Sex determination networks evolve rapidly and have been studied intensely across many species, particularly in insects, thus presenting good models to study the evolutionary plasticity of gene networks.We study the evolution of an unlinked gene capable of regulating an existing diploid sex determination system. Differential gene expression determines phenotypic sex and fitness, dramatically reducing the number of assumptions of previous models. It allows us to make a quantitative evaluation of the full range of evolutionary outcomes of the system and an assessment of the likely contribution of sexual conflict to change in sex determination systems. Our results show under what conditions network mutations causing differential regulation can lead to the reshaping of sex determination networks.The analysis demonstrates the complex relationship between mutation and outcome: the same mutation can produce many different evolved populations, while the same evolved population can be produced by many different mutations. Existing network structure alters the constraints and frequency of evolutionary changes, which include the recruitment of new regulators, changes in heterogamety, protected polymorphisms, and transitions to a new locus that controls sex determination. In rentiation ,7, or brentation . In contentation ,10 and wentation . Althougentation ,13, wormentation , fishes entation  and mammentation . Sex detSex-lethal (Sxl), an upstream regulator of sex determination first found in D. melanogaster [doublesex (dsx) is conserved across insects, worms [en) appear highly conserved and where the degree of conservation becomes progressively reduced for genes both upstream and downstream [transformer (tra) autoregulates in the Mediterranean fruit fly Ceratitis capitata [Sxl was recruited as an upstream regulator in Drosophila. Likewise, high regulatory variability is seen in the phylogenetically common dsx locus, which is regulated via alternative splicing of RNA by tra in many Diptera [tra-1 in worms [Comparative study shows that sex determination networks evolve by recruitment of novel regulators higher up the pathway . For exanogaster , does nonogaster ,19,20. Is, worms ,22 and ms, worms . A similwnstream ,25. In scapitata  but lost Diptera , but viain worms .D. melanogaster in a step-by-step fashion [D. melanogaster, particular evolutionary outcomes were addressed to account for the peculiarities of the genes involved in the network, for example multiple promoter sites, alternative splicing, and premature stop codons [Previous theoretical study showed how regulatory changes causing alterations in signal strength, could account for the evolution of the sex determination regulatory cascade of  fashion . In seekp codons . This dep codons -30. Thisp codons  and sexuHere we present a model that combines gene network evolution with population genetics, allowing us to study the effect of differential gene expression with general applicability and minimal assumptions. Standard approaches to gene network evolution have used haploid models to simplify the dynamics -38. Thisi may be regulated by an allele j at another locus (e.g. via cis-regulatory elements or RNA splicing sites), indicated by a parameter i, j I∈ {-1, 0, 1} which is 1 for up-regulation, -1 for down-regulation and 0 for no regulation. Second, an allele i may code for a regulatory domain (e.g. transcription factor or RNA recognition motif), indicated by a parameter i Z∈ {0, 1} which is 1 when the allele is regulatory and 0 otherwise. Third, each allele i has a constitutive output level defined by a parameter iT, which is either low (i T= -1) or high (i T= 1). These features determine the (time-dependent) expression level i Sof each allele i via the dynamical systemWe extend a general model of gene regulation ,39, usinj, and we assume thatThe summation is over all alleles h (see Table iS(0) = σ(ikT) which are equilibrium expression levels if there is no regulation. The parameter k > 0 is a global constant that defines the relative contribution of the constitutive output to total gene expression. Note that the steady state output i is the solution ofis a sigmoid function. Most gene regulatory interactions can be approximated using this class of function -42 whichi in the summation term of Eq(1)).attained from these initial conditions. Note that this model can also incorporate autoregulation by allowing alleles at the same locus to regulate their own expression  simplifies toTm = -1) and high (Tf = + 1) output levels respectively. We consider an XY male heterogametic system consisting of m/f males and f/f females  expression determines somatic sex in Drosophila, where high expression of the female form of the dsx protein is required for a female phenotype [θ = σ (k)+1/2. Thus, larger values of k mean a larger difference in gene expression around the threshold value θ between the two sexes.The D locus controls sex determination. Specifically, if the sum of outputs of the two D locus alleles, d1 and d2, exceeds a threshold henotype . In our Za = 0. Consider a mutant allele A at the R locus that has a regulatory domain able to interact with the D locus, ZA = 1. In order for a regulatory interaction to evolve, the R locus allele A must be present together with a variant m or f allele at the D locus that is capable of being regulated by A. The m and f variant alleles are labeled according to whether the interaction causes up-regulation of expression  to calculate the expression level of the alleles at the R locus, and then use Eq(3) to calculate the regulated expression of the alleles at the D locus.We study the evolution of regulation controlled by a second locus R. We start from a situation in which the R locus is fixed for an allele a that does not regulate the D locus, + allele (D locus) which contains a novel input binding domain. This creates a positive regulatory connection from the R locus to the D locus. We denote this example a→A/f→f+ (background/mutant). If we reverse the order to f→f+/a→A, then the allele f+ already exists in the background state and the connection is completed by the mutation of the a allele to the A allele which contains a novel output regulatory domain.As the evolution of regulation by the R locus of the D locus requires change at both loci, we consider that one part of the connection exists in the background state, with the remaining part being completed by a subsequent mutation at the other locus. For example, if the allele A (R locus) is already present in the background state, it can complete a connection through the mutation of the f allele to the f-, (2) a→A/f→f+, (3) a→A/m→m-, (4) a→A/m→m+, (5) f→f-/a→A, (6) f→f+/a→A, (7) m→m-/a→A, (8) m→m+/a→A . In cases (5) to (8), either f-, f+, m- or m+ already are present in the background state (having replaced f or m), and we follow the mutant A allele introduced at the R locus. Note that the first four cases involve a cis mutation at the D locus occurring after a trans mutation at the R locus, and vice versa for the second four cases.There are eight possible combinations of background state and mutant that give rise to a novel regulatory connection: (1) a→A/f→f-,  a→A/f→f+W) of each genotype. In the background state, male (WM) and female (WF) fitness are set to 1. The fitness of mutant genotypes is measured relative to the background state genotypes: +/f and expression in males TA = 1 - see Methods). If the ancestral male was a/a; m+/f then the ancestral expression is wM and wF define the direction and magnitude of selection in males and females respectively. Within the simulations (see Methods), we use random numbers in the range  for both WF and WM to avoid negative fitness values for WF and WM . For each run, we recorded whether the mutation spread and caused a -/a→A . The mutant A is then introduced at low frequency. The A mutant down-regulates f-, so the expression of - males than in ancestral males. The A mutant also reduces -/f- genotype. If -/f- males and homozygous a/a;f-/f- females. There is no change in the female genotype, but the dominant masculinizing m allele at the D locus is replaced by the dominant masculinizing A allele at the R locus. This occurs in Region I of Figure To illustrate our approach, we consider the mutation pair f→fA Figure . In this-/f- is female  produces two new genotypes that are AA homozygous: A/A;m/f- and A/A;f-/f-. The genotype A/A;m/f- is male because its -/f- can be male or female. If 2σ(-2(k)+k)-(σ(k)+1/2) < 0 then it is male, which can lead to a population composed of A/A;f-/f- males and a/A;f-/f- females , and has a minor effect on the evolutionary outcome . In addition, the outcome depends on the fitness of each genotype, which we consider in a separate section below.The outcomes depend on the values of e Figure . When k  σ of Eq , and has-/a→A and m→m+/a→A -(3)) and the A allele causes a large change in gene expression at the D locus. When this is sufficient for θ threshold, it causes a change in genotypic sex . It can then lead to fixation of the regulated allele at the D locus (either f- or m+), with transition of the control of sex determination to genetic variation at the R locus  following mutation at the D locus. Under these conditions we again observed sex determination locus transitions with the f- and m+ mutation pairs, but not with f+ and m- . However, as the A allele up-regulates f+, the output + homozygous genotype impossible. Similarly, for the m→m-/a→A mutation pair, the A allele down-regulates m- and makes a female m- homozygous genotype impossible. In these cases, transition of sex determination to the R locus cannot occur and build-up of the sex determination cascade is impossible [A second constraint governs the absence of transitions for f→fpossible , a condipossible ).-/a→A and m→m+/a→A , whereas in the a→A/f→f- mutation pair, the new allele is a recessive masculinizer . The pattern is more complex with a→A/m→m+ mutation pairs. In this case the up-regulation of m+ caused by the A alleles is sufficient to cause θ and so result in sex change. There are three possibilities. Two of these cause a change in heterogamety: a dominant m+ feminizer leading to A/A;m/m+ females, or an m+ allele which only feminizes in conjunction with the f allele leading to A/A;m+/f females. Alternatively the m+ allele is a recessive feminizer leading to A/A;m+/m+ females, which remain the homogametic sex. In contrast, changes in heterogamety never occur with the m- mutation (either a→A/m→m- or m→m-/a→A), as the m- allele is a dominant masculinizer and so can never be expressed in a female.With lower values of s Figure . For exaθ) to result in a change in genotypic sex.Changes in heterogamety thus require the new regulatory connection to cause sufficient change in gene expression . The condition for selection to favor spread is WM > 1. As there is no mutant female genotype, WF = 1. For example, in the mutation pair a→A/m→m- . Male-only mutants  were found in all mutational classes, except for f→f+/a→A and a→A/f→f+. In these two cases, there are no conditions under which the f+ mutation is ever restricted to males. There are no cases of female-only mutants . Under conditions of ancestral female heterogamety this pattern is reversed with female-only mutants but no male-only mutants . However, there are many examples of sexual conflict in which the new regulatory connection is favored in one sex but deleterious in the other . Consider the mutation pair a→A/f→f- when k is large  is male and the other two (f-/f and f-/f-) are female . The new male genotype m/f- has lower expression at the D locus (-/f and f-/f-) also have lower wM < 0, wF < 0), the new genotypes raise fitness in both sexes . However when lower expression is only favored in one sex  there is sexual conflict . Under this condition, recruitment occurs as long as the combined fitness across the sexes is raised, (WM - 1)+(WF - 1) > 0 , polymorphism occurs at the D locus, while for X/a→A mutation pairs , polymorphism occurs at both the A and D loci. Protected polymorphisms are restricted to those sub-regions  is not sufficient to eliminate the new f- allele that is favored in f-/f- males alone.As an example, consider Region II of mutation pair a→A/f→f- Table . Here, t- Table . Protects Figure . Protect0 Figure , where s-/f in this example) cannot be the most favored genotype as its expression lies between the new and ancestral homozygotes. So when selection favors lower expression in males and females , the new f- allele is favored and goes to fixation. The same pattern is seen for f+, m- and m+ mutation pairs.Protected polymorphisms are abundant in some regions Figure . With a→With X/a→A mutation pairs, protected polymorphisms require retention of multiple alleles across both the A and D loci. They are abundant in regions Figure  in whichcis and trans mutations contribute to evolutionary change in sex determination. Previous population genetic models [+s). Instead we let sex determination and fitness arise through the expression dynamics of the network. We then study evolution following a cis mutation in an existing sex determining allele  followed by a trans gain-of-function mutation at a locus not previously involved in sex determination (R locus) or vice versa.In this paper, we develop a diploid gene network model that explicitly considers how c models -30,44 haGenerally, we observe a many-to-many relationship as the same mutation can produce many outcomes and the same outcome can arise through many mutations Figure , Table 3-/a→A and m→m+/a→A, in which the f- and m+ alleles exist prior to the mutation of a to A). In these cases, a single allele at the ancestral sex determination locus (D) is driven to fixation, with the A allele at the regulatory locus (R) becoming the new determiner of sex. For f→f-/a→A, the f- allele goes to fixation. When the f- homozygote is down-regulated by A it produces a male, but in the absence of A (or a lower dose of A) it is female  of A. Such switching is not possible for mutations involving f+ and m- alleles. The up-regulation of f+ and down-regulation of m- homozygotes caused by the A regulator merely strengthens existing female and male signals respectively. Hence for these mutants, the ability to determine both male and female sexes requires retention of polymorphism at the ancestral D locus , and sex determination cannot pass to the new R locus.Some constraints are identifiable. Of the eight possible mutation pairs  has retained the ancestral, non-sexual, regulatory functions as its expression pattern is similar to the non-duplicated version of Sxl found in the related fly Megaselia scalaris [+/a→A sequence of mutations, in which the novel Sxl allele  was capable of up-regulating an ancestral m+ allele of tra (D locus). In this reconstruction we assume that the ancestral sex determination system was based on tra locus polymorphism [There is a further constraint as transitions to a new upstream regulator are only possible when mutation to fr Figure . This cor Figure . However network . In the scalaris . In termmorphism .WF, WM > 1), or are favored in one sex but do not segregate in the other , spread with surprising frequency as well (Table WM - 1)+(WF - 1) > 0. That is, given the sex ratio is constrained to be 1:1, there must be an overall fitness gain summed across the mutant male and female genotypes, as has been pointed out in other contexts [As well as these network features, recruitment of mutants is most likely when they are favored in both sexes . Alternatively, the new regulatory arrangement causes a change in genotypic sex accompanied by a switch from male to female heterogamety . The latter occurs when the effect of the upstream regulator A is relatively strong and causes a change in the sex of some genotypes. In either eventuality, A is fixed in the derived population. There are many potential examples of fixed regulators of sex determination genes. For example, the splicing activity of the SXL protein in Drosophila is dependent on interactions with a number of other proteins like SNF and PPS [Sxl in sex determination.Many mutations establish a new regulatory connection with the recruitment of new alleles but without change to a new sex determination locus Table . Many of and PPS -50. WhatMusca domestica [Xiphophorus maculates [The conditions that give rise to changes in heterogamety can also result in protected polymorphisms in which more than one male or female genotype occurs at equilibrium Figure . Protectomestica  and the aculates . These maculates ,52 or coaculates , that reaculates ,51.+/a→A and m→m-/a→A mutation pairs , but is dependent on ancestral heterogamety.We have extensively studied evolutionary change when the ancestral condition is male heterogamety. Symmetrical constraints apply when the ancestral condition is female heterogamety. Here, transitions to a new sex determination locus only occur with the f→fk  are relatively weak and thus major re-organisation of the sex determination systems does not occur. In effect this stabilizes the established sex determination mechanism. A high value of k might therefore explain the rareness of heterogamety changes in birds [k is small, regulation is relatively strong, opening up the possibility of changes in genotypic sex, transitions of the sex determination system and changes in heterogamety. The latter are common in frogs [The importance of the model parameters in birds  and mammin birds . In contin frogs , medaka in frogs  and insein frogs ,59. Diffin frogs ,47 and sin frogs  are likeDrosophila melanogaster and related species [cis and trans mutations, for predicting transitions to a new upstream sex determination locus as well as the recruitment of other regulators which establish new regulatory interactions at sex determining loci. Our network approach allows sex and fitness to emerge directly from the regulatory interactions rather than being imposed by assumptions made about "modifiers". This approach demonstrates that the same mutation can produce many different evolutionary outcomes, while the same evolved state can be produced by many different mutations.The work in this paper was motivated by the complexities of the sex determination mechanism of  species ,13. We hWM, WF) of each genotype. Random mating amongst adults assuming unlinked loci was used to define the zygote frequencies in the following generation. This procedure was repeated until the population reached equilibrium. We measured the maximum difference  between successive timesteps, e(t) = maxG|p(t) - p(t - 1)|, where p(t) is the frequency of a genotype at generation t. The system is considered stable when e(t) < 10-12 . We imposed a maximum of 1011 timesteps, however, in every simulation the criterion was reached before this maximum number of steps. A mutant allele was classified as non-invasive if it was driven out, with the final population being the same as the ancestral population. Invasive mutants resulting in recruitments or transitions caused the loss of one of the ancestral alleles. To distinguish invasive mutants resulting in protected polymorphism from neutral or very weakly selected mutants, we first removed genotypes at ≤1% frequency . If more than one female or male genotype was observed (i.e. protected polymorphism), a second genotype threshold of 0.1% was used to ensure inclusion of all relevant genotypes. Simulations were performed using a custom-built C++ program capable of generating novel genotypes in real time and assigning sex and fitness dynamically. Examples of genotype frequency dynamics for simulations leading to both recruitment and protected polymorphism are shown in Additional file We use a standard population genetics simulation to study the evolutionary fate of each mutation. The model assumes an infinite diploid population with non-overlapping generations, with a 1:1  sex ratio. Each mutant allele was introduced at low frequency (0.5%) in the heterogametic sex . At each generation the following steps were taken. First, gene expression h, k, wM, and wF) which remain fixed for the entire duration of each simulation. A uniform distribution is assumed for all parameters. For h, we assume the biologically realistic range  observed for a wide range of behavior in vitro in the lac operon , since no interesting behavior is observed for higher values  to avoid negative fitness values [the range for θ is calculated once h and k are known and remains fixed throughout the simulation. Separate experiments were performed for different strengths of the regulatory allele A (i.e. TA = -1 or +1). In the main text we only report the case TA = +1 (i.e. high constitutive expression) as the other case is qualitatively equivalent; see Additional file TA= -1).For each of the eight network mutations, 10,000 independent evolutionary simulations were performed, with a set of random parameter values .Click here for fileGenotype ordering with respect to Click here for fileSimulation examples. Per generation change in genotype frequency is shown for two cases, one leading to recruitment, the other to protected polymorphism.Click here for fileA = -1Simulation results with T. In the text we consider the case of high constitutive expression of the A allele (i.e. TA = +1). We demonstrate qualitatively similar results with low constitutive expression of the A allele (i.e. TA = -1).Click here for file


Intergroup conflict is often driven by an individual's motivation to protect oneself and fellow group members against the threat of out-group aggression, including the tendency to pre-empt out-group threat through a competitive approach. Here we link such defense-motivated competition to oxytocin, a hypothalamic neuropeptide involved in reproduction and social bonding. An intergroup conflict game was developed to disentangle whether oxytocin motivates competitive approach to protect (i) immediate self-interest, (ii) vulnerable in-group members, or (iii) both. Males self-administered oxytocin or placebo (double-blind placebo-controlled) and made decisions with financial consequences to themselves, their fellow in-group members, and a competing out-group. Game payoffs were manipulated between-subjects so that non-cooperation by the out-group had high vs. low impact on personal payoff , and high vs. low impact on payoff to fellow in-group members (in-group vulnerability). When personal vulnerability was high, non-cooperation was unaffected by treatment and in-group vulnerability. When personal vulnerability was low, however, in-group vulnerability motivated non-cooperation but only when males received oxytocin. Oxytocin fuels a defense-motivated competitive approach to protect vulnerable group members, even when personal fate is not at stake. Intergroup relations are often marked by non-cooperation and competitive behavior, creating levels of aggression and violence that bring about severe societal costs Competitive approach of, and defense-motivated non-cooperation towards rivaling out-groups serves the individual's personal interests, as it signals the individual's loyalty and commitment to fellow group members, encouraging inclusion rather than exclusion from profitable within-group exchange and cooperation Because of its functionality to individual and group survival, the human brain may have evolved neurobiological mechanisms that support and sustain defense-motivated non-cooperation towards rivaling out-groups Three lines of evidence suggest that oxytocin not only promotes cooperation, but is involved also in defense-motivated non-cooperation towards rivaling out-groups. In free-living meerkats, infusion of oxytocin versus placebo motivated an array of cooperative behaviors including longer time-on-guard Disentangling these different possibilities would advance our understanding of the role of oxytocin in the evolution of group life. If, in intergroup conflict, oxytocin-motivated competitive approach varies as a function of the extent to which self-interest is at stake, we have to re-interpret previous work as showing that oxytocin up-regulates what Adam Smith called “enlightened self-interest.” But if oxytocin-motivated competitive approach varies  as a function of the extent to which the interests of fellow in-group members is at stake, we may be in a position to infer that oxytocin shifts the individual's focus away from immediate self-interest and towards in-group interests, and that oxytocin's functions include a tendency to tend-and-defend the in-group.To disentangle these possibilities, we developed a behavioral game in which participants acted as the representative of a group of three that competed with a protagonist representing a three-person out-group. Cardinal payoffs in the game were manipulated so that non-cooperation by the out-group had strong versus weak impact on the participant's personal outcome  and, independently, the outcomes for the two other in-group members that were represented by the participant (in-group vulnerability). We expected to replicate earlier work In keeping with past work The game was modeled after the Prisoner's Dilemma PD;  so that In Following instructions using the games in F = 7.86, p = 0.006, partial η2 = 0.076, a trend towards an interaction between In-Group Vulnerability and Treatment, F = 3.19, p = 0.077, and a significant three-way interaction, F = 5.97, p = 0.016, partial η2 = 0.06. Fs<1. When Personal Vulnerability was low, however, non-cooperation was higher when In-Group Vulnerability was high rather than low, but only among individuals given oxytocin rather than placebo ×2 ×2 (In-Group Vulnerability: High/Low) between-subjects ANOVAs. For non-cooperation there was a main effect for Personal Vulnerablity, M = 3.828 vs. M = 3.002, F = 7.23, p = 0.008, partial η2 = 0.071  In-group defending was measured in 72 participants  = 7.18, p<0.010, partial η2 = 0.093. F = 6.18, p<0.015 rather than placebo, F = 1.89, p<0.178. Further supporting hypothesis (ii), in-group defending positively related to non-cooperation, r(72) = 0.428, p<0.001.Oxytocin-induced non-cooperation appears motivated by the desire to protect vulnerable in-group members, as predicted in hypothesis (iii). Indeed, as predicted in hypothesis (i), in-group tending was higher when participants received oxytocin rather than placebo, icipants , and wasF<1.41, ps>0.238, partial η2<0.015; Moverall = 2.873, SD = 1.978): Oxytocin's effects on participants' non-cooperation cannot be attributed to altered expectations of out-group behavior.The game structure was symmetrical see , and parM = 0.715) rather than low (M = −0.095), F = 5.59, p = 0.020, partial η2 = 0.056. Second, we observed a Treatment by In-Group Vulnerability interaction, F = 4.14, p<0.045, partial η2 = 0.042  (see M = 0.115) or low (M = 0.522), F = 0.65, p = 0.424. When given oxytocin, however, participants' level of non-cooperation was higher when in-group vulnerability was high (M = 0.778) rather than low (M = −0.192), F = 4.01, p = 0.048. In fact, and as shown in t[27] = 2.294, p<0.030; all other t<|1.199|, ps>.243). Thus, males engaged in excessive non-cooperation when in-group vulnerability was high and they received oxytocin rather than placebo.To explore whether in-group protection creates excessive non-cooperation, we analyzed the difference between participant non-cooperation and expected out-group non-cooperation. This revealed, first, more excessive non-cooperation when personal vulnerability was high (.22) see . When giThe neuropeptide oxytocin not only motivates cooperation towards familiar others, and those belonging to one's in-group Because groups were ad hoc and formed on the basis of a trivial criterion the (vulnerable) individuals protected here were relative strangers and not genetically related to the participant, findings are at odds with kin-selection theory of altruism that predicts altruism to be close to absent for genetically unrelated others There is no evidence that oxytocin motivates greed and spiteful tendencies towards rivaling out-groups Whether self-interest and the interest of fellow in-group members can be truly separated may be debatable. For example, human and non-human cooperation may be explained as serving the individual's long-term personal interests in survival and (re)productive success, and defense-motivated non-cooperation towards an out-group accrues quality signals to the individual that provide long-term benefits Participants engaged in decision making without feedback. In as much as cooperation tends to elicit cooperation, non-cooperation often begets non-cooperative responses N = 105; Mean age = 21.13 years, SD = 1.29) were recruited via an on-line system and offered €10 (approx. USD 13) for participating in a study on medication and decision-making. Exclusion criteria were significant medical or psychiatric illness, prescription-based medication, smoking more than five cigarettes per day, and drug or alcohol abuse. Data of three participants were discarded because they erred on all six questions verifying their understanding of the experimental game. The experiment was approved by the Psychology Ethics Committee of the University of Amsterdam, and adhered to the guidelines set forth in the Declaration of Helsinki. Participants provided informed consent prior to the experiment.Males (Participants were instructed to refrain from smoking or drinking (except water) for 2 hours before the experiment and randomly assigned to the oxytocin or placebo group . Participants self-administered a single intranasal dose of 24 IU oxytocin  or placebo. The placebo contained all the active ingredients except for the neuropeptide, was prepared according to Good Manufacturing Practice (GMP) and Good Clinical Practice (GCP), and delivered in the same bottles as Syntocinon.N = 75), and in Spring 2012 (N = 30). Analyses revealed no interaction effects involving data collection wave on any of the dependent variables and this factor is further ignored. Participants were seated in individual cubicles preventing them from seeing others and communicating, signed an informed consent, and self-administered the medication under experimenter supervision. The experimenter left and participants completed a series of unrelated questionnaires and tests that were presented on their computer screen, using the keyboard to answer questions.Participants came to the laboratory and learned that pay was equivalent to their show-up fee and their earnings during the decision task (range €1—€8). Data were collected in Spring 2011 (Because effects of oxytocin plateau after approximately 35 min Participants then read that their income to “Triangle” (their in-group) and to “Circle” (the out-group) depended on the participant's own decisions, and those of a representative of Circle's whom they would be paired with through the computer network. A table showed the payoffs to Triangle (in-group) and Circle (out-group) as a function of the four possible combinations of choices . We altered the cardinal payoffs to create variation in Personal and In-Group Vulnerability while at the same time maintaining the ordinal structure of the game as well as Greed and Cooperator's Gain (see main text). This resulted in four different games , were assured that decisions would remain confidential, and asked five times to make a choice between 1 (cooperation) and 2 (non-cooperation) (no feedback was given). To motivate serious decision making, participants were reminded prior to each choice that this choice might be randomly selected for pay-out to all members of Triangle and Circle. As participants interacted through the computer network they could not see each other. Following decision making, we assessed in-group tending (“during decision making I tried to serve the interests of my group” and “during decision making I tried to help my team”)  and in-group protection . Due to a programming error, data on in-group protection were recorded only for the Spring 2011 wave. The main experimental task  took 14—17 min. Upon finishing the questionnaire, participants were thanked and dismissed. They returned four to six weeks later to pick up a sealed envelope containing their credits, additional earnings, and a full debriefing. We used a time-lag between experimental session and debriefing to prevent that any insight on methods and materials became known before the entire experiment was completed. All participants agreed to this procedure.


Each window generates its own measurements using a random sensing matrix. The more significant elements are contained by more windows, so they are captured by more measurements. This design makes the EW-CS scheme have more convenient implementation and better overall recovery quality for non-uniform compressible signals than ordinary CS schemes. These advantages are theoretically analyzed and experimentally confirmed. Moreover, the EW-CS scheme is applied to the compressed acquisition of image signals and networked data where it also has superior performance than ordinary CS and the existing unequal protection CS schemes.Many practical compressible signals like image signals or the networked data in wireless sensor networks have non-uniform support distribution in their sparse representation domain. Utilizing this prior information, a novel compressed sensing (CS) scheme with unequal protection capability is proposed in this paper by introducing a windowing strategy called expanding window compressed sensing (EW-CS). According to the importance of different parts of the signal, the signal is divided into several nested subsets,  In the CS methodology, the signal which is sparse or compressible on a certain orthonormal basis can be successfully recovered from a highly incomplete set of samples, called measurements. Moreover, the measurements can be obtained by multiplying the signal by a randomly generated sensing matrix that is incoherent with most of the orthonormal basis. Thus, CS greatly improves the efficiency and decreases the complexity of signal compression.Compressed sensing (CS) ,2 is an The compressible signal can be indicated by the index of the sparse non-zero components and the value of the non-zero components, where the index of the sparse non-zero components is called sparse support. The ordinary CS algorithms are designed without any constraint on the distribution of the support of the sparse signal. Actually, many natural signals do have special support structures. For example, the image signal is compressible in the discrete cosine transform (DCT) basis or discrete wavelet transform (DWT) basis. The transform coefficients constitute a non-uniform compressible signal where the significant coefficients mostly appear at lower frequency, as shown in Considering these largely existing non-uniform compressible signals, if we can utilize the prior-knowledge of the support distribution to provide unequal protection for different parts of the signal, we can instinctively achieve better performance. In this paper, such a CS algorithm is proposed to improve the sensing and recovery efficiency for the non-uniform compressible signals, called the expanding window compressed sensing (EW-CS). The windowing method is inspired by the expanding window fountain codes ,6, whereThe proposed EW-CS scheme treats the different parts of the compressible signal discriminately to pursue the improved overall performance. The more attention on the more important parts is at the expense of the less important parts. Nevertheless, it is worthwhile to do this, because most of the energy or the useful information is contained in the more important parts. The overall performance improvement also has its prerequisite that is the prior knowledge of the rough non-uniform distribution of the significant elements. This prior information is not difficult to get in most cases. For image signals, the significant transform coefficients mostly appear at lower frequency. For networked data, the significant data is surrounding the emerging event. The above statements about the EW-CS are presented and proved from theoretical and numerical perspectives in our paper. Moreover, the EW-CS is applied to image signals and networked data, and shown to provide better performance than the ordinary CS and the existing unequal protection CS schemes.The rest of this paper is organized as follows: in Section 2, the key issues of CS are briefly reviewed, and the related existing CS algorithms considering non-uniform compressible signals are presented and compared with our EW-CS algorithm. The details of the EW-CS scheme are introduced in Section 3. Section 4 is devoted to analyze the recovery error upper bounds of the proposed EW-CS to compare with the ordinary CS. In Section 5, the variation of basic EW-CS algorithm is discussed. The experimental results are shown and analyzed in Section 6. Section 7 concludes this paper and gives some directions for future work.2.2.1.X ∈ ℝN is said to be sparse, if the transform coefficient vector Θ = { iθ, i = 1,2, …, N}, of X in an orthogonal basis ΨN×N are mostly zero. The sparse support of Θ (or X) is defined as S = {ii: θ ≠ 0, i = 1,2,…, N}, and the length of S is the sparsity K = |S|, K ≪ N, so signal X is called as K-sparse signal. We consider a linear sparse case that K = αN, 0 < α ≪ 1 is a constant. If the most coefficients are not exactly zero but with small magnitude, signal X is called compressible signal. The elements with larger absolute value are regarded as significant. CS theory l1-norm mCompared with the unequal protection methods like the hidden Markov tree model in . which u3.The proposed EW-CS scheme is detailed in this section. First, the non-uniform compressible signal is formularized. Then, the general EW-CS encoding and decoding algorithms are presented. Finally, we simplify the EW-CS to a two-window case which is quite important for applications and analysis.3.1.X = {ix | i = 1,2,…N}T is compressible in the canonical basis, i.e., the orthogonal basis ΨN×N = I. The scheme can be directly applied to other basis. A more tractable definition of the compressible signal X is using the power law that the k-th largest entry of the signal obeys |(k)x| ≤ pC·k−1/p, where pC > 0 and 0 <p <1. pC represents the energy of the signal which is a constant depending on p, and p is the speed of decay. The sparsity is defined as K when there are K significant elements containing the most energy of the compressible signal, i.e., the first K largest elements |(k)x|, k = 1,…K.In the proposed EW-CS scheme, for clearer explanation, we assume that the signal X is divided into W non-overlapped importance classes. The size of the w-th class is defined by ws so that w = 1, 2, …, W, 0 ≤ ws ≤ N. We further assume that the importance of a class decreases with the class's index, i.e., the w-th class is more important than the (w + 1)-th class. The division can be described using a generating polynomial (GP) k = (k/Ns) ϵ  is the ratio of the elements in the importance class w to all the N elements. The sparsity distribution is given as w ≤ 1 is the proportional factor representing the number of significant elements placed in the w-th class.The non-uniform compressible signal means that the distribution of the significant elements in the sparse support is non-uniform, that is, the support distribution has some structured characteristics. We use importance classes to describe this distribution. From the sparsity perspective, the importance of a class is corresponding to how many significant elements it contains. The compressible signal 3.2.3.2.1.w-th window consists of all the first w classes, so the size of the window is, w = 1, 2, …, W; thus, the last window contains all the signal's elements with wn = N. The structure of the EW-CS is shown in The importance class determines a sequence of strictly increasing subsets of the signal's elements, which we call windows. The N . Given the overall sensing rate R, the number of the random projections is M = RN. The measurements allocated for each window can also be given by a measuring polynomial (MP) w ≤ 1 denotes the ratio of measurements assigned for the w-th window to all the measurements. It means that we generate wm = ΩwM random projections X is the vector of the elements in w-th window, and (w)X = X.In the classical CS algorithm, one method to generate the random sensing matrix is by picking the entries from Gaussian distribution w-th importance class belongs to the w-th window and all its subsequent windows, so the elements of w-th importance class are sampled by the w-th and all the subsequent classes of measurements. For example, the first importance class  is sampled in all M measurements, and the last importance class is sampled only in ΩwM measurements. Therefore, the elements in importance class with smaller index corresponding to more measurements obtain more protection.It can be noticed from w is the probability that the w-th window is chosen. Encoding with the window selection distribution may bring uncertain sensing rate, but it can be roughly regarded that wm = ΓwM. As in a CS system each measurement is actually the inner product of the corresponding row of the sensing matrix and the signal vector, it can be calculated separately. For instance, if one measurement k = 1, 2, …, wm, j = 1, 2, …, M is the k-th measurement assigned to the w-th window, we get kn and k-th row of the sensing matrix Although the classes of measurements are described to be generated sequentially in 3.2.2.X simultaneously through CS reconstruction method. If we use the sequential generation method, the joint sensing matrix ФM×N can be written as a combination of all the window sensing matrix Фw, as shown in The encoding strategy of the EW-CS is presented class by class. This is sometimes necessary for constrained encoder or distributed coding scenarios, but it is usually more efficient to use joint decoder, which combines the measurements together, and recovers the original M×N, i.e., Y = ФM×NX. Thus, the signal X can be recovered using ordinary CS recovery algorithms mentioned in Section 2.Thus, the joint decoding can be implemented using this joint sensing matrix. At the decoder side, all the received random projections compose a measurement vector 3.3.In the previous subsection, we described the proposed EW-CS scheme in general format. Nevertheless, the most common situation is that the significant elements of a natural compressible signal are concentrated at a certain part of the signal. Therefore, two importance classes are enough for the usual non-uniform compressible signal. The first importance class consists of more large elements than the second importance class. The first importance class is also the first window, and the entire signal is the second window. The two-window EW-CS has wider application prospects; thus, this special case of the EW-CS is discussed in detail below.x) = Π1x + (1 − Π1)x2 which is determined by only one coefficient Π1 ∈ . Similarly, the sparsity distribution can be written as Λ(x) = Λ1x + (1 − Λ1) x2. If the first class really has more significant elements, 0.5 < Λ1 ≤ 1; otherwise 0 < Λ1 ≤ 0.5. For clarification, we adopt the sequential generation as shown in x) = Ω1x + (1−Ω1)x2. By increasing Ω1, we progressively increase the protection of the first importance class. The extreme cases of Π1 = M1 = 0 and Π1 = M1 = 0 are the ordinary CS problems.In the two-window EW-CS, the GP is Π(1 for short form), and2 =  for short form). Then the encoding procedure can be given as:Y1 and Y2 denote the measurement vectors for the two windows respectively. The encoding can also be written in joint coding format that:Based on above definitions, the joint sensing matrix is given as:X1 and X2 denote the signal elements of the two importance classes not the two windows, which are defined as different from X(1) and X(2). The joint coding format is necessary for facilitating the performance analysis of the EW-CS and contrast with the ordinary CS in the next section.It must be noted that 4.In this section, the reconstruction error upper bounds of the EW-CS is analyzed and contrasted with the ordinary CS scheme (using CS for short). The simple two-window EW-CS is firstly discussed, and then the results are further extended to the general EW-CS.4.1.l2-norm recovery error defined as ‖X − X̂‖l2 is adopted to judge the recovery performance. The performance analysis is presented by contrasting between the CS and the EW-CS. According to the joint coding format of the EW-CS in Subsection 3.3, the CS problem is also formulated by correspondingly divided the signal vector X, the measurement vector Y and the sensing matrix Ф into different parts. It is given as:The 1,2 with all zero matrix of the same size, and then the CS problem becomes the EW-CS as shown in The most direct relationship between the CS and the EW-CS can be obtained by replacing the sub-matrix Фi.e., Y1CS and Y1EW. However, the joint recovery algorithms for the CS and the EW-CS use both of the two classes of measurements, so we need a joint coding representation to reveal the difference shown in X can be written as N dimensional vector X for the first n1 elements, and the remaining (n2 − n1) elements of X for the last (n2 − n1) elements, and the remaining elements of It can be found that the only difference between the CS and the EW-CS is the different generation of the first class of measurements, X1 and X2 separately. This is equal to consideringFor analyzing the discriminational protection of different importance classes, we should consider The first terms on the right hand of l2-norm recovery error from inaccurate measurements have the upper bound as:sf denotes the truncated vector corresponding to the S largest values of compressible signal f . S is chosen such that δ3S + 3δ4S < 2, and f's sparsity K ≤ S. ε is the maximum l2-norm of the noise e, i.e., ∥e∥ℓ2 ≤ ε. The constants C1,S and C2,S depend on the reasonable value of δ4S. The second term on the right hand side of This result can also be proved with the aid of mathematical formulae. From the Theorem 2 in , the l2-For the X2 is all zero vector. Based on ε1EW ≤ ε1CS. It means that the upper bound of the EW-CS for X, i.e., the subset of elements in Note that the second terms on the right side of 1) percentage of all the measurements, so they may not guarantee the best recovery. Oher looser bounds for approximation error are introduced here for analyzing Comparing with l1-norm obeys the following result with overwhelming probability:M ≥ logN is the number of measurements, and N is the length of signal f. pC, the fixed decay speed p and α. The parameter α is a sufficiently small positive number to ensure f∥ℓ1R and p = 1 when For compressible signals obeying the power law, there is an earlier result in  and 2]  2] whichM2 is the number of effectual measurements for i.e., 1 is defined in previous section as the ratio of number of measurements assigned to the first window . Obviously, p2. It is easy to find that when 0 < p2 < 2, the CS's bound is lower than the EW-CS's; when p2 = 2, they are equal; when p2 > 2, the EW-CS's bound is lower than CS's in return. However, the error bound is behaved for compressible signal usually with 0 < p2 < 1 or with 0 < p2 < 2 [This is a looser one than X is discussed. The square error of signal X is given as:Now, the comparison between the CS and the EW-CS for the entire signal X using the CS and the EW-CS can be derived by substituting Thus, the overall recovery error upper bounds for ε1 and M2 which are determined by sparsity distribution and MP, i.e., the parameters Λ1 and Ω1. However, if there are really more significant elements placed in i.e., 0.5 < Λ1 ≤ 1, the first term will dominate the overall error upper bounds; otherwise, the second term will do so. Thus, the EW-CS is superior to the CS for a non-uniform compressible signal with proper importance classes assignment.We assume that 4.2.W ≥ 3 windows case. The encoding of the W-window EW-CS is written as:Based on the ana1ysis of the two-window EW-CS, the results are easily extended to EW is a lower triangular matrix. We only consider one importance class Note that the EW-CS's sensing matrix Φw is, the w-th importance class has better recovery quality. Finally, the overall error upper bound for the EW-CS is given as:Comparing with the conventional CS, only for the first importance class vector 5.i.e., 0.5 < Λ1 ≤ 1 in the two-window case. Thus, the extension of the EW-CS is necessary for this case. The two basic variations are shown in During the introduction of the EW-CS scheme in Section 3, there may be a question that what happens if the importance of classes doesn't decrease with the class index as we assumed. From the analysis in last section, we know that the performance of the EW-CS degraded badly when the more important class doesn't contain more significant elements, It doesn't mean that the EW-CS can only be used in the simple cases where the significant elements concentrate in the front, in the middle or at the back of the signal. It has an even more complicated variation in a certain case. Recall that we have designed a window selection distribution such that each measurement can select the window it belongs to. Similarly, the signal element can also choose the window that it belongs to. It looks a little abnormal in our usual practice, for the signal element may not know its own importance or even do the selection. However, it can be realized in certain case, the wireless sensor network scenarios.N sensors' data is regarded as a compressible signal X = {ix | i = 1, 2, …, N}, where ix is the data of the i-th sensor. Using ordinary CS, each sensor send ijy = jixiφ to the sink node, and then the sink can collect all the received data to generate one measurement X. This mechanism assumes that all the sensors' data are equal importance, but it is a common situation in wireless sensor networks that a warning line is set a priori for the temperature, pressure or gas strength detection systems. In this case, the EW-CS scheme can be used to simplify this collection process. Each sensor can decide its sensed data is important or not according to the warning line, and then choose the window it belongs to. With one warning line, the two-window EW-CS is applied. If the sensor's data is beyond the warning line, it is in the first window and sends its jiy for M times. If its data is within the security region, it is in the second window and sends its jiy for only m2 < M times. This leads to the better recovery quality for the warning sensor's data, and resaves the transmission energy for the safe sensors.Let us consider the CWS  problem.6.6.1.l2-norm of the recovery error, i.e., ∥ X − X̂ ∥ℓ2, is used to evaluate the performance of the proposed EW-CS algorithm. A compressible signal X ∈ ℝN is generated obeying the power law with the parameters pC = 10 and p = 1 The length of the signal is N = 512, and the sparsity is set as K = 50. The two-window EW-CS is used to compare with the ordinary CS. For constructing the signal in a non-uniform format, the randomly selected Λ1K elements from the first K K largest elements are placed in the first importance class, and the rest (1−Λ1)K elements are placed in the second importance class. Other (N−K) smaller elements are distributed randomly. The parameters defining the size of the first importance class and its corresponding number of measurements are fixed as Π1 = 0.3 and Ω1 = 0.5.In our simulation, the R, and the total number of measurements is M. The sensing matrix ФEW is constructed by first creating a M × N matrix, i.e., the sensing matrix ФCS, with i.i.d. draws of a Gaussian distribution N, then the right upper Ω1M × (1−Π1)N sub-matrix is replaced by all zero matrix with the same size. The recovery algorithm we used is the l1 based method which is implemented by using a package for specifying and solving convex programs [The overall sensing rate is programs ,24.1 = 0.8 and R = 0.4. The original signal and its recovered version are plotted in l2-norm error for the component signals l2-norm error for the signal X is 1.1808. Note that the significant elements of the signal are almost well recovered and the elements in the first importance class have better recovery quality than that in the second class.In the first example, we consider a compressible signal with Λ1, the l2-norm error of the signal X and the component signals R = 0.2 and R = 0.4. The results indicate that the performance of the EW-CS varies with the ratio Λ1, while the ordinary CS is not impacted by Λ1. With the increase of Λ1, the recovery error of the EW-CS decreases. Roughly speaking, when 0 ≤ Λ1 ≤ 0.5, the CS outperforms the EW-CS. This because that the first importance class is not the really most important one. It means that using the EW-CS with wrong matched window settings will introduce more errors.For various choices of Λ1 ≤ 1, the EW-CS begins to outperform the CS. In this case, the window settings match the signal's features, so the superiority of the EW-CS is demonstrated. It can also be noticed that the performance for the component signal Nevertheless, when 0.5 ≤ Λ6.2.i.e., “Lena”, “Boat”, “Peppers” and “Aerial”, are used for simulation. The images are divided into 32 × 32 blocks for computational facility.For testing the practical performance of the proposed EW-CS, instead of using artificially generated signals, we used real-world non-uniform compressible signals. The image signals' DCT or DWT coefficients constitute non-uniform compressible signals. With this prior knowledge, the random sensing with the EW-CS can be accomplished. The 512 × 512 test gray images with different features, l1 based method to recover the wavelet coefficients, and did the inverse wavelet transform to recover the original image. In our simulation, the three level DWT is used in M-CS with the measurement allocation rule in [The M-CS scheme in  is simul rule in . The levAlthough the importance class design in the EW-CS can also directly use the sub-bands of 2-D DWT coefficients, the additional transform process is not willing to do. Thus, we choose 1-D DCT as the sparse representation basis which will be used only at the decoder so that the low-complexity encoder is guaranteed. The ordinary CS is also simulated with the 1-D DCT.1 = 0.3 and Ω1 = 0.5. The visual quality comparison for “Lena” is given in Firstly, we use the two-window EW-CS with the parameters ΠIn M-CS, the significant coefficients are only sampled by the measurements allocated to the sub-band they belong, not all the measurements, so its performance is worse than the EW-CS at most sensing rates. At low sensing rate, the number of measurements for the most significant coefficients in the M-CS is fixed to guarantee successful recovery, and these measurements are noiseless. However, the EW-CS cannot recover the elements in the first importance class from the noisy measurements even though they are more. When the sensing rate increases, this problem will not exist.R = 0.4. In order to compare the PSNR performance of the original CS method and the EW-CS method, we fix the signal power, and compensate the power of the all zero matrix Φ1,2 to the Φ1,1 to enlarge the signal power of the most significant class. The PSNR performances with different signal-to-noise ratio (SNR) for the four images are shown in In the second simulation, we reconstruct the images from the noisy measurements which are transmitted through an AWGN channel. The sensing rate is fixed as We can observe that the EW-CS is worse than the CS at lower SNR, but outperforms the CS when the SNR increases. The M-CS's PSNR is lowest at the same SNR, but its decay speed is similar to the CS and is slower than the EW-CS. When the channel noise energy gets greater, the advantage of recovery the first importance class of the EW-CS is weaken, and the recovery quality of the second importance class degrades further. Thus, the EW-CS algorithm is more applicable to the mild transmission environments.1 is given in 1 for different measurement allocation parameters Ω1 will be different. That's why the x axis for each curve in 1, there is a optimal first window size, but the general trend is the first window should not be too large.Then, we investigate the impact of changing window size on the recovery quality of the two-window EW-CS. The PSNR performance of “Lena” with different Π1 when Π1 = 0.2, Π1 = 0.3 and Π1 = 0.4. The available ranges of Ω1 for different Π1 are different according to the design rule of the joint sensing matrix. The simulation results are plotted in 1 = 0.2 and Π1 = 0.3, there is an optimal number of measurements that should be assigned to it. For Π1 = 0.4, however, the more measurements, the better.We also evaluate the PSNR performance of the EW-CS with different Ωx) = 0.3x + 0.2x2 + 0.5x3 and MP Ω(x) = 0.5x + 0.2x2 + 0.3x. The four-window EW-CS is designed withΠ(x) = 0.1x + 0.2x2 + 0.3x3 + 0.4x4 and Ω(x) = 0.1x + 0.2x2 + 0.3x3 + 0.4x4. The five-window EW-CS is designed with Π(x) = 0.1x + 0.1x2 + 0.1x3 + 0.2x4 + 0.5x5 and Ω(x) = 0.1x + 0.1x2 + 0.3x3 + 0.2x4 + 0.3x5. The PSNR performance for different window designs for image “Lena” is shown in Finally, we design the EW-CS with more than two windows. The rank law should also be obeyed. So the three-window EW-CS is designed with the GP Π(6.3.N = 256 sensors are randomly distributed within this area to monitor the events of interest. When E events happen, the sensor's data is affected by all the events, and the relationship between them is assumed to be a distance decaying model, which is determined by the distance i,jd from the sensor i to the event j, where i = 1, 2, …, N and j = 1, 2, …, E, and the attenuation factor. If the j-th event's magnitude is jC, the i-th sensor's data is calculated as α is the propagation loss factor. Here we assume that E = 3, and all jC are equal to 100, α = 3.8.The variation of the EW-CS applied in wireless sensor networks is implemented here. We define a 500 m × 500 m sensing area. 1 = 0.3. The first window size is determined by the threshold given to each sensor from the collection centre (not shown in 1 = 0.5. The l2-norm recovery error of this example is 0.2401. More simulation results with different transmission rates are plotted in l2-norm recovery error with different SNR is given in For the two-window EW-CS, 1 = 0.5 and the transmission channel is noiseless. The EW-CS in CWS case has the feature that the Π1N elements in the first window are expected to be the first Π1N largest ones. With the same ratio Ω1, the smaller the first window is, the more measurements are assigned to the most largest or significant elements, so the overall performance is inversely proportional to the size of the first window as shown in Finally, the performance of the EW-CS with changing first window size is shown in 7.i.e., image signals and networked data, to verify its superior performance. However, its noise-resilient performance is not very good, which is the problem we decided to solve in future work. The adaptive version of the proposed scheme that can optimize the parameters of designed windows is also an interesting direction to be investigated.A novel compressed sensing scheme called expanding window compressed sensing is proposed in this paper to provide unequal protection for non-uniform compressible signals. The efficiency of the proposed scheme is analyzed from the recovery error upper bounds perspective by comparing with ordinary compressed sensing. Different from weighted methods, the windowing technology is adopted to make the scheme more flexible and efficient. Comparing with the blocked sensing method, the nested window design gets more benefit from the joint recovery algorithm for the nested window. The scheme is further applied to practical non-uniform compressible signals,


One of the most fundamental and challenging tasks in bio-informatics is to identify related sequences and their hidden biological significance. The most popular and proven best practice method to accomplish this task is aligning multiple sequences together. However, multiple sequence alignment is a computing extensive task. In addition, the advancement in DNA/RNA and Protein sequencing techniques has created a vast amount of sequences to be analyzed that exceeding the capability of traditional computing models. Therefore, an effective parallel multiple sequence alignment model capable of resolving these issues is in a great demand.O(1) run-time solutions for both local and global dynamic programming pair-wise alignment algorithms on reconfigurable mesh computing model. To align m sequences with max length n, we combining the parallel pair-wise dynamic programming solutions with newly designed parallel components. We successfully reduce the progressive multiple sequence alignment algorithm's run-time complexity from O(m × n4) to O(m) using O(m × n3) processing units for scoring schemes that use three distinct values for match/mismatch/gap-extension. The general solution to multiple sequence alignment algorithm takes O(m × n4) processing units and completes in O(m) time.We design O(m) run-time. We also provide a new parallel algorithm for the Longest Common Subsequence (LCS) with O(1) run-time using O(n3) processing units. This is a big improvement over the current best constant-time algorithm that uses O(n4) processing units.To our knowledge, this is the first time the progressive multiple sequence alignment algorithm is completely parallelized with  The advancement of DNA/RNA and protein sequencing and sequence identification has created numerous databases of sequences. One of the most fundamental and challenging tasks in bio-informatics is to identify related sequences and their hidden biological significance. Aligning multiple sequences together provides researchers with one of the best solutions to this task. In general, multiple sequence alignment can be defined as:Definition 1Given: m sequences, , over an alphabet ∑, where each sequence contains up to n symbols from ∑; a scoring function h: and a gap cost function. Multiple sequence alignment is a technique to transform  to where is si ∪ '-' [gap insertions], that optimizes the matching scores between the residues across all sequence columns  as in  and 29]29]. In , the indO(m2n2) to O(n) and step (iii) from O(mn4) to O(m3n) ≈ O(n4), [or O(m4) if n <m]. The overall run-time complexity of the original progressive multiple sequence alignment algorithm is still dominated by step (iii) with an order of O(m3n) regardless of how many processing units are used. The bottle-neck is the pair-wise group alignments must be done in order dictated by the dendrogram (O(m)), and each alignment requires all the column pair-wise scores be calculated (O(m2)). To address these issues, we design our parallel progressive multiple sequence alignment on a reconfigurable mesh (r-mesh) computing model similar to the ones used in , the unary 1UN presentation of x in n-bit is: x = , where bi = 1 for all i ≤ x and bi = 0 for all i > x  can be found in O(c) time on an n × n r-mesh . As a result, a DP r-mesh can be built with 1-bit input components to handle all pair-wise alignments using constant scoring schemes that can be converted to  range. For instance, the scoring scheme for the longest common subsequence rewards 1 for a match and zero for mismatch and gap extension.ci, j loads or computes its symbol matching score for the symbol pair at row i column j, initially. The next step is to configure all the adder/subtractor units based on the loaded values and the gap cost g. Finally, a signal is broadcasted from c0,0 to its neighboring cells c0,1, c1,0, and c1,1 to activate the DP algorithm on the r-mesh. The values coming from cells ci-1, j and ci, j-1 are subtracted with the gap costs. The value coming from ci-1, j-1 is added with the initial symbol matching score in ci, j. These values will flow through the DP r-mesh in one broadcasting step, and cell cn, n will receive the correct value of the alignment.To align two sequences, O(1). Each cell uses 10n processing units (4n for the 1-bit max switch and 2n for each of the three adder/subtrator units). These processing units are bounded by O(n). Therefore, the n × n dynamic programming r-mesh uses O(n3) processing units.In term of time complexity, this dynamic programming r-mesh takes a constant time to initialize the DP r-mesh and one broadcasting time to compute the alignment. Thus, its run-time complexity is k × n adder/subtractor r-meshes and n × n max switches must be used. In addition, to avoid overflow (or underflow) all pre-defined pair-wise symbol matching scores may have to be scaled up (or down) so that the possible smallest (or largest) number can fit in the 1UN representation. With this configuration, the dynamic programming r-mesh takes O(n4) processing units.To handle all other scoring schemes, g = 0).The complication of signed numbers does not exist in the longest common subsequence problem. The arithmetic operation in LCS is a simple addition of 1 if there is a match. The same dynamic programming r-mesh as seen in Figure x and y, each max switch in the DP r-mesh is configured as in Figure ci-1, j-1 is fed into the North-West processing unit, and the other values are fed into the North-East unit. Then, ci, j loads in its symbols and fuses the South-East processing unit (in bold) as NS,E,W if the symbols at row i and column j are different; otherwise, it loads 1 into the adder unit and fuses N,E,SW. These configurations allow either the value from cell ci-1, j-1 or the max value of cells ci-1, j and ci, j-1 to pass through. These are the only changes for the DP r-mesh to solve the LCS problems.To find the longest common subsequence between two sequences O(n3) processing units. However, this is an order of reduction comparing the current best constant parallel DP algorithm that uses an r-mesh of size O(n2) × O(n2)  of the progressive MSA algorithm is following the dendrogram, built in the earlier step, to perform pair-wise dynamic programming alignment on two pre-aligned groups of sequences. The dynamic programming alignment algorithm in this step is exactly the same as the one in step (i); however, quantifying a match between two columns of residues are no longer a simple constant look-up, unless the hierarchical expected probability (HEP) matching scoring scheme is used . The mosf is a column from one pre-aligned group of sequences and g is a column from the other pre-aligned group of sequences. fi and gj are residue symbols from columns f and g, respectively, and s is the matching score between these two symbols fi and gj. For example, to calculate the sum-of-pair of the following two columns f and g:where anda to residue b is the same as the matching between residue b to residue a, these pairs become , 3, , 3, , 3, 3. These redundancies occur since the set of symbols representing the residues is small (1 for gap plus 20 for protein [or 4 for DNA/RNA]). Thus, if we combine the two column symbols with their number of occurrences, the sum-of-pair method can be transformed into a counting problem and can be defined as:we will have to score 15 residue pairs:, , , , , , , , , , , , , , . Since the matching between residue f, g are the two columns, T is the number of different residue symbols (T = 4 for DNA/RNA and T = 20 for proteins), s is the pair-wise matching score, or substitution score, between two residue symbols i and j, and ni and nj are the total count of symbols/types i and j (i.e. the occurrences of residue symbols/types i and j), respectively. Since residues from both column f and g are merged, there is no distinction in which column the residue are from. Since T is constant, the summations in Equation remain constant, regardless how many sequences are involved.where Thus, the sum-of-pair score of the two columns given above will be:m processing units as follows. First, map each residue symbol into a numeric value from 1 to T. Next, m residues from any two aligning columns are assigned to m processing units. Any processing unit holding a residue sends a 1 to processing unit pk, where k is the number represents the residue symbol it is holding. pk sums the 1's it receives. The sum-of-pair score can be computed between the pairs of processing units containing a sum larger than 0 calculated from previous steps. All of these steps are carried out in constant time. There are n2 possible pair-wise column arrangements of two pre-aligned groups of sequences of max length n. Thus, the sum-of-pair column pair-wise matching scores for two pre-aligned groups of sequences can be done in O(1) using m × n2 processing units.This scoring function can be implemented on an array of O(1) using O(m) time using O(m) r-meshes. The latter is preferred since the dendrogram [step (ii)] and the progressive alignment [step (iii)] each takes O(m) time to complete. Then, a dendrogram is built, using the parallel neighbor-joining clustering algorithm described earlier, from all the pair-wise DP alignment scores from step (i). Lastly, [step (iii)], for each pair of pre-aligned groups of sequences along the dendrogram, the sum-of-pair column matching scores are pre-calculated for the DP r-mesh initialization before proceeding with the dynamic programming alignment. There are m - 1 branches in the dendrogram leading to m - 1 pair-wise group alignments to be performed. In terms of complexity, the progressive multiple sequence alignment takes O(m) time using O(n) DP r-meshes to complete all the pair-wise sequence alignments [step (i)] - (or O(1) time using O(m) time using O(m3) processing units. Finally, the progressive step, [step (iii)], takes O(m) time using a DP r-mesh. Therefore, the overall run-time complexity of this parallel progressive multiple sequence alignment is O(m). The number of processing units utilized in this parallel algorithm is bounded by the number of DP r-meshes used and their sizes. The general DP r-mesh uses O(n4) processing units to handle all scoring schemes with affine gap cost. And step (i) needs m of such DP r-meshes resulting in O(mn4) ≈ O(n5) processing units used.Progressive multiple sequence alignment algorithm is a heuristic alignment technique that builds up a final multiple sequence alignment by combining pair-wise alignments starting with the most similar pair and progressing to the most distant pair. The distance between the sequences can be calculated by dynamic programming algorithms such as Smith-Waterman's or Needle-Wunsch's algorithms (step i). The order in which the sequences should be aligned are represented as a guiding and can be calculated via hierarchical clustering algorithms similar to the one described in Section (step ii). After the guiding tree is completed, the input sequences can be pair-wise aligned following the order specified in the tree (step iii). In the previous Sections, we have described and designed several r-meshes to handle individual operations in the progressive multiple alignment algorithm. Finally, a progressive multiple sequence alignment r-mesh configuration can be constructed. First, the input sequences are pair-wise aligned using the dynamic programming r-mesh described previously in Section. These O(mn3) ≈ O(n4) processing units to complete in O(m) time.For alignment problems that use constant scoring schemes without affine gap cost, this parallel progressive multiple sequence alignment algorithm only needs Table m sequences with max length n, we are able to reduce the algorithm run-time complexity from O(m × n4) to O(m) using O(m × n4) processing units. For a scoring scheme that rewards 1 for a match, 0 for a mismatch, and -1 for a gap insertion/deletion, our algorithm uses only O(m × n3) processing units. Moreover, to our knowledge, we are the first to propose an O(1) run-time dynamic programming pair-wise alignment algorithm using only O(n3) processing units.In this study, we have designed various r-mesh components that can run in one broadcasting step, which enabling us to effectively parallelize the progressive multiple sequence alignment paradigm. to align The authors declare that they have no competing interests.KN designed parallel models used in this study. YP and GN participated in designing and criticizing the parallel models and their analysis. All authors read and approved the final manuscript.


Darwinian selection should preclude cooperation from evolving; yet cooperation is widespread among organisms. We show how kin selection and reciprocal altruism can promote cooperation in diverse 2×2 matrix games . We visualize kin selection as non-random interactions with like-strategies interacting more than by chance. Reciprocal altruism emerges from iterated games where players have some likelihood of knowing the identity of other players. This perspective allows us to combine kin selection and reciprocal altruism into a general matrix game model. Both mechanisms operating together should influence the evolution of cooperation. In the absence of kin selection, reciprocal altruism may be an evolutionarily stable strategy but is unable to invade a population of non-co-operators. Similarly, it may take a high degree of relatedness to permit cooperation to supplant non-cooperation. Together, a little bit of reciprocal altruism can, however, greatly reduce the threshold at which kin selection promotes cooperation, and vice-versa. To properly frame applications and tests of cooperation, empiricists should consider kin selection and reciprocal altruism together rather than as alternatives, and they should be applied to a broader class of social dilemmas than just the prisoner’s dilemma. Darwinian selection precludes any action that increases the competitive ability of others at the expense of one’s self c), a benefit to the recipient (b), and their genetic relatedness (r), Hamilton r>c/b. The concept is based on ‘inclusive fitness’: the sum of an individual’s reproductive success plus the effects the individual has on the reproductive success of its relatives. For example, sterile worker ants can accrue reproductive benefits by helping their relative, the queen. In so doing, their shared genes survive and get passed on to the next generation.The three standard motives for the evolution of cooperation include kin selection, reciprocity, and group selection Parallel to kin selection, Trivers Kin selection and reciprocal altruism are often viewed and tested as alternatives. Furthermore, theories of kin selection rely on population genetic models while models for reciprocal altruism focus on the specifics of repeated interactions and the capacity to shape conditional strategies. The two have never melded easily The germs of kin selection and reciprocal altruism can be traced back to Darwin r, the probability that like-individuals interact with like) and repeated interactions ; and 2) develop a general model for the evolution of cooperation that satisfies the requirements of all three games. While simple and straightforward, this combined treatment of kin selection and reciprocal altruism across a variety of social dilemmas is necessary for empiricists to properly frame applications and tests of cooperative behaviours.Here we formally combine kin selection and reciprocal altruism and show how they are mutually inclusive properties of games. We apply a game theoretic approach We describe three games – prisoner’s dilemma, snowdrift, and hawk-dove game – separately, to illustrate why individuals should act selfishly and under what conditions they should cooperate. We incorporate elements of both kin selection and reciprocal altruism, and combine all three games into a single general model.The prisoner’s dilemma provides the archetype for games pitting community interests against those of the individual. Two prisoners being questioned each have the choice to either defend the other’s innocence or betray their guilt. It is better for both players to defend rather than betray each other. The highest payoff of all, however, accrues to one who betrays while being defended by the other. The worst outcome accrues to a player that defends a betraying opponent.b) to its opponent at cost (c) to itself. A defector incurs no costs and bestows no benefits. We assume that b>c insuring that two co-operators enjoy a higher payoff than two defectors. While cooperation maximizes group payoffs, a defector will always enjoy higher payoffs than a co-operator when played against the same opponent. For this game, D is the non-invadable evolutionarily stable strategy (ESS), also known as the Nash equilibrium in conventional games As a 2×2 matrix game, the prisoner’s dilemma  has straDefection is an ESS so long as interactions occur at random with respect to strategy, and if the game is played but once. We relax these assumptions by considering non-random interactions and an iterative game by which individuals can gain information about others’ predispositions.r be the probability of non-random interactions where like-individuals interact with like, independent of the frequencies of co-operators and defectors in the population r occurs with like-individuals while the portion 1-r occurs with randomly selected individuals  and reciprocal altruism (w>c/b) into a single model by simultaneously considering non-random interactions (represented by r) in an iterative game (represented by w). These adjustments to the prisoner’s dilemma yield a new payoff matrix  game, opponents have the opportunity to play Hawk and fight , or play Dove and give way . Payoffs are maximized when both players give way and play Dove (cooperate). Unfortunately, in a world of doves, it pays to defect and play Hawk (defect). This game’s payoffs can be couched in terms of costs and benefits and modified to consider the joint consequences of kin selection and reciprocal altruism .a>d in b+c)/2; and 4) C played against C yields less payoff than D played against C (c>a). In a social dilemma, the always-cooperate (All-C) strategy, that is, individuals cooperating in all situations, provides the best collective outcome, but there is an incentive to cheat and play the strategy of defect (D) in a world of co-operators. Always-cooperate strategy is not an ESS. These games have a mixed strategy ESS when b>d, and always-defect strategy (All-D) is the global ESS when d>b.Any game with a social dilemma can be considered in terms of kin selection and reciprocal altruism, with the following elements: 1) Games with social dilemmas must be non-zero sum; 2) The strategy of cooperation (C) played against cooperation must produce a higher payoff than the strategy of defect (D) played against D a>d in ; 3) The r >0) with no prior knowledge of one’s opponent (w = 0) (We make this a model of kin selection by permitting non-random interactions ( (w = 0) .We combine kin selection and reciprocal altruism into a single model, by simultaneously considering non-random and repeated interactions .r occurs with like-individuals while the portion 1-r occurs with randomly selected individuals, with the following outcomes +(1−r)(b−c)>r(0)+(1−r)(b)r<c/b).Always-defect (All-D) strategy is the ESS when the condition is reversed  we obtain a different payoff matrix  is the ESS when:w(b−c)+(1−w)(b−c)>w(0)+(1−w)(b)− (1−w)c.Note that the always-defect strategy is an ESS for this matrix since 0> w, exceeds the cost-to-benefit ratio Reciprocal altruism only leads to the evolution of cooperation if the probability of recognizing others, r>c/b) and reciprocal altruism (w>c/b) combine to yield a new payoff matrix when we simultaneously permit non-random interactions (represented by r) and an iterative game (represented by w) (The matrix models for kin selection (ed by w) .We can examine when always-cooperate, tit-for-tat, and always-defect strategies are possible ESSs :All-C is an ESS when All-C played against All-C yields higher rewards than All-D played against All-C:r(b−c)+(1−r)(b−c)>r(0)+(1−r)(b)TFT is an ESS so long as TFT played against TFT serves better than All-D played against TFT :r(b−c)+(1−r)(b−c)>r(0)+(1−r)(1−w)(b)r = 0), tit-for-tat strategy can still be an ESS so long as the probability of recognizing others is greater than the cost-to-benefit ratio: w>c/bIt is easier for tit-for-tat strategy to be an ESS than it is for the always-cooperate strategy. Individuals using tit-for-tat strategy can benefit both from non-random interactions, and from having an iterative game that provides knowledge of others. If there are no non-random interactions (All-D is an ESS so long as All-D played against All-D serves better than TFT played against All-D:r(b−c)+(1−r)(1−w)( −c)0> w or r increases the likelihood of always-defect being an ESS. When there are no non-random interactions (r = 0), defection is always an ESS .Decreasing either sensuw as a function of r, thus providing the isoleg in the state space of familiarity, w, versus non-random interactions, r. Outside of the C-ESS (or TFT-ESS) isoleg, always-cooperate (or tit-for-tat) strategy is an ESS . Inside these isolegs, always-cooperate (or tit-for-tat) is not an ESS. Inside of the D-ESS isoleg, always-defect is an ESS, and outside of this isoleg it is not.We can consider all of the combinations of non-random interactions and foreknowledge of others that permit cooperation to evolve . The thrr) and familiarity (w) increases the range over which cooperation can evolve, and reduces the likelihood that All-D will be an ESS. Rather than alternative hypotheses for the evolution of cooperation, kin selection and reciprocal altruism can be considered jointly  and iterative games  extends to other games of social dilemmas, such as the snowdrift and hawk-dove games.b/2– c >0, always-defect (All-D) is not an ESS either. Thus, the ESS is a mixture of cooperators (C) and defectors (D) (mixed strategy). When b-c >0> b/2– c, always-defect is an ESS even though always-cooperate would provide each player with higher payoffs. Regardless of whether the snowdrift game has a mixed ESS or an ESS of All-D, it represents a social dilemma.The results in snowdrift game are interesting  in that r>c/b), and for repeated interactions remains w>c/b.As in the prisoner’s dilemma, kin selection or reciprocal altruism can allow for All-C to be an ESS. The conditions for cooperation to be the ESS under non-random interactions remains Hamilton’s Rule All-C is the ESS when b/2−c/2> b/2(1−r)(1−w)TFT is the ESS when b/2+cr/2−bw+brw−c+cw−crwAll-D is the ESS when 0> b/2– c >0), there are All-C and All-TFT isolegs , the TFT-ESS isoleg intersects the D-ESS isoleg producing four outcomes for the ESS , always-defect is the global ESS – there is no cooperation. With high costs (b/2−c>0), a mixed strategy of cooperation and defect is the global ESS. High costs and a mixed-strategy ESS are the typical form of the hawk-dove game. Both kin selection and reciprocal altruism permit additional outcomes to the game favouring the evolution of cooperation.Like snowdrift, the hawk-dove game has a low and high cost form. Regardless of cost, always-cooperate is never an ESS. With low costs (w = 0), always-cooperate can be the ESS when r>b/(b+2c). Under strict reciprocal altruism (r = 0), tit-for-tat can be an ESS when w>b/(b+2c). When we modify the hawk-dove game to include both non-random interactions and iterative plays of the game, we get the following matrix +(1−r)w(b/2−c)+(1−r)(1−w)bTFT is the ESS when b/2−c>r(b/2)+(1−r)(w)(b/2−c)All-D is the ESS when r and w. At higher w and low r, always-defect or tit-for-tat is the local ESS resulting in alternate stable states. A mixed strategy ESS results at high r but low w. With alternate stable states, a small increase in non-random interactions can make tit-for-tat the global ESS. Similarly, with a mixed strategy ESS, a small increase in the knowledge of one’s opponent can make tit-for-tat the global ESS.The low cost hawk-dove game generates the same configuration of ESSs as the high cost snowdrift game . Always-r and w), tit-for-tat as the global ESS, or always-cooperate as an ESS once the level of non-random interactions is sufficiently high +(1−r)a>r(d)+(1−r)cFor All-C to be ESS, r(d)+(1−r)d>r(a)+(1−r)bFor All-D to be ESS, Both All-C and All-D may be local ESSs  when w >0 and r = 0, All-D is always an ESS +(1−w)a>w (d)+(1−w)c w>(d−a)/(c−d).For All-TFT to be an ESS, When we combine kin selection and reciprocal altruism into a single model, by simultaneously considering non-random and repeated interactions , we get 1For All-TFT to be ESS:a>r(d)+(1−r)(1−w)c+(1−r)wdr = 0, then w>(c−a)/(c−d), and w must be positive for any cooperation to evolve.When 2For All-D to be ESS,d>r(a)+(1−r)(1−w)b+(1−r)(wd)Prisoner’s dilemma, snowdrift, and hawk-dove games pose a dilemma for Pareto efficiency. The natural inclination of an individual player is to defect, even though both players would benefit from cooperation. Our model shows various “doses” of reciprocity and kin selection together can generate cooperation as the sole ESS, both cooperation and defection as local ESSs, cooperation and defection as mixed strategy ESS, and defection as the sole ESS.r), or the probability of knowing the identity of one’s opponent (w). We suggest that non-random and iterative interactions occurring together ease the evolution of cooperation: non-random interactions (kin selection) reduce the threshold of w necessary for cooperation, and iterative interactions that increase the probability of knowing one’s opponent reduces the threshold of r necessary for cooperation. A similar finding on the importance of joint effect of assortment (kin selection) and reciprocity for understanding cooperation has recently been made Research on kin selection and reciprocal altruism have followed independent paths r) may have obscured the connections between reciprocal altruism and kin selection. This may obscure the ecological factors promoting assortative interactions and iterated games. For instance, in many vertebrate species, the direct benefits of helping may be sufficient to maintain cooperative societies Modellers’ preoccupation with genetic relatedness (r). Such game theoretical models show a transition from models that consider well-mixed populations to spatial grids and complex networks Although we explicitly integrated kin selection and reciprocal altruism, with matrix model, we note that other mechanisms besides the synergistic conditions generated by kin selection and reciprocal altruism may influence the evolution of cooperation