Re: altruism

["Bryan Atinsky" <bryan@xxxxxxxxxxxxxxxx>]

Look at Elliott Sober, David Sloan Wilson titled "Unto Others"

http://www.hup.harvard.edu/reviews/SOBUNT_R.html


Sorry if what's below is long, but I had actually discussed this book with a
friend a couple of months ago, so I have extensive notes, and I think it
will be of interest (kind of a "Cliff Notes" for the book), and I haven't
really contributed to the discussion here in a long time, so I am making up
for it.

They define Altruism: "Despite the importance of motives in conventional
definitions, evolutionary biologists define altruism entirely in terms of
survival and reproduction. A behaviour is altruistic when it increases the
fitness of others and decreases the fitness of the actor. The challenge for
the evolutionary biologist is to show how such self-sacrifical behaviors can
evolve, regardless of how or even whether the individual thinks or feels as
it performs the behavior."  (p.17)

Then from the "Mathematical model of altruistic behavior" from p.19-21:

"The fitness of an individual includes both its ability to survive and its
ability to reproduce. In this model, an altruistic behavior influences
reproduction only, so number of offspring serves as a measure of fitness.
Consider a population containing n individuals. There are two genetically
encoded traits, alturism (A) and selfishness (S), which occur in frequencies
p and (1-p), respectively. The group therefore contains np altruists and
n(1-p) nonaltruists. All individuals have the same average number of
offspring (X) in the absence of the altruistic behavior. Each altruist
behaves in a way that causes itself to have c fewer offspring and a single
other member of the group to have b more offspring.  The fitness of
altruists (Wa) and nonaltruists (Ws) can then be specified by the following
equations:

Wa = X - c + [b(np - 1)/(n-1)]

Ws = X + [bnp/(n-1)]

Each altruist experiences the cost of its altruistic behavior (-c) but also
serves as a possible recipient of benefits from the  (np-1) other altruists
in the group. Since the other altruists are dispensing their benefits among
(n - 1) individuals (to all n members except themselves), the total expected
benefit that each altruist experiences is b(np -1)/(n-1). Nonaltruists do
not experience the cost of altruism and also serve as possible recipients
from all np altruists. Thus, not only do altruists suffer a direct cost (-c)
but they also serve as possible reciepients from fewer altruists than do
selfish individuals (np-1 vs. np). It is obvious that Wa is always less than
Ws, so altruists will always be selected against within this population.

Suppose that the parameters in the model have the following values:

    Population size (n)                    100
    Frequency of altruists (p)              0.5
    Baseline of Fitness (X)               10
    Benefit to recipient (b)                  5
    Cost to altruist (c)                         1

The altruistic type increases the fitness of a single recipient in its group
by b=5 units at a cost to itself of c=1 unit. Each altruist can recieve a
benefit b from the 49 other altruists in the group, while selfish types can
be recipients from all 50 altruists in the group. These numbers enable us to
calculate the fitnesses of altruists and nonaltruists:

    Fitness of altruists: Wa = 10 - 1 + 5(49)/99 = 11.47

    Fitness of nonaltruists: Ws = 10 + 5(50)/99 = 12.53

Everyone's fitness is increased by the presence of altruists in the group,
but the selfish S types benefit more than the altruistic A types.  From
these figures we can calculate the population size n' and the frequency of
altruists p' among the offspring.

    Total number of offspring: n' = n[pWa + (1 - p)Ws] = 1200

    Frequency of altruists among offspring: p' = npWa/n' = 0.478

(Bryan says:  Remember that the frequency at the beginning was 0.5 altruists
to non-altruists, so for each iteration (generation), the gap between
altruists and nonaltruists will grow, to the relative detriment of the
altruists.)

The population cannot grow to infinity, so we assume that mortality operates
on all types equally, returning  the population to a size of n = 100 without
changing the new frequency of altruism (p' = .478). In this fashion, the
altruists decline in frequency every generation and ultimately go extinct.


This model would seem to make the likelihood of altruism ever arising highly
unlikely, due to the fact that it will inevitably lead to its own
extinction.  However, what Sober and Wilson bring to the arguement, is that
while altruism is selected against within groups, it is selected for between
groups.

Imagine two different population groups of the same species:  Group 1 a high
nonaltruistic percentage population group and Group 2 A high altruistic
percentage population group.

This is the example in the book, but they have a pretty pie chart, I will
give you the numbers version instead:

    Group 1 (mostly nonaltruistic):
    Population size (n)                                100
    Frequency of altruists (p)                       0.2
    Fitness of Altruists (Wa)                        10 - 1 + 5(19)/99 =
9.96
    Fitness of Nonaltruists (Ws)                   10 +  5(20)/99 = 11.01
    Population after iteration (n')                   1080
   Frequency of altruists after iteration (p')   0.184  (remember that the
frequency before iteration was 0.2)


    Group 2
    Population size (n)                                100
    Frequency of altruists (p)                      0.8
    Fitness of Altruists (Wa)                       10 - 1 + 5(79)/99 =
12.99
    Fitness of Nonaltruists (Ws)                  10 +  5(80)/99 = 14.04
    Population after iteration (n')                 1320
   Frequency of altruists after iteration (p')  0.787  (remember that the
frequency before iteration was 0.8)

Now looking at the global population
Overall population (N)
100 + 100 = 200
Overall Frequency of Altruists (P)
[0.2(100) + 0.8(100)]/200 = .5
Overall population after iteration (N')                                 1080
+ 1320 = 2400
Overall Frequency of Altruists after iteration (P')
[0.184(1080) + 0.787(1320)]/2400 = 0.516 (remember that the frequency before
iteration was 0.5)


What this shows is that while altruism is selected against at the within the
group (inter-group) level (Group 1: p = 0.2 becomes p' = 0.184 and Group 2:
p = 0.8 becomes p' = 0.787), it may be selected for at the between
group(intra-group) level (P = 0.5 becomes P' = 0.516).

This occurs because the benefit to the group as a whole, of having altruists
within a group, outweighs the relative within-group cost to the altruists.
The population of the altruist group grows much larger due to the altruism
of the altruists, compared to the nonaltruist group (altruism beats
selfishness at the intra-group level, though it may be seen as a cost to the
individual altruist).

Again to quote: "We need to emphasize that adding the progeny from the two
groups is just statistical sleight of hand unless it can be justified
biologically. If the two groups are permanently isolated from each other,
natural selection will eliminate the altruists within each group, as we have
already shown. The global increase in the frequency of altruists will be a
transient phenomenon of little interest. Suppose, however, that the progeny
of both groups disperse and then physically come together before forming new
groups of their own.  In this case our adding procedure is appropriate and
the increased frequency of altruists...will become the aerage frequency for
the next generation.  If the process is repeated over many generations,
altruists will gradually replace the selfish types, just as the selfish
types replaced the altruists in the one-group example.

Here is a link to a site that shows an example from the
book. (http://www.bun.kyoto-u.ac.jp/~suchii/Bworm.html)  Look over the
webpage because it will really help clarify what was talked about above.
However, disregard what it says at the top of the page "This is an imaginary
example; but it looks fairly realistic." This mistake was made because
whoever made the webpage read on p. 27 "imagine that the parasite population
consists of two types..."  and didn't read earlier on p. 18 when this
specific parasite is first talked about. Therefore, the example is of a real
species, as it says in the book on p. 18:

 "To see why evolutionists cannot resist talking about altruism, consider
the trematode parasite Dicrocoelium dendriticum, which spends the adult
stage of its lifecycle in the liver of cows and sheep (Wickler, 1976). The
eggs exit with the feces of the mammalian host and are eaten by land snails,
which serve as hosts for an asequal stage of the parasite life cycle. Two
generations are spent within the snail before the parasite forms yet another
stage, the cercaria, which exits the snail enveloped in a mucus mass that is
ingested by ants. About fifty cariae enter the ant along with its meal. Once
inside, the parasits bore through the stomach wall and one of them migrates
to the brain of the ant (the subesophagal ganglion), where it forms a thin
walled cyst known as the brain worm. The other cercariae form thick walled
cycst.  The brain worm changes the bahavior of the ant, causing it to spend
large amounts of time on the tips of grass blades. Here the ant is more
likely to be eaten by livestock, in whose bodies parasites may continue
their life cycle. This is one of the many facinating examples of parasites
that manipulate the behavior of their hosts for their own benefit. Fo our
purposes, however, the example is interesting because the brain worm, which
is responsible for putting the ant in the path of a grazing animal, loses
its ability to infect the mammalian host. It sacrifices its life and thereby
helps to complete the lifecycle of the other parasites in its group."


The authors warn about what they call the "Averaging Fallacy":

"Group selection, the mechanism that we have proposed to explain the
evolutionj of altruism, is often rejected as an important evolutionary
force.  Behaviors that seem to benefit others at the expense of self are
often said to be only 'apparently' altruistic, with 'genuine' altruism in
nature remaining elusive.  To understand the nature of the debates, let us
return to our two-group model...(above)...It shows that altruism declines in
frequency in each group but nevertheless evolves because the altruistic
group is more fit than the nonaltruistic group.  Another way to shwo that
altruism evolves is by simply averaging the fitnesses of individuals across
groups. The 20 A types in group 1 have 9.96 offspring each and the 80 A
types in group 2 have 12.99 offspring each, for an average of 12.38
offspring.  The 80 S types in group 1 have 11.01 ofspring each and the 20 S
types in group two have 14.04 offspring each, for an average of 11.62
offspring.  The average A type is more fit than the average S type in the
global population and therefore the A trait evolves.
    This method of calculating fitness does not change any facts about the
model, and its simplicity has a certain appeal.  In fact, it is easy to
conclude that A types evolve by 'individual selection' and are selfish after
all because the average A type is more fit than the average S type.  In
short, a single trait can appear to be altruistic or selfish, depending on
whether fitnesses are compared within groups or are averaged across groups
and then compared.
    Why not use fitness averaged across groups to define individual
selection?...A reason to reject the averaging approach is that it fails to
identify the separate causal processes that contribute to the evolutionary
outcome.  When altruism evolves, there typically are two processes at work.
Between-group selection favors the evolution of altruism; within-group
selection favors the evolution of selfishness.  These two processes oppose
each other.  If altruism manages to evolve, this indicates that the
group-selection process has been strong enough to overwhelm the force
pushing in the opposie direction. When this two-level process occurs in a
population, an appropriate causal analysis should describe what is going
on...This is a problem that any science is prey to; it is not peculiar to
the theory of natuaral selection.  Suppose Sam pushes a billiard ball east
while Aaron pushes it west.  If Aaron pushes harder, the ball moves west.
There is a single resultant, but there are two component causes.  To
represent this Newtonian problem in terms of vectors, you draw an arrow
pointing east and a longer arrow pointin west; these represent the component
forces.  Then you add the two vectors together, yeilding an arrow that
points west; this represents the resultant force.  If you cared only about
predicting the ball's trajectory, knowing the resultant would suffice.  But
the point is to understand the processes at work, the resultant is not
enough.  Simpson's paradox shows how confusing it can be to focus only on
the net outcomes without keeping track of the component causal factors. This
confusion is carried into evolutionary biology when the separate effects of
selections within and between groups are expressed in terms of a single
quantity."