Why Cyanobacteria Produce Toxins ? Evolutionary Game Theory Suggests the Key

Cyanobacteria are a source of potent toxins among which the microcystin (a hepatotoxic peptide encoded by the mcy gene cluster of Microcystis spp.) is a frequent cause of poisoning in inland waters worldwide. Although the molecular basis of microcystin production is known, its role is still unknown. It was suggested that microcystin production have a metabolic cost that could be offset by some benefit (e.g. protection from grazing). We check that: i) microcystin-producing and non-producing strains occurs simultaneously in the Microcystis spp. blooms, ii) evolutionary forces (mutation, genetic drift) control frequencies of microcystin production and non-production strains, and iii) microcystin producing strains have diminished fitness compared with non-producing strains. We employ evolutionary game theory to explain the maintaining of microcystin-producing genotypes in natural populations of Microcystis spp. A two-strategy (to produce or not microcystin), two-players game of cooperators (microcystin-producing genotypes) and cheaters (non-producing genotypes) explains the coexistence of both genotypes in the same bloom. A bloom composed mostly by the microcystin-producing “cooperators” genotype, the “temptation of defection” (increase of non-producing genotypes) is counteracted by kin selection, which enable that natural selection can favour the cooperators. The closest related individuals occur within cyanobacteria blooms, cyanobacteria reproduces asexually providing sets of clones.

Over the last years, the molecular basis of how Microcystis produce microcystin has been discovered.Microcystin is a peptide synthesised non-ribosomally via a thio-template mechanism (Arment & Carmichael, 1996) by the microcystin synthetase enzyme complex, which is encoded by the microcystin (mcy) gene cluster (Kurmayer & Christiansen, 2009).The mcy gene cluster of Microcystis has been already sequenced (Nishizawa et al., 2000;Tillett et al., 2000).Molecular analysis shows that evolution of the mcy genes occurs through asexual reproduction and horizontal gene transfer, with ancestral wild type microcystin-producing genotypes and strains with non-functional genes (Bjørg et al., 2003).
Unfortunately, the molecular basis of the myc gene cluster does not explain the biological role of microcystin.The classic approach assumes that microcystin production has a metabolic cost, but generates some advantages that compensate the cost.In this sense, numerous evidences suggest that microcystin production prevent grazing of Microcystis by zooplankton, filter feeders and others.Toxin-producing Microcystis often have lethal effects upon zooplankton, or significant reduce the growth of these primary consumers (De Mott, Zhang, & Carmichael, 1991;Kinder, 1995;Rohrlack, Henning, & Kohl, 1999;Trubetskova & Haney, 2000).Daphnia species actively evade Microcystis blooms through vertical migrations (Kinder, 1995).Filter-feeding animals as zebra mussels employ a sophisticated mechanism based on the selective alimentation eliminating living Microcystis in pseudo-feces to avoid microcystin producers (Vanderploeg et al., 2001).It is known that animals that consume Mycrocystis scum die due to the toxic effect of cyanotoxins (Alonso-Andicoberrt et al., 2002;López-Rodas et al., 2008;Francis, 1878;Galey et al., 1987;Soll & Williams, 1985;Matsunaga et al., 1999).Thus, the protection against grazing will compensate the metabolic cost of microcystin production.Other useful functions for microcystin have been suggested such as binding iron (Utkilen & Gjølme, 1995) or involvement in quorum sensing (Dittmann et al., 2001).Despite this, experiments with cultures of Microcystis that had the myc gene knockout showed no apparent differences with m+ functional cultures (Dittmann et al., 2001).Producing microcystin does not seem to be a substantial cost under laboratory conditions.Additionally, other laboratory experiments show that the values of heritability of microcystin production were significantly higher than those found in fundamental physiological characters (López-Rodas et al., 2006).It is generally assumed that only the quantitative traits with little or no selective advantage show high values of heritability (Falconer & Mackay, 1996).
Surely, microcystin production is more complex than which can be explained from the current knowledge of the molecular basis of the myc gene complex, because microcystin production seems to be a complex quantitative trait.In fact, laboratory studies have shown that changes in environmental conditions induce changes in microcystin concentration within a strain by a factor of three to four times, whereas microcystin production between strains grown under identical culture conditions may vary in the three or more orders of magnitude (reviewed by Sivonen & Jones, 1999;Carrillo et al., 2003;Lopez-Rodas et al., 2006).
Consequently, the role played by microcystin production in the biology of Microcystis is still far from clear.Einstein said once that you cannot solve a problem with the same mentality it has been posed, but rather you must change the way you approach it.So, we decided to address this controversy in a different perspective.The key question is to analyse why usually microcystin-producing and non-producing strains appear together in the same Microcystis bloom and neither of the strains prevail over the other.A population genetics approach could find out what kinds of evolutionary forces are acting (i.e.mutation, natural selection, genetic drift...) on microcystin-producing and non-producing strains and calculate their genotypic frequencies and their evolution (throughout of fitness values, selection coefficients, effective population sizes...).
Consequently, first we performed a classic population genetics experiment to estimate the role played by the evolutionary forces on the frequency of microcystin-producing and non-producing strains.Afterwards, the results obtained were analysed employing evolutionary game theory.
Evolutionary game theory could explain the cases in which producing microcystin has an evolutionary advantage in a population of Microcystis aeruginosa and viceversa.Since von Neumann & Morgenstern (1944) and Nash (1950) presented game theory as a mathematical approach to evaluate the results of the different strategic decisions among the complex interactions of self-interested individuals, this discipline has been able to successfully resolve complex problems of population genetics.The application of game theory to evolving populations of life organisms (i.e.evolutionary game theory) is focused on the effect of the frequency with which various competing strategies are found in the population.Evolutionary game theory has been particularly useful to explain complex aspects of biology that had not been explained within the context of Darwinian process by classic population genetics, such as the evolutionary basis of altruistic behaviours (Maynard-Smith, 1982).
The conceptual basis of our approach is based on three steps: 1) Isolate microcystin-producing and non-producing strains from the same population of Microcystis aeruginosa (because the evolutionary phenomena occur within the populations).
2) Demonstrate that classic evolutionary forces (mutation, genetic drift and natural selection) can change the frequency of the toxin producing and no toxin producing genotypes (to prove that microcystin production is not only a physiologic phenomenon).
3) Applicate evolutionary game theory to estimate the best strategy (i.e.producing or non-producing toxins) according to the population conditions (i.e. the frequencies of the producing and non-producing cells).

Isolation of Strains and Culture Conditions
Twenty-one different clonal cultures of M. aeruginosa, numbered from one to twenty-one, from the Algal Culture Collection, Veterinary Faculty, Complutense University, Madrid, were used (Figure 1).All the strains were isolated from same area of Guadalquivir basin (SE Spain), in order to compare the population genetics parameters of different strains within the same population, because the evolutionary forces (e.g.natural selection) act within populations.Each strain was isolated as follows: First of all colonies morphologically identified as M. aeruginosa based on morphologic characteristics according to Komarek & Anagnostidis (1998) were isolated using micro-pipettes.Only colonies within the middle of the range of cell and colony sizes with clear M. aeruginosa morphotypes were isolated.Afterwards, a single vegetative cell was isolated from each colony using a Zeiss-Eppendorf (Carl Zeiss, Hamburg, Germany) micromanipulator-microinjector.Since M. aeruginosa cells divide asexually, the clonality of each culture was assumed.The strains were grown in 100 mL ventilated cell culture flasks covered with a filter cap (Greiner, Bio-One Inc., Longwood, 155 NJ, USA) with 20 mL of BG-11 medium (Sigma, Aldrich Chemie, Taufkirchen, Germany) at 24ºC with a continuous photon irradiance of 80 µmol photons m -2 s -1 over the waveband 400-700 nm, supplied by daylight fluorescent tubes.Cells were maintained axenically in balanced growth (mid log exponential growth) by serial transfers of an inoculum to fresh medium (Cooper, 1991).Periodic controls (i.e. by observation under fluorescence microscope after acridine orange staining and plating in standard bacterial cultures) assure the absence of detectable bacteria.The position of each culture flask in the incubator chamber was randomly changed once every day.More details on culture of Microcystis are given in Lopez-Rodas et al. (2006) and Rouco et al., (2011).In order to allow full environmental acclimation, the strains were grown under these constant experimental conditions during two months.The maintenance of the strains under the same stable environmental conditions is necessary for disengaging environmental and genetic influences on the phenotypic variability, which ensures that differences found among strains are exclusively due to genetic variability (Brand, 1981;Costas, 1990).

Microcystin Determination
The microcystin production of the different strains was measured in mid log exponential growth cultures (i.e.acclimated, balanced growth (Cooper, 1991)) of 3 x 10 6 cell ml -1 using a microcystin commercial kit MicroCystest (ZEU-INMUNOTEC, Zaragoza, Spain), based on inhibition of the protein phosphatase 2A (PP2A) by microcystins, and therefore capable of detecting all potentially toxic microcystins with a detection limit of 0.08µg/L and a working range 0.25-2.5 µg/L.This test was approved by Environmental Technology Verification program of the USA Environment Protection Agency (EPA).Extraction of toxins and total microcystin (water dissolved microcystin + microcystin within cells) was measured following the manufacturer's recommendations and expressed as µgrams per litre (µg/L).Two different operators performed triplicate measurements of microcystin.The reliability, reproducibility and precision of microcystin measurements were established according to the British Standards Institute (1979) and Thrusfield (1995).Reliability was determined based on the agreement between three iterations of measurements made by the same observer on the same replicate, whereas reproducibility was determined as the agreement among three sets of observations made by two different observers.The measurements to guarantee reliability, reproducibility and precision were performed on two lots of reagents using (i) microcystin-LR controls (Sigma-Aldrich) at 1.0 and 4 µg/L, and (ii) extracts from Ma2, Ma7 and Ma14 strains containing 3 x 10 6 cell ml -1 .We select these three strains in order to have representation of a non-producing strain (Ma2), a strain with an average production (Ma7) and the highest microcystin-producing strain (Ma14).Precision was determined as the minimum variation in microcystin, which could be detected.

Fitness Estimation
The Malthusian parameter of fitness (m) was estimated as previously described (Costas, 1991) as the acclimated maximal growth rate from the general equation of growth: (1) where N 0 is the initial cell number (after the lag period), and N t is the cell number after 7 d; therefore, m was computed as Log e (N 7 / N 0 )/ 7. Cells were counted using settling chambers, by two independent observers who counted three replicates per strain.The number of samples counted per replicate was determined using the progressive mean procedure to ensure a counting error of ≤ 5%.The Darwinian fitness (i.e.relative fitness) of each genotype was estimated as the ratio: where m i is the Malthusian parameter of the strain i and m max is the maximum Malthusian parameter.Consequently, the maximum value of fitness will be 1.The growth rates were estimated using triplicates of each genotype.More details on estimation of fitness in Microcystis aeruginosa (including heritability and evolution of fitness and microcystin production) are given in López-Rodas et al. (2006) and Rouco et al. (2011).The reliability, reproducibility and precision of microcystin measurements and fitness estimations were established as previously described for Microcystins.Ma2, Ma7 and Ma14 strains.
Afterwards, we use linear regression to modelling the relationship between fitness (dependent variable y) and microcystin production (explanatory variable x) using InStat package (GraphPad Software, La Jolla, CA, USA).

Population Genetics Experiments
We assume the simplest theoretical model of population genetics that might well explain the observed results: i) the functional microcystin-producing genotypes (m+) could become non-functional (m-) due to occurrence of spontaneous mutation (m+ → m-); ii) conversely non functional microcystin-producing genotypes (m-) can become functional (m+) due to reversion (m-→ m+).Within a microcystin-producing population should have a majority of m+ genotypes and perhaps a few m-genotypes originated by mutation.On the contrary, within a non-producing population should have a majority of m-genotypes and possibly a few m+ genotypes originated by reversion In a small population the alleles m+ and m-should be under a mutation-genetic drift balance.
We can essay this model in the laboratory using experimental populations of Microcystis aeruginosa.The experimental populations were laboratory cultures microcystin producing (m+ strains) and non-producing (m-) strains maintained by serial transfers of a small inoculum.In these experimental populations act mutation and genetic drift.The possibility of losing an allele by genetic drift in small populations is high.Consequently, sometimes microcystin-producing cultures could lose their toxicity by random genetic drift, because only mgenotypes (originated by mutation m+ → m-) were transferred in the small inoculum.And just the opposite, sometimes non-producing cultures could became toxic also by random genetic drift, because only m+ genotypes (originated by reversion m- m+) were transferred in the small inoculum.To experimentally check this model, two experiments were performed simultaneously: i) experiments maximizing random genetic drift: Twenty-one clonal cultures were grown until a cell number of about 10 8 .Afterwards the cultures were transferred to fresh medium using extremely small inoculum (around 100 cells) to maximize genetic drift.The probability that some allele is lost in such small inoculum is very high.This flash-crash process was repeated periodically during 20 times.
ii) experiments minimizing random genetic drift (controls): The same twenty-one clonal cultures were grown until a cell number of about 10 8 cells.Afterwards the cultures were transferred to fresh medium using large inoculum (around 10 5 cells) to prevent genetic drift.The probability that some allele is lost in such inoculum is extremely low.This serial transfer process was also repeated periodically during 20 times.
In both experiments, the microcystin production was measured at the start of and after the 20 flash-crash (i.e.mutation-genetic drift) cycles in exactly the same conditions.

Evolutionary Game Theory Model of Microcystin Production
We assume that a bloom is a Microcystis aeruginosa population where m+ is a microcystin-producing wild type genotype, and m-is a non-producing mutant genotype.Relative frequency of m + is p, relative frequency of m -is q.
Fitness of m+ genotype is w 1 and fitness of m-genotype is w 2 .
We can systematize all possible cases by considering an evolutionary game between two strategies, i) produce microcystin (m + genotype) and ii) not produce microcystin (m -genotype), playing in two different populations, population 1 with predominant m + genotypes and ii) population 2 with predominant m -genotypes.
The payoff matrix of both strategies is: playing against ( 3) The entries of the matrix denote the fitness for the row player.A m+ genotype obtains a payoff w 1 (+) when playing another m+ genotype, but payoff w 1 (-) when playing a m-genotype.Likewise, m-genotype obtains a payoff w 2 (+) when playing against m+ genotype, or w 2 (-) when playing against m-genotype.This is a case of two-players, two-strategy game, whose evolutionary dynamics has studied in detail (Rapoport & Chammah, 1965;Axelrod, 1984;Taylor & Nowak, 2009).
When the 21 clonal strains were subjected to experiments maximizing random genetic drift (the cultures were transferred using inoculum around 100 cells during 20 times), most of the strains maintained similar microcystin production (Table 1).But four clones (Ma3, Ma13, Ma20, Ma21) that initially had produced microcystin became no producing after the experiment (Table1).Inversely, two clones that had not produced microcystin at first (Ma6, Ma16) became able to produce at the end of the experiment (Table 1).In contrast, when the twenty-one clonal strains were maintained by serial transfers using large inoculum (10 5 cells) to prevent genetic drift, toxicity of each strain remained unchanged (Table 1).These results suggest that m-genotypes could occur in strains of m+ genotype as a result of spontaneous mutation and also could become fixed in populations by genetic drift.Previous work show that genetic drift is an important component in the evolutionary changes affecting to microcystin production, that occur in Microcystis populations as response to eutrophication and temperature increase (Rouco et al., 2011) as well as in other harmful algae (Flores-Moya, Costas, & López-Rodas, 2008;Flores et al., 2012).
Initially, a high inter-strain variation was found for the fitness measured under identical laboratory conditions (Table 2).It should be noted that no microcystin-producing strains has higher fitness than microcystin-producing.Fitness of non-producing strains ranges from 0.8 to 1.0 (mean = 0.90; sd = 0.09), whereas fitness of microcystin producing strains range from 0.4 to 0.8 (mean = 0.65; sd = 0.13).Statistically significant differences (p = 0.0006, t = 4.12, d.f.0 19 in Student t-test) were observed between producing and non-producing strains.A regression analysis of microcystin production (measured in ppb of microcystin LR-equivalent in cultures with 3 x 10 6 cell/ml) and Darwinian fitness of the 21 different strains of M. aeruginosa also show that the genotypes that produce more amount of microcystin have less Darwinian fitness than those non-producers genotypes (statistically significant negative regression, P< 0.001, R 2 = 0.71 was observed; Figure 2).
When these strains were subjected to experiments maximizing random genetic drift most of the strains maintained similar fitness values.But two strains (Ma3 and Ma20) increase in fitness after losing the ability to produce microcystin, whereas the strain Ma20 decrease in fitness after recovering the ability to produce microcystin (Table 2).In contrast, when the twenty-one clonal strains were maintained by serial transfers using large inoculum (10 5 cells) to prevent genetic drift, toxicity of each strain remained unchanged.
www.ccsen Linear reg cell ml -1 ) a  An outstanding fact that emerges from our results is that producing microcystin has a strong cost in fitness.This interesting fact had not been highlighted previously because the studies that characterize the fitness of different strains (genotypes) isolated from the same population are scarce.In the literature there are studies comparing Microcystis strains isolates from different populations, forgetting that natural selection acts within populations and not between populations (Lewontin, 1974;Spiess, 1989;Gould, 2002).In contrast, all strains used in our study were isolated as close as possible in space and time, so that they should belong to the same population.A recent study analysing DNA sequencing and genetic variability for physiological and morphological traits show that these strains are very close at genetic level (Lopez-Rodas, 2013).
According to classic population genetics results obtained by fitness valuation suggest that non-producing genotype (m-) during a Microcystis bloom should be more numerous than microcystin-producing genotype (m+) due to it higher fitness.But numerous evidences reveal that the non-toxin producing cells do not prevail massively during a bloom (reviewed in Sivonen & Jones, 1999; data for South Spain populations in Alvarez et al., 1998;Carrillo et al., 2003;Martin et al., 2004;Lopez-Rodas, 2006).Consequently, it is necessary to find an explanation for the natural maintenance of a high frequency of microcystin producing cells in a bloom population.

The Model of Population Genetics and Game Theory of m+ and m-Genotypes
We propose a theoretical approach of game theory model (two-player and two-strategy model) to explain the abundance of microcystin producing cells.Similar approach was tackle for explaining apparently low fitness behaviours as altruism (Maynard Smith, 1982;Thrusfield, 1995) Game theory, it has long been employed to determine the best strategy for a genotype interacting with other genotypes to reach the best outcome to himself (Hamilton, 1964;Trivers, 1971;Maynard Smith & Price, 1973).In essence, an evolutionary game is related to reproductive success so that the fitness of a genotype depends on payoff of his strategy interacting in cooperative or non-cooperative strategies with other various strategies in the population (Samuelson, 1997;Hofbauer & Sigmund, 2003;Nowak & Sigmund, 2004;Nowak, 2006).If w 1 (+) + w 2 (-) < w 2 (+) + w 1 (-) then r C >r D .Three possibilities: i) if r C >r D >r then defectors dominate; ii) if r C >r>r D then co-operators and defectors are not a ESS; iii) if r>r C >r D then cooperators dominate.
Based on the payoff matrix of two players (m+ and m-) with each of them competing against the other for the same ambient, different strategies can take place as a function of the payoff which leads to different final populations.Evolutionarily stable strategies (i.e. is stable against invasion by a fraction of mutants using the other strategy) can occur depending of payoffs (Figure 2): two strategies of the matrix are Nash equilibrium (the best strategy of a player in order to acquire the maximum possible payoff, knowing the strategy that perform the other player) (Nash, 1950): The first is if w 1 (+) > w 2 (+) and the second if w 1 (-) < w 2 (-).In a large mixed population (without small subpopulations), a Nash equilibrium strategy is an evolutionary stable strategy (Maynard Smith, 1982).In practice, the huge blooms of Microcystis composed of billions of individuals mixed by the water movements are as close as possible to a theoretical infinite, well-mixed population.Consequently, in such populations 3 different evolutionary stable strategies are possible (Figure 3): i) If w 1 (+) > w 2 (+) and w 1 (-) > w 2 (-), then m+ dominates m-.In this case is better to produce microcystin (i.e.be a wild type m+ genotype) because the expected payoff to produce microcystin (m+ genotype) is greater than that of not produce microcystin (m-genotype) in any Microcystis population.Consequently, wild type the m+ genotypes always prevail in the population.
ii) In the reverse situation w 1 (+) < w 2 (+) and w 1 (-) < w 2 (-), then m-dominates m+.Obviously, in this case the expected payoff of m-is greater than that of m+.Here, m-mutants always prevail in the population.
iii) If both conditions of Nash equilibrium w 1 (+) > w 2 (+) and w 1 (-) < w 2 (-) occurs together, then both strategies can be a evolutionary stable strategy.In a population where most genotypes are wild type m+ it is the bests to be m+.
In contrast, in a population where most genotypes are m-mutants it is the bests to be m-.
Since in the blooms of Microcystis simultaneously coexist microcystin-producing and non-producing genotypes, obviously do not occur Nash equilibrium in natural conditions.But another solution is possible when strategies generate payoff that are different to those that allow Nash equilibrium.This solution is the key to understand why wild type microcystin-producing m+ genotypes and non-producing m-genotypes always appear together in the Microcystis blooms.
iv) If w 1 (+) < w 2 (+) and w 1 (-) > w 2 (-), then there is stable co-existence between both genotypes.In a Microcystis bloom where most genotypes are microcystin-producing wild type m+, (p > q) it is the bests strategy to be a non-toxic m-genotype.Contrarily, in a Microcystis population where p < q, it is the best strategy to be m+ genotype.Thus, equilibrium of frequency-dependent selection is achieved.In this case, there is a stable co-existence between the both genotypes in the Microcystis populations.Only this theoretical solution of the payoff matrix presents a stable coexistence of both genotypes (i.e. in a Microcystis bloom where most genotypes are m+ it is the best strategy to be m-and viceversa).In this case, the frequency dependent selection leads to equilibrium as shown in the Microcystis aeruginosa blooms.
At the biological level, there is an explanation to this model of stable coexistence of both genotypes.Although producing toxins is useful to prevent grazing by zooplankton filter feeders and large animals (Alonso-Andicoberry et al., 2002;López-Rodas et al., 2008;De Mott et al., 1991;Kinder, 1995;Rohrlack et al., 1999;Trubetskova & Haney, 2000;Vanderploeg et al., 2001;Frances, 1878;López-Rodas & Costas, 1999), it is also costly in terms of fitness, whereby the toxin-producing m+genotypes showed diminished fitness with respect to non-producing mgenotypes in the absence of grazers (Carrillo et al., 2003;López-Rodas et al., 2006).Our results also show significant negative regression between fitness and toxin production.
Let us assume a Microcystis bloom constituted by individuals with the m+ ancestral genotype.In this bloom appears a new genotype m-by a rare spontaneous mutation, which does not produce microcystin, so it fitness is slightly above than those of m+ ancestral genotypes and is also protected from grazing although he do not produce microcystin.As its fitness is greater than the ancestral m+ genotypes, the frequency of m-mutants will increase gradually.In this population it is best to be m-, it is tempting to be a m-genotype.But there will come a point where if there are not enough m+ genotypes, the bloom would not be protected any more.
This can be interpreted as that the m+ genotypes forgo some of their potential for the common good of the population, performing a cooperative strategy.But the temptation for cheating (m-genotype) plays an important role.Under this view, the Microcystis blooms comprise two strategies: i) the cooperators (m+ genotypes), which would invest in microcystin production for the good of the entire population, and ii) the cheaters (m-genotypes), which would take the advantage conferred by the m+ cooperators to acquire the maximum profit from the situation, giving nothing in return.
Consequently, the maintenance of cooperation requires a specific mechanism to enable that natural selection can favour to the cooperators instead of to the cheaters.Kin selection could be the mechanism.Classic view of kin selection is based on the concept that usually the evolutionary game is played among genetic relatives individuals (Hamilton, 1964;Samuelson, 1997;Cavalli-Forza & Felman, 1978).A gene encodes some kind of cooperative behaviour promotes its own survival if it is also present in the beneficiary of the cooperation.Cyanobacteria reproduce asexually.Consequently, cyanobacteria populations are formed by sets of clones (López-Rodas & Costas, 1997) of his act of cooperation becomes a clone of herself.Clones are more likely to benefit from (pseudo)altruistic behaviour than distantly related individuals.
From the seminal works of Maynard-Smith (1982), Nowak (2006) and Taylor & Novak (2009) arises an intriguing idea.Cooperators and cheaters could coexist in a population where the values of the payoff of both strategies (m+ cooperators and m-cheaters) meet the following condition: (Hofbauer & Sigmund, 2003) (4) r cooperators > r total population > r cheaters where: a m+ genotype obtains a payoff w 1 (+) when playing another m+ a m+ genotype obtains a payoff w 1 (-) when playing a ma m-genotype obtains a payoff w 2 (+) when playing a m+ a m-genotype obtains a payoff w 2 (-) when playing a mand r = coefficient of genetic relatedness between individuals (an estimation of the average genetic relatedness between the playing individuals) Apparently r can be high in the blooms of cyanobacteria, because experimental data show that Microcystis blooms are usually constituted by few different genotypes (Alvarez et al., 1998;López-Rodas & Costas, 1997;Martín-Montaño et al., 2000).In addition, the approximation described above determinates that for the coexistence of the m+ and m-must be also satisfied that: r cooperators > r total population > r cheaters (5) so is said that the coefficient of cooperators should be higher than the total coefficient of genetic relatedness of the population and in turn, the coefficient of cheaters should be lower than the other two.For this to happen, within the population the majority of the population should be the m+ genotype, which fit with the experimental evidences (Alvarez et al., 1998;López-Rodas & Costas, 1997;Martín-Montaño et al., 2000).Whereupon it could be said that the strategy perform by cyanobacteria depends in last term on the kinship of the cooperators genotype.
Other causes (such as group selection, graph selection, direct and indirect reciprocity, reviewed by Nowak, 2006;Taylor & Nowak, 2009) could explain microcystin production, but as cyanobacteria are very simple organisms, it seems reasonable to propose a lex parsimoniae explanation.
Experimental evidence allows to validate a population genetics model based on a two-strategy (to produce or not produce microcystin), two-players game of cooperators (the wild type m+ microcystin-producing genotypes) and cheaters (the m-non-producing mutants), which explain the coexistence of both genotypes in the same population and provides a clear explanation of the role played by microcystin.Our model for explaining toxin production by Microcystis is based on the following assumptions: i) mutation from wild type toxin-producing m+ genotypes to non-producing m-mutants producers occurs spontaneously; ii) reversion from non-producing m-mutants to toxin-producing m+ genotypes also occurs spontaneously; and iii) in the main, toxin-producing m+ genotypes have less fitness than non-producing m-mutants.
For the moment, an experimental demonstration of this game theory model of two strategies and two players not easily approachable.Instead, we have provide a list of indirect experimental evidences.In any case, our approach seems to be a "gedanken experiment" type of problem (a thought experiment, a hypothetical scenario carried out to understand a real problem).At present, there is a tendency to interpret the phenomenon of microcystin production under the reductionist perspective of what we know about its molecular basis (specifically on the myc gene cluster).These studies have often assumed that myc genes operate in a closed system in which the presence or absence of certain gene sequences directly determines microcystin production.However, cyanobacteria blooms exhibit a wide range of variability in microcystin production, which is the result of barely measurable interactions between a particular genotype and its corresponding environment.In such cases, classical models of population genetics have a great power to explain biological phenomenon under an evolutionary level.There is also a tendency to seek new functions to explain the role of microcystin, relegating to a second place its toxic effect, despite that continuously produces countless mass mortalities among the consumers of cyanobacteria.In contrast, our model follow an Ockham´s razor type argument (among competing hypothesis, the one with less assumptions should be selected), which takes into account the environment and operates whatever the genetic basis of toxin production (because the selection unit is the complete genotype).After all, Charles Darwin masterfully explained the mechanisms of evolution nearly 100 years before the development of molecular genetics.

Figure 1 .
Figure 1.Microphotographs of two different clonal cultures of M. aeruginosa Two microphotographs of two different strains of M. aeruginosa from the Algal Culture Collection, Veterinary Faculty, Complutense University, Madrid.a) a non-toxic strain and b) a toxic strain.As can be seeing in the figure M. aeruginosa does not make colonies in laboratory cultures.

Figure 2
Figure 2. e interval betw different strain

Figure 3 .
Figure 3. Kin selection can lead to the evolution of cooperation

Table 1 .
Population genetics experiments to check the role of mutation, reversion and genetic drift between microcystin-producing and no-producing strains (+ microcystin producing strain;no-producing strain) a initially microcystin-producing strains, which became no-producing after the experiments maximizing random genetic drift.binitially no-producing strains, which became producing after the experiments maximizing random genetic drift.