We will take the fact of evolution and the general efficacy of Darwinian natural selection for granted here. [a] The aim here is to show that the modern sciences of evolutionary psychology, ethology, primatology and anthropology provide what is increasingly clear to be the correct explanation for the origins of our moral values. Note however that we are not talking about Spencerian "Social Darwinism" where the lessons drawn from evolution is supposedly the basis of moral values. We are presenting evidence for how the process of evolution via natural selection could have given rise to a species that possesses the senses of justice and morality.
Since the mid 1970's a large body of evidence has accumulated demonstrating that animal behaviors are tightly controlled by genes.  I quote one example from David P. Barash's Sociobiology and Behavior:
Furthermore numerous studies have also shown that differences in behavior can be hereditary and can thus be worked on by natural selection. Some examples:
We also see in animal behaviors which closely resemble what we would call moral behaviors. Bats have been known to exhibit food sharing behavior where the successful bats (or the one that was successful in its hunt that night) would regurgitate its food-essentially blood-to share it with other bats.  Indeed the closer the animals are related to us on the evolutionary scales the more they are like us in their behaviors. Chimpanzees at the Tai National Park in Ivory Coast have been observed "licking away wounds, carefully removing dirt and prevent flies from coming near wounds" of their wounded comrades.  As noted by eminent primatologist, zoologist and ethologist, Frans de Waal noted:
For human beings evidence has long been available that at least some parts of our morality are rooted in our biology. The most often cited case is that of Phineas Gage. In 1848 while working on a railroad track in New England, Phineas was hit by a pointed tamping iron that went straight through his left eye, brain and skull. It left a hole in his head but Phineas survived. Phineas recovered from the accident with his speech, memory and general intellectual capabilities intact. However friends begin to note a personality change. From being a respectable, decent person, he turned into a compulsive liar and would often times curse uncontrollably. He no longer showed any sense of responsibility and could no longer be trusted to keep his promises. Modern studies of his skull shows damage in the ventromedial frontal region of his brain. This is consistent with what is known to modern science. Patients suffering brain-damage to this region generally have their logical and memory skills intact but show a loss of social skills. "It is as if the moral compass of these people have been demagnetized, causing it to spin out of control." 
There is also growing evidence that much of our feelings and states of mind have firm biochemical bases. Studies in velvet monkeys show that those in dominant position tends to have higher levels of the neurotransmitter [c] serotonin than those in less dominant roles. In studies on college fraternities, officers in general show higher level of the same neurotransmitter than their less dominant fraternity brothers. Other examples abound. The naturally occurring oxytoxin have been found to be strongly correlated with feelings of love. While the synthetic drug Ecstacy induces a state of benignness akin to that of Gandhi's! 
The above two paragraphs show that human behavior is controlled by our neurophysiology and biochemical molecules. These are products of genes: and thus strongly suggests that behavior and differences in behavior are hereditable in humans as well as animals. While we are unable to do direct experiments on the hereditability of human behavior, there have been statistical studies on fraternal and identical twins which gives strong support to this. Fraternal twins are not identical twins and like most siblings share 50% of their genes. Identical twins are genetically identical, sharing a 100% of their genes. Studies in twins-both fraternal and identical- reared apart in both intelligence and personality shows that identical twins exhibited higher correlations that fraternal twins. Of course the correlation even between identical twins is not perfect. For IQ scores the correlation is 0.75 for identical twins and 0.38 for fraternal twins-almost exactly the difference in their genes. That the correlation is not 1 shows that the environment does play a factor in the development of intelligence and personality. The point is that human behavior has a hereditable component. 
Another important concept to keep in mind is the epigenetic rule; a concept introduced by evolutionary psychologist, E.O. Wilson and physicist Charles Lumden in their work Genes, Mind and Culture (1981). This is a constraint on anatomical, physiological, cognitive or behavioral trait due to the specific path of growth development of the organism of a given species. One example of the epigenetic rule is our perception of colors. If you think about this, our perception of color is rather strange. Light intensity varies continuously and our eyes are able to perceive its continuously varying nature. We know, like intensity, the wavelengths of visible light vary continuously as well. Yet unlike the former case, we perceive light of varying wavelengths in four more or less discrete categories: blue, green, yellow and red. Wilson and Lumden investigated 20 cultures around the world and found that these cultures have names for colors that correspond to these four categories. This proves that perception of continuously varying wavelengths as discontinuous discrete colors is a fundamental epigenetic rule of the human species. 
It is obvious that the perception of discrete, instead of continuous, colors is due to the physiology of our eye, Experiments first done by Thomas Young in 1801 at St. George's Hospital in London and later on in the mid-twentieth century at Cambridge University showed that color perception is caused fundamentally by the cones cells in the retina which are sensitive to light at different wavelengths. Experiments on animals and studies in humans with some form of color-blindness show that color sensitivity is strongly controlled by the genes. [d]
Another example of epigenetic rule is the categorizing of taste and the universal human preference for sweet over sour taste. This strong preference is genetic and has a very plausible evolutionary explanation. Ripe fruits, honey etc are generally sweet while unripe fruits are generally sour-the nutritional benefits of being able to perceive the difference in taste and preferring the sweet are obvious.
Thus far we have looked at epigenetic rules governing perception and sensation. Less pronounced epigenetic rules (called "secondary epigenetic rules") can be discerned in human behavior. The human incest barrier is a good example. Studies have shown that all cultures, with rare exceptions, have strong taboos against marriage between siblings. Again the evolutionary benefit is obvious: children born of such incestuous unions have a higher chance of being born horribly handicapped-due to the high probability of homozygous alleles which are normally not formed in other unions. It is obvious that people who have a genetic predisposition to be attracted to their siblings do not normally leave viable progenies. The action of the genes is very likely indirect here and may involve a predisposition against developing a sexual attraction to anyone whom one intimately shares early childhood with (i.e. "share the same potty"). That unrelated Jewish couples very rarely form in a kibbutzim (a Jewish form of communal living) provides strong evidence in favor of this epigenetic rule: a human social experiment have "fooled" the genes into thinking that the person you grew up with is a close relation and hence unattractive as a sexual partner. 
It is important to note that these genetic "triggers" of behavior works on a subconscious level and are manifested basically as emotions or feelings. A couple of examples would do.
The first is the so-called kindchenschema (German for infantile traits). Mammalian babies including humans have large eyes and rounded features. We humans instinctively find such features in human babies, or in pups or kittens, cute; it "melts our hearts." Cartoon artists make their characters look cute by essential incorporating kindchenschema into their characters. A cursory thought would show why such an instinct is important. Any mammalian parent that does not feel a strong emotional tug towards its own infants will probably not be able to bring them up successfully-thus not leaving its "non-children loving" genetic predisposition for the next generation.  Yet at no time is this realization conscious, we simply find babies "cute" and not reason by "this baby has to look cute otherwise I will not take care of it."
The second example will strike closer to another organ rather than the heart. The psychologist Devendra Singh studied Playboy centerfolds and winners of beauty contests over a period of thirty years and found that despite the fact that these models have gotten thinner over the years, the basic waist-to-hip ratio (WHR) remained constant at 0.70. He also found that men find women with a 0.70 WHR more attractive than those with 0.80 WHR, who are in turn considered more attractive than those with 0.9 WHR. It also turns out that women with WHR's between 0.67 and 0.80 are physiologically the most reproductively capable: i.e. capable of having more babies easier. Again the evolutionary origins for such a male preference is clear. Men who get turned on by women who are not reproductively capable do not tend to have too many children. Thus what we have today is the sieving of preferences by natural selection. Note that at no time do men consciously measure the WHR. It is just that those women with the right WHR have the figures normally referred to as hourglass figures which tend to "turn men on". 
Armed with these preliminary facts, we are now ready to look at the mechanisms that evolved moral feelings and moral behavior.
The amazing thing is that only two evolutionary mechanisms are required to explain the origins of morality and moral values. These mechanisms are kin selection and reciprocal altruism. Let's begin at the beginning.
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The revolution came in 1963 via to the brilliant insight of a young British biologist named William Hamilton. Hamilton realized that the currency of natural selection is not the individual but his or her genes. "Success" in natural selection means ensuring copies of your genes are passed on to the next generation. However copies of your genes are not just passed on to your children (who have 50% of your genes), your nieces and nephews have 25% of your genes. Thus any altruistic act that ensures your siblings have children, even when you can't have any, ensures the survival of your genes. Hamilton showed that the behaviors of these insects make perfect evolutionary sense once we see them from the point of view of their genes. He pointed out that due to a quirk in their genome, these insects share 75% (not 50%) of their genes with their fellow sister workers (workers are all female). [e] So each worker, by working to ensure the care and survival of the queen's offsprings, is merely ensuring the survival of her own genes. [f] Since the workers share more of their genes with one another than species of other animals we would expect altruism between siblings, the workers, to be more pronounced than in other species. 
This mechanism, by which individual promote the survival of their genes through altruistic acts toward siblings, is known as kin selection. Micheal Ruse, professor of Philosophy and Zoology at the University of Guelph in Ontario, Canada, has called this "one of the great triumph of twentieth century biology."  Kin selection tells us that by enabling species to behave altruistically, the genes are, metaphorically speaking, selfishly promoting their own survival into the next generation. This realization led the Oxford biologist, Richard Dawkins to coin the phrase "selfish gene" to describe the process by which this mechanism works. 
Altruistic behavior directed at relatives have, of course, been observed in mammals. Take the case of the ground squirrel. When it sees a predator nearby, a squirrel may give out a warning call; which it does by standing on its hind legs at the same time emitting a loud noise. This will put the rest of the ground squirrels on high alert. Of course broadcasting the warning is life threatening for the one sounding the call; for the predator could then spot it easier. Field studies have shown that ground squirrels are more likely to make such potentially suicidal calls when close relatives are nearby. Similar studies in primates have also shown strong supportive sibling relationships. All these are understandable in the light of kin selection. 
Hamilton introduced a mathematical equation to quantitatively describe such altruism between kin. The equation is simple:
In words, the equation is telling us that as long as the cost to the altruist is less than the benefit to recipient times the degree of relatedness between the two, the act of altruism makes evolutionary sense. This explains the high altruism among workers of the order Hymenoptera since they have R of 0.75. It also explains human relationships and our closeness to our relatives seems to follow this order: siblings (R = 0.5), nieces and nephews (R = 0.25), first cousins (R = 0.125) and so on. 
Since kin selection shows how altruistic behavior can benefit genes from an evolutionary standpoint and since we know that much of our emotions and feelings are based on epigenetic rules, the conclusion by Robert Wright as to the result of kin selection is apt:
Note that in the equation above, there is no mention of the benefit to the one who provides the benefit. All that is important is that the cost of providing the benefit is correlated with the degree of relatedness between the giver and the receiver. Thus in the real world, we normally help someone because "he's family" and do not normally expect anything in return.
What about people whose familial relationship to us are remote (R ~ 0)? In that case, we do expect something in return, a kind of reciprocity. This will be the focus of the second major mechanism: reciprocal altruism.
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Trivers noted the roles emotions and psychological processes play in such interactions. Animals, including humans, do not generally execute evolutionary logic via reasoned thought but by epigenetic rules. Since the process of reciprocal altruism is more complicated than simple cooperation there seems to be some minimal requirements on the species and groups for it to work. It requires good memories and groups that are fairly small and stable - otherwise it is hard to keep track of who owes whom what. 
It is important to remember that in most social mammals, the size of the group is not large. This is as true for bats, whales, dolphins, chimpanzees as it is for humans. It must be remembered that the first distinctly modern human forms appeared only about 100,000 years ago. The invention of agriculture and with it large impersonal cities happened only 10,000 years ago. Thus 90% of the evolution of uniquely human behavior happened in hunter-gatherer societies where the total number is less than 200. Thus we have to look for behavior which makes genetic sense in such small societies - whether human or animals. 
The next step then is to apply the mathematics of Game Theory. Game Theory was developed in the 1920's and is used mainly in the social sciences and the military. The classic example of the use of game theory is the Prisoner's Dilemma, first developed by Rand Corporation in the 1950's to model a global nuclear strategy. It is worthwhile understanding this as it will provide a major insight into the mechanism we are interested in.
In this we have two criminals who were arrested for a crime and are now being interrogated in separate rooms. The interrogators know that there is not enough evidence to convict on the major crime but they have enough to put both in jail for one year based on a lesser charge. They need to get the criminals to confess in order to convict them of the more serious charge. Thus they gave each of the criminals three scenarios:
Note however that if the game is iterated - i.e. played over again and again over an unknown number of trials - a different logic arises. Now the two criminals gets a chance to see the other's behavior-whether they will confess ("cheat") or keep silent ("cooperate")- over the various trials. In that case cooperation becomes the norm. The logic of the iterated prisoner's dilemma is essentially similar to the logic that underlies reciprocal altruism. 
Application of game theory to evolution requires two basic constraints: the object of the game is to maximize genetic proliferation and the environment is that of a small group of animals (like the ancestral hunter gatherer society.) In 1979 Robert Axelrod, a political scientist and psychologist, set up a competition in which he invited game theorists to submit computer programs that would have a strategy for dealing with the iterated prisoner's dilemma. The programs will have their own rules about cooperating and/or cheating. Each program would have a memory of what happen on previous encounters and could adjust its future behavior accordingly. A few dozen programs were submitted (nicely approximating the size of hunter-gatherer societies!) and the game was iterated 200 times.
The winner of that competition was the Canadian game theorist, Anatol Rapoport who submitted the program called Tit-for-tat. At only five lines long, the program was the shortest among the programs submitted. It was guided by the simplest of rules: it would cooperate with any program at the first encounter and would do whatever the other program did the last time they met. Thus the program is nice (it starts by cooperating), retaliatory (it would cheat the same program that cheated it previously) and forgiving (if the other program reverts to cooperation-it would do the same).
With hindsight the advantage of such a program is obvious. It never gets repeatedly victimized, upon being cheated the first time it withholds cooperation and never gets played for a sucker. Since it starts by being nice, it enjoys the benefits of cooperating with other cooperative programs straight away. Also it does not initiate cheating-thus avoiding costly battles with others who would also retaliate heavily. "Nice" programs get played for suckers and "nasty cheater" programs were caught by other programs and never stood to make any large gains as the game wore on.
Note that Tit-for-tat has no foresight programmed into it. It just reciprocates cooperation or retaliates when cheated. That the program is simple is an added benefit-for we would expect natural selection to come up with simple algorithms rather than complicated ones. Furthermore the program has much in common with how the average human beings behave ("Fool me once, shame on you; fool me twice, shame on me!") Indeed it is the game theory equivalent of "do unto others as they have done unto you."
Of course, game theorists did not stop there. Other strategies were experimented, including ability of the program to randomly "forgive" some defections, ability to remember more than the last interaction between the program it is "meeting" and ability to ostracise those programs that defected in the past etc. The logic developed from Tit-for-tat, and now in these various programs, which involves being nice but remembering transgressions and sometimes either forgiving them or simply avoiding the cheats, is the basis of reciprocal altruism. Applied to the field of evolution, a strategy resembling these, which ensures the animal "playing" it will not be worse off than those trying the same or other strategies, is called an "evolutionary stable strategy", a term coined by geneticist John Maynard Smith. 
Reciprocal altruism have been observed countless of times in mammals. We can flesh out the examples of vampire bats given above. Vampire bats go out at night and get their food by sucking blood from large sleeping mammals. Not all bats are successful all the time. Thus we see some bats regurgitating their food upon return to share with other bats. But not just any other bat. Researches have found that there is a kind of "buddy system" among bats where two bats would more or less take turns to feed one another. They found that bats that are observed together more often tend to share food together as well. 
We have other examples. Franz de Waal conducted experiments in food sharing with the chimpanzees at the Yerkes Field Station in Atlanta. In one, food was placed in a bucket that need to be hauled up over a barrier. The problem is the job needs the cooperation between two chimpanzees but only one can manage to get at the food. De Waal noted that when the chimpanzee who took the food did not share it with the one who helped, the latter would refuse to cooperate in subsequent trials. De Wall studied five thousand cases of food transfers in the chimpanzee colony and found that the principle of reciprocity holds true. "If A shared a lot with B, the B shared a lot with A, and if A shared little with C, C also shared little with A." Furthermore the reciprocity may not in kind. If A grooms B earlier, the former's chances of getting food from B later increases. Similar reciprocal behaviors have been observed in monkeys, whales and dolphins. 
The flip side of reciprocal altruism, revenge, has also been observed in monkeys and chimpanzees. De Waal noted that in political battles for control of the hierarchy in the chimpanzee community he was studying, dominant males tend to retaliate against those who supported their opponents. 
How do all these relate to human morality? We have noted earlier how evolution favors the development of epigenetic rules that would help the genes to replicate. Remember again the point that much the logic of how evolution functions is not known to the protagonist. We can find many epigenetic rules that arose due to reciprocal altruism: 
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We see almost all of our moral senses are thing which drives us away from selfishness and towards selflessness. The things we condemn on moral grounds - murder, theft, rape and fraud - are things we do to others. The things we praise - cooperation, altruism, sympathy and generosity - are all things we do for others. This moral condemnation and praise permeate all human cultures.  This leads us to the correct evaluation of morality. Morality developed in a society where selfish behavior of an individual - built into its biology over many millions of years - have to be over-ridden if his genes are to be successful within that new environment. As Michael Shermer concluded in his book The Science of Good and Evil:
Of course there is no pre-ordained or logical reason why we should have evolved into moral beings. Indeed we have seen how the "altruistic" behavior of insects is under firm genetic control. It is not the same with human beings - or for that matter, with chimpanzees. Having such a system as insects would not give us enough flexibility to react to different circumstances and that would not mean an optimal use of our mental capabilities. On the other hand, the question may by asked: Why had natural selection not evolved a purely rational selfish creature that evaluates every action based on the ultimate success for its own genetic proliferation?
The answer is that such a creature, which would have to compute millions of permutations as to the results of its action would require a brain size probably more massive than a supercomputer. In other words pure rationality would not have been led to sufficiently rapid reactions in real life. [g] Imagine an ancient human being seeing a lion nearby and he stops to compute whether he should sound an alarm to safe his brother's children whose paternity is uncertain or should he just keep quiet and run for it himself! No, the best solution is such cases is to have such a person already develop feelings, like fondness and love, for his nephews and nieces and that he ought to warn them in order to outweigh the adrenaline flowing through his body which is telling him to run as fast as he can.
Thus we have developed moral feelings of ought and feelings of sympathy and compassion for others which drive us to certain actions. It allows room for our intelligence to evaluate the specifics of the situation if and when the need arises. 
That we feel moral compulsion as ought, not just as a preference, is also embedded in the logic of our evolved genes. For example we do not feel incest is just something we ourselves dislike but we feel strongly that it is wrong, for everyone. The strong innate biological drive to copulate with a member of the opposite sex is strong and can only be neutered by a stronger , and equally biological, sense of ought to steer us away from it. 
Again it must be reiterated, we are moral animals because it is built in to our biology by evolution over the last few millions years that we share with the higher apes and, specifically, over the last one hundred thousand years or so when we become distinctly human. The sense of ought is unconscious in us, it leads us to do what is right and what is wrong. As Michael Ruse noted in his book Taking Darwin Seriously:
When we behave morally we are not pretending to be moral, we are being moral. Evolution have embedded this in us for economical reasons: it is easier to be moral than to pretend to be moral. Michael Shermer:
All this is not to say that there aren't things labeled under "morality" which are clearly due to cultural differences and are largely non-biological in origin. Thus the Jewish and Muslim revulsion for pork and the Hindu abstinence from beef are clearly prohibitions which develop due to different, contingent cultural and historical backgrounds. However the evidence from anthropology is clear that there are many moral universals which permeates all cultures. All these can be explained by either one or two or both of the mechanisms described above. The anthropologist Donald E. Brown in a comprehensive study has compiled a list of 357 human universals, a large part of which relates to morality and ethics. We give below a sample of the universals listed by Brown and provide the evolutionary mechanism most likely responsible for its development: 
Of course no one is claiming that evolutionary psychology has dotted all the i's and crossed all the t's - but the evidence amassed after only three decades is impressive. It is clear that our moral values, our sense of ought was brought about by a process of evolution which involves reasonable intelligent species needing to live together in a small group.
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Hume's Law was first raised by the Scottish philosopher, David Hume (1711-1776) in his book A Treatise of Human Nature (1737-1740). The "Law" states that discourse about facts ("is") is logically distinct from discourse about morals ("ought"). One cannot derive "ought" from "is". It is debatable whether Hume actually intended his critique to be labeled a law - hence my inverted commas above - and it is also quite unclear if Hume was complaining against specific cases of is/ought discourses or whether he meant the is/ought barrier to be absolute and unbreachable.
Hume's argument was taken up and re-polished by the English philosopher, G.E. Moore (1873-1958) in his work Principia Ethica (1903). Moore explain that certain "simple properties", such as, say, the color yellow, cannot be defined in terms of anything else. For whatever it is that explains yellow, is contingent to it and not logically connected to it. Even defining yellow as a certain range of electromagnetic waves does not do it. For it is not known before hand (i.e. not logically deducted) that such a wavelength gives the sensation of the color yellow in our retina. Applied to the concept of ethics, it means that something that is good, may also be something else (e.g. helping the poor, increasing happiness etc), but defining that something else does not tell us what good is - for the connection, like that of the color yellow - is contingent and not a logically necessary connection. Thus if you define "good" in terms of other properties, and think that you have actually defined "good", you are committing what Moore called the "naturalistic fallacy". Moore argued that we sense "good" intuitively, just like we sense the color yellow visually. There is no other more basic explanation for these. 
It should be mentioned here that not all philosophers are convinced that these lines of arguments are valid; Hume "Law" may not be a law, and the naturalistic fallacy may not be fallacious. Micheal Ruse had this to say about Moore's naturalistic fallacy: "[A]s with Hume's law, merely invoking a great authority and a clever label is no substitute for detailed criticism."  Michael Martin had this to say about the naturalistic fallacy: "[T]o suppose that this is a fallacy is to beg the question...anyone who simply assumes without argument that this [i.e. arguing "ought" from "is"-PT] cannot be done is assuming what must be proven."  Thus it would not do for someone to simply say "Aha! Arguing ought from is - naturalistic fallacy!" and end all discussion. The philosophical underpinning of the naturalistic fallacy is itself open to question.
However we will not be wasting our time discussing philosophical minutiae. Our presentation of the evolutionary origin of our moral senses does not violate the "is/ought" divide, nor does it commit the naturalistic fallacy. I quote from Michael Ruse again:
A useful analogy is that perception of the color yellow that G.E. Moore originally raised. The color yellow is a "simple perceptual fact". Now explaining the perception of the color yellow by showing how electromagnetic waves of a certain wavelengths - say 564 nanometers - react with the cones cells which then sends an electric signal to the brain is not fallacious. Neither does explaining how color perception could have evolved in mammals who switched from a nocturnal to a diurnal lifestyle violate any insurmountable boundary. These explanations provides the naturalistic base on how the color is perceived and how it got to be that way in certain animals.
Similarly we have provided explanations above about how the moral sense is biologically based and how it evolved to be what it is today. The moral sense is still a simple and basic property that is perceived by humans. However like the case of color perception, the color yellow is not really "out there" in an absolute sense (an insect who can see in the ultra violate range may see different colors for what we would label yellow) but is a result of our biology interacting with the world around us. Morality does not have an ontological existence outside the human species who are doing the sensing.
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