the benefits to close genetic relatives (or what biologists call 'kin') who may also carry and propagate the trait. A significant group of biologists support inclusive fitness as the explanation for social behavior in a wide range of species, as supported by experimental data. An article was published in Nature with over a hundred coauthors.

One of the questions about kin selection is the requirement that individuals must know if other individuals are related to them, or kin recognition. Any altruistic act has to preserve similar genes. One argument given by Hamilton is that many individuals operate in "viscous" conditions, so that they live in physical proximity to relatives. Under these conditions, they can act altruistically to any other individual, and it is likely that the other individual will be related. This population structure builds a continuum between individual selection, kin selection, kin group selection and group selection without a clear boundary for each level. However, early theoretical models by D.S. Wilson et al. and Taylor showed that pure population viscosity cannot lead to cooperation and altruism. This is because any benefit generated by kin cooperation is exactly cancelled out by kin competition; additional offspring from cooperation are eliminated by local competition. Mitteldorf and D. S. Wilson later showed that if the population is allowed to fluctuate, then local populations can temporarily store the benefit of local cooperation and promote the evolution of cooperation and altruism. By assuming individual differences in adaptations, Yang further showed that the benefit of local altruism can be stored in the form of offspring quality and thus promote the evolution of altruism even if the population does not fluctuate. This is because local competition among more individuals resulting from local altruism increases the average local fitness of the individuals that survive.

Another explanation for the recognition of genes for altruism is that a single trait, group reciprocal kindness, is capable of explaining the vast majority of altruism that is generally accepted as "good" by modern societies. The phenotype of altruism relies on recognition of the altruistic behavior by itself. The trait of kindness will be recognized by sufficiently intelligent and undeceived organisms in other individuals with the same trait. Moreover, the existence of such a trait predicts a tendency for kindness to unrelated organisms that are apparently kind, even if the organisms are of a completely different species. The gene need not be exactly the same, so long as the effect or phenotype is similar. Multiple versions of the gene—or even meme—would have virtually the same effect. This explanation was given by Richard Dawkins as an analogy of a man with a green beard. Green-bearded men tend to cooperate with each other simply by seeing a green beard, where the green beard trait is incidentally linked to the reciprocal kindness trait.

Multilevel selection theory

Kin selection or inclusive fitness is accepted as an explanation for cooperative behavior in many species, but there are some species, including some human behavior, that are difficult to explain with only this approach. In particular, it doesn't seem to explain the cause of the (relatively) rapid rise of human civilization. David Sloan Wilson has argued that other factors must also be considered in evolution. Since the 1990s, group selection models have seen a resurgence and further refinement.

Early group selection models were flawed because they assumed that genes acted independently; but genetically-based interactions among individuals are ubiquitous in group formation because genes must cooperate for the benefit of association in groups to enhance the fitness of group members. Additionally, group selection on the level of the species is flawed because it is difficult to see how selective pressures would be applied; selection in social species of groups against other groups, rather than the species entire, seems to be the level at which selective pressures are plausible. On the other hand, kin selection is accepted as an explanation of altruistic behavior. Some biologists argue that kin selection and multilevel selection are both needed to "obtain a complete understanding of the evolution of a social behavior system".

In 1994 David Sloan Wilson and Elliott Sober argued that the case against group selection had been overstated. They considered whether groups can have functional organization in the same way as individuals, and consequently whether groups can be "vehicles" for selection. They do not posit evolution on the level of the species, but selective pressures that winnow out small groups within a species, e.g. groups of social insects or primates. Groups that cooperate better might survive and reproduce more than those that did not. Resurrected in this way, Wilson & Sober's new group selection is called multilevel selection theory.

In 2010, M. A. Nowak, C. E. Tarnita and E. O. Wilson argued for multi-level selection, including group selection, to correct what they saw as deficits in the explanatory power of inclusive fitness. The response was a back-lash from 137 other evolutionary biologists who argued "that their arguments are based upon a misunderstanding of evolutionary theory and a misrepresentation of the empirical literature".

David Sloan Wilson and Elliott Sober's 1994 Multilevel Selection Model, illustrated by a nested set of Russian matryoshka dolls. Wilson himself compared his model to such a set.

Wilson compared the layers of competition and evolution to nested sets of Russian matryoshka dolls. The lowest level is the genes, next come the cells, then the organism level and finally the groups. The different levels function cohesively to maximize fitness, or reproductive success. The theory asserts that selection for the group level, involving competition between groups, must outweigh the individual level, involving individuals competing within a group, for a group-benefiting trait to spread.

Peter Turchin uses the same analogy of matryoshka dolls, but uses it to show the stepwise increase in size of social groups, from villages, tribes, regional societies, to nations, and finally to empires or civilizations. He points out that humans have the capability to consider themselves as a member of the entire range of affiliations, like the smallest doll inside the entire assembly of dolls.

Multilevel selection theory focuses on the phenotype because it looks at the levels that selection directly acts upon. For humans, social norms can be argued to reduce individual level variation and competition, thus shifting selection to the group level. The assumption is that variation between different groups is larger than variation within groups. Competition and selection can operate at all levels regardless of scale. Wilson wrote, "At all scales, there must be mechanisms that coordinate the right kinds of action and prevent disruptive forms of self-serving behavior at lower levels of social organization." E. O. Wilson summarized, "In a group, selfish individuals beat altruistic individuals. But, groups of altruistic individuals beat groups of selfish individuals."

Wilson ties the multilevel selection theory regarding humans to another theory, gene-culture coevolution, by acknowledging that culture seems to characterize a group-level mechanism for human groups to adapt to environmental changes.

MLS theory can be used to evaluate the balance between group selection and individual selection in specific cases. An experiment by William Muir compared egg productivity in hens, showing that a hyper-aggressive strain had been produced through individual selection, leading to many fatal attacks after only six generations; by implication, it could be argued that group selection must have been acting to prevent this in real life. Group selection has most often been postulated in humans and, notably, eusocial Hymenoptera that make cooperation a driving force of their adaptations over time and have a unique system of inheritance involving haplodiploidy that allows the colony to function as an individual while only the queen reproduces.

Wilson and Sober's work revived interest in multilevel selection. In a 2005 article, E. O. Wilson argued that kin selection could no longer be thought of as underlying the evolution of extreme sociality, for two reasons. First, he suggested, the argument that haplodiploid inheritance (as in the Hymenoptera) creates a strong selection pressure towards nonreproductive castes is mathematically flawed. Second, eusociality no longer seems to be confined to the hymenopterans; increasing numbers of highly social taxa have been found in the years since Wilson's foundational text Sociobiology: A New Synthesis was published in 1975. These including a variety of insect species, as well as two rodent species (the naked mole-rat and the Damaraland mole rat). Wilson suggests the equation for Hamilton's rule:

rb > c

(where b represents the benefit to the recipient of altruism, c the cost to the altruist, and r their degree of relatedness) should be replaced by the more general equation

rb_k + b_e > c

in which b_k is the benefit to kin (b in the original equation) and b_e is the benefit accruing to the group as a whole. He then argues that, in the present state of the evidence in relation to social insects, it appears that b_e>rb_k, so that altruism needs to be explained in terms of selection at the colony level rather than at the kin level. However, kin selection and group selection are not distinct processes, and the effects of multi-level selection are already accounted for in Hamilton's rule, rb>c, provided that an expanded definition of r, not requiring Hamilton's original assumption of direct genealogical relatedness, is used, as proposed by E. O. Wilson himself.

Spatial populations of predators and prey show restraint of reproduction at equilibrium, both individually and through social communication, as originally proposed by Wynne-Edwards. While these spatial populations do not have well-defined groups for group selection, the local spatial interactions of organisms in transient groups are sufficient to lead to a kind of multi-level selection. There is however as yet no evidence that these processes operate in the situations where Wynne-Edwards posited them.

Rauch et al.'s analysis of a host-parasite situation, which was recognised as one where group selection was possible even by E. O. Wilson (1975), is broadly hostile to the whole idea of group selection. Specifically, the parasites do not individually moderate their transmission; rather, more transmissible variants "continually arise and grow rapidly for many generations but eventually go extinct before dominating the system."

Applications

Differing evolutionarily stable strategies

The problem with group selection is that for a whole group to get a single trait, it must spread through the whole group first by regular evolution. But, as J. L. Mackie suggested, when there are many different groups, each with a different evolutionarily stable strategy, there is selection between the different strategies, since some are worse than others. For example, a group where altruism was universal would indeed outcompete a group where every creature acted in its own interest, so group selection might seem feasible; but a mixed group of altruists and non-altruists would be vulnerable to cheating by non-altruists within the group, so group selection would collapse.

Implications in population biology

Social behaviors such as altruism and group relationships can impact many aspects of population dynamics, such as intraspecific competition and interspecific interactions. In 1871, Darwin argued that group selection occurs when the benefits of cooperation or altruism between subpopulations are greater than the individual benefits of egotism within a subpopulation. This supports the idea of multilevel selection, but kinship also plays an integral role because many subpopulations are composed of closely related individuals. An example of this can be found in lions, which are simultaneously cooperative and territorial. Within a pride, males protect the pride from outside males, and females, who are commonly sisters, communally raise cubs and hunt. However, this cooperation seems to be density dependent. When resources are limited, group selection favors prides that work together to hunt. When prey is abundant, cooperation is no longer beneficial enough to outweigh the disadvantages of altruism, and hunting is no longer cooperative.

Interactions between different species can also be affected by multilevel selection. Predator-prey relationships can also be affected. Individuals of certain monkey species howl to warn the group of the approach of a predator. The evolution of this trait benefits the group by providing protection, but could be disadvantageous to the individual if the howling draws the predator's attention to them. By affecting these interspecific interactions, multilevel and kinship selection can change the population dynamics of an ecosystem.

Multilevel selection attempts to explain the evolution of altruistic behavior in terms of quantitative genetics. Increased frequency or fixation of altruistic alleles can be accomplished through kin selection, in which individuals engage in altruistic behavior to promote the fitness of genetically similar individuals such as siblings. However, this can lead to inbreeding depression, which typically lowers the overall fitness of a population. However, if altruism were to be selected for through an emphasis on benefit to the group as opposed to relatedness and benefit to kin, both the altruistic trait and genetic diversity could be preserved. However, relatedness should still remain a key consideration in studies of multilevel selection. Experimentally imposed multilevel selection on Japanese quail was more effective by an order of magnitude on closely related kin groups than on randomized groups of individuals.

Gene-culture coevolution in humans

Humanity has developed extremely rapidly, arguably through gene-culture coevolution, leading to complex cultural artefacts like the gopuram of the Sri Mariammam temple, Singapore.

Gene-culture coevolution (also called dual inheritance theory) is a modern hypothesis (applicable mostly to humans) that combines evolutionary biology and modern sociobiology to indicate group selection. It treats culture as a separate evolutionary system that acts in parallel to the usual genetic evolution to transform human traits. It is believed that this approach of combining genetic influence with cultural influence over several generations is not present in the other hypotheses such as reciprocal altruism and kin selection, making gene-culture evolution one of the strongest realistic hypotheses for group selection. Fehr provides evidence of group selection taking place in humans presently with experimentation through logic games such as prisoner’s dilemma, the type of thinking that humans have developed many generations ago.

Gene-culture coevolution allows humans to develop highly distinct adaptations to the local pressures and environments more quickly than with genetic evolution alone. Robert Boyd and Peter J. Richerson, two strong proponents of cultural evolution, postulate that the act of social learning, or learning in a group as done in group selection, allows human populations to accrue information over many generations. This leads to cultural evolution of behaviors and technology alongside genetic evolution. Boyd and Richerson believe that the ability to collaborate evolved during the Middle Pleistocene, a million years ago, in response to a rapidly changing climate.

In 2003, Herbert Gintis examined cultural evolution statistically, offering evidence that societies that promote pro-social norms have higher survival rates than societies that do not.

Gintis wrote that genetic and cultural evolution can work together. Genes transfer information in DNA, and cultures transfer information encoded in brains, artifacts, or documents. Language, tools, lethal weapons, fire, cooking, etc., have a long-term effect on genetics. For example, cooking led to a reduction of size of the human gut, since less digestion is needed for cooked food. Language led to a change in the human larynx and an increase in brain size. Projectile weapons led to changes in human hands and shoulders, such that humans are much better at throwing objects than the closest human relative, the chimpanzee.

Criticism

The use of the Price equation to support group selection was challenged by van Veelen in 2012, arguing that it is based on invalid mathematical assumptions.

Richard Dawkins and other advocates of the gene-centered view of evolution remain unconvinced about group selection. In particular, Dawkins suggests that group selection fails to make an appropriate distinction between replicators and vehicles.

The psychologist Steven Pinker concluded that "group selection has no useful role to play in psychology or social science", as it "is not a precise implementation of the theory of natural selection, as it is, say, in genetic algorithms or artificial life simulations. Instead it is a loose metaphor, more like the struggle among kinds of tires or telephones."

The evolutionary biologist Jerry Coyne summarized the arguments in The New York Times in non-technical terms as follows:

Group selection isn't widely accepted by evolutionists for several reasons. First, it's not an efficient way to select for traits, like altruistic behavior, that are supposed to be detrimental to the individual but good for the group. Groups divide to form other groups much less often than organisms reproduce to form other organisms, so group selection for altruism would be unlikely to override the tendency of each group to quickly lose its altruists through natural selection favoring cheaters. Further, little evidence exists that selection on groups has promoted the evolution of any trait. Finally, other, more plausible evolutionary forces, like direct selection on individuals for reciprocal support, could have made humans prosocial. These reasons explain why only a few biologists, like [David Sloan] Wilson and E. O. Wilson (no relation), advocate group selection as the evolutionary source of cooperation.

Evolutionary algorithm

From Wikipedia, the free encyclopedia

 

In artificial intelligence, an evolutionary algorithm (EA) is a subset of evolutionary computation, a generic population-based metaheuristic optimization algorithm. An EA uses mechanisms inspired by biological evolution, such as reproduction, mutation, recombination, and selection. Candidate solutions to the optimization problem play the role of individuals in a population, and the fitness function determines the quality of the solutions (see also loss function). Evolution of the population then takes place after the repeated application of the above operators.

Evolutionary algorithms often perform well approximating solutions to all types of problems because they ideally do not make any assumption about the underlying fitness landscape. Techniques from evolutionary algorithms applied to the modeling of biological evolution are generally limited to explorations of microevolutionary processes and planning models based upon cellular processes. In most real applications of EAs, computational complexity is a prohibiting factor. In fact, this computational complexity is due to fitness function evaluation. Fitness approximation is one of the solutions to overcome this difficulty. However, seemingly simple EA can solve often complex problems; therefore, there may be no direct link between algorithm complexity and problem complexity.

Implementation

Step One: Generate the initial population of individuals randomly. (First generation)

Step Two: Evaluate the fitness of each individual in that population (time limit, sufficient fitness achieved, etc.)

Step Three: Repeat the following regenerational steps until termination:

1. Select the best-fit individuals for reproduction. (Parents)
   
2. Breed new individuals through crossover and mutation operations to give birth to offspring.
   
3. Evaluate the individual fitness of new individuals.
   
4. Replace least-fit population with new individuals.

Types

Similar techniques differ in genetic representation and other implementation details, and the nature of the particular applied problem.

• Genetic algorithm – This is the most popular type of EA. One seeks the solution of a problem in the form of strings of numbers (traditionally binary, although the best representations are usually those that reflect something about the problem being solved), by applying operators such as recombination and mutation (sometimes one, sometimes both). This type of EA is often used in optimization problems. Another name for it is fetura, from the Latin for breeding.
• Genetic programming – Here the solutions are in the form of computer programs, and their fitness is determined by their ability to solve a computational problem.
• Evolutionary programming – Similar to genetic programming, but the structure of the program is fixed and its numerical parameters are allowed to evolve.
• Gene expression programming – Like genetic programming, GEP also evolves computer programs but it explores a genotype-phenotype system, where computer programs of different sizes are encoded in linear chromosomes of fixed length.
• Evolution strategy – Works with vectors of real numbers as representations of solutions, and typically uses self-adaptive mutation rates.
• Differential evolution – Based on vector differences and is therefore primarily suited for numerical optimization problems.
• Neuroevolution – Similar to genetic programming but the genomes represent artificial neural networks by describing structure and connection weights. The genome encoding can be direct or indirect.
• Learning classifier system – Here the solution is a set of classifiers (rules or conditions). A Michigan-LCS evolves at the level of individual classifiers whereas a Pittsburgh-LCS uses populations of classifier-sets. Initially, classifiers were only binary, but now include real, neural net, or S-expression types. Fitness is typically determined with either a strength or accuracy based reinforcement learning or supervised learning approach.

Comparison to biological processes

A possible limitation of many evolutionary algorithms is their lack of a clear genotype-phenotype distinction. In nature, the fertilized egg cell undergoes a complex process known as embryogenesis to become a mature phenotype. This indirect encoding is believed to make the genetic search more robust (i.e. reduce the probability of fatal mutations), and also may improve the evolvability of the organism. Such indirect (a.k.a. generative or developmental) encodings also enable evolution to exploit the regularity in the environment. Recent work in the field of artificial embryogeny, or artificial developmental systems, seeks to address these concerns. And gene expression programming successfully explores a genotype-phenotype system, where the genotype consists of linear multigenic chromosomes of fixed length and the phenotype consists of multiple expression trees or computer programs of different sizes and shapes.

Related techniques

Swarm algorithms include

• Ant colony optimization – Based on the ideas of ant foraging by pheromone communication to form paths. Primarily suited for combinatorial optimization and graph problems.
• The runner-root algorithm (RRA) is inspired by the function of runners and roots of plants in nature 
• Artificial bee colony algorithm – Based on the honey bee foraging behaviour. Primarily proposed for numerical optimization and extended to solve combinatorial, constrained and multi-objective optimization problems.
• Bees algorithm is based on the foraging behaviour of honey bees. It has been applied in many applications such as routing and scheduling.
• Cuckoo search is inspired by the brooding parasitism of the cuckoo species. It also uses Lévy flights, and thus it suits for global optimization problems.
• Particle swarm optimization – Based on the ideas of animal flocking behaviour. Also primarily suited for numerical optimization problems.

Other population-based metaheuristic methods

• Hunting Search - A method inspired by the group hunting of some animals such as wolves that organize their position to surround the prey, each of them relative to the position of the others and especially that of their leader. It is a continuous optimization method  adapted as a combinatorial optimization method.
• Adaptive dimensional search – Unlike nature-inspired metaheuristic techniques, an adaptive dimensional search algorithm does not implement any metaphor as an underlying principle. Rather it uses a simple performance-oriented method, based on the update of the search dimensionality ratio (SDR) parameter at each iteration.
• Firefly algorithm is inspired by the behavior of fireflies, attracting each other by flashing light. This is especially useful for multimodal optimization.
• Harmony search – Based on the ideas of musicians' behavior in searching for better harmonies. This algorithm is suitable for combinatorial optimization as well as parameter optimization.
• Gaussian adaptation – Based on information theory. Used for maximization of manufacturing yield, mean fitness or average information. See for instance Entropy in thermodynamics and information theory.
• Memetic algorithm – A hybrid method, inspired by Richard Dawkins' notion of a meme, it commonly takes the form of a population-based algorithm coupled with individual learning procedures capable of performing local refinements. Emphasizes the exploitation of problem-specific knowledge, and tries to orchestrate local and global search in a synergistic way.

Examples

The computer simulations Tierra and Avida attempt to model macroevolutionary dynamics.

Gallery

• A two-population EA search over a constrained Rosenbrock function with bounded global optimum.
  
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  A two-population EA search over a constrained Rosenbrock function. Global optimum is not bounded.
  
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  Estimation of distribution algorithm over Keane's function
  
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  A two-population EA search of a bounded optima of Simionescu's function.