I think the answer is yes. Since male and female can live on their own. But for the sake of reproduction and child rearing some form of symbiosis can develop.
"Symbiosis (from Ancient Greek σύν "together" and βίωσις "living") is close and often long-term interaction between two or more different biological species."
Assuming these married people belong to the same species, their pair-bond is not an example of symbiosis, by definition. In order for your idea to work, you would need to change the accepted definition of symbiosis.
You and your gut bacteria are in symbiosis. It's true that they don't cook you breakfast; but they do help you digest it.
Among humans? Or among mating organisms in general? Also, in what circumstances?
Suppose a couple who value what most people value, and who value those things about as much as most people value them.
If they share fixed costs (shelter, utilities, and furnishings), then the arrangement will effect more value for each of them; presuming, living with another person doesn't offset the added value. Otherwise, parasitism better characterizes the arrangement than symbiosis does.
Whether we ought to regard cohabitating as symbiotic, or regard it as parasitic, depends on the circumstances: Can either party force the other to mate with it? How would doing so affect either party's absolute reproductive success (the number of organisms at an arbitrary future time that will have descended from the ancestor in question)? Game theory explicates this intertesselation well. The game proceeds as follows.
First note the following game parameters.
- The players in the game comprise 50% men and 50% women
- The players inherit one of two strategies: girly, manly
- Conception requires that a man and a woman agree to mate.
- Conception requires that a woman wants the mating to produce her mate's offspring
- A man does not know whether his mate wants the mating to produce his offspring
- Only a woman knows whether she conceived a given offspring
- Any player can refuse to mate with any player
- A woman can conceive no more than n offspring
- A man can conceive no more offspring than the number of ova he can fertilize
- Half of the offspring have their mother's gender and strategy ;half of the offspring have their father's gender and strategy
- Every offspring has half its mother's genes and half its father's genes.
- Every player has an amount of time that equals n
- The expected reproductive success of an offspring increases commensurately with the time invested in it.
- Womanly strategies invest resources in their offspring; manly strategies do not.
- Every player knows the gender and the strategy of every other player.
- No player knows another player's moves.
- Every player endeavors to maximize its expected reproductive success
- Expected reproductive success equals the probability-adjusted most probable number of a player's genes expected to be in all the players of the game in a later turn.
- Players can cooperate
Suppose two manly players have a child: MM
- By 12: they invest 0 time in their offspring
- By 11: the expected reproductive success of the offspring equals 0.
Suppose a manly and a girly have a child: MG
- By 12: they invest 1 time in their offspring
- By 11: the expected reproductive success of the offspring equals 1.
Suppose two girlies have a child: GG
- By 12: they invest 2 time in their offspring
- By 11: the expected reproductive success of the offspring equals 2.
the expected reproductive success of a countless number of MM children equals 0. So a manly-woman can find a girly-man and have all her n offspring with him. A strategy that effects a value of n x 1 for each of the two players: The girly-man invests all his n time on their n children. So in keeping with his girly strategy he does not endeavor to conceive more children. The manly-woman has had all her n offspring with the girly-man, so she can have no more children.
A manly-man's expected reproductive success does not change by mating with a manly-woman since it does not decrease the number of girly-women he mates.
But then, why would a girly-woman want to mate with a manly-man when she can mate with a girly-man and invest 2 time into their children.
So things look bleak for manly-man.
But, by common-knowledge (in the game-theoretic sense), every woman apprehends that a man can only presume that the offspring of one of his mates has his genes (given that only children of his mates can possibly have his genes). So then, she chooses to mate with a girly-man, and with a manly-man, but only to have the offspring of the manly-man. Thus conceiving some manly-men offspring who receive 1 or 2 time investments.
This effects a state of affairs that comprises nearly all manly-men and girly-women. The men sleep around as much as possible, and the women invest time in the offspring. All offspring get 1 time investment, and, on average, every man has the same number of children.
At this point the women can justify cooperating. If they agree to stop deceiving their mates then after a few generations they can have the same number of children, but each with 2 time investments instead of just 1. However, it is always in the woman's best interest to defect from the pact and deceive her girly-man, so the pact fails.
So, interestingly that model explains:
- Why being a "slut" has been much more damaging to a woman's reputation among women than to her reputation among men.
- All the research at www.facelab.org
- Why women care about monogamy (they will have all the kids they can have no matter what, they want investment in those kids).
- Beatlemania and why women are attracted to men when they have girlfriends. (Men that women like are more likely to be successful at passing on the woman's genes, the more women there are that like a man, the more women find him attractive)
- Why women are attracted to 'jerks' but marry 'nice guys'. (Or why they're attracted to guys who show little interest in investing in them, but mary guys who do show interest in doing so).
Reproductively speaking, being in a 'couple' is a parasitic relationship, in which the female and manly-man are the parasites and the girly-man the host.