r.B > C
NVG meeting, 26 November 2010, Soesterberg
~
~
z  cov( z a , D a )  ave((z)da )  cov( z d , Pd )
If you want to know whether a trait will spread or not you also have
to take into account the effects on relatives

Idea of kin selection or inclusive fitness theory
(W.D. Hamilton 1964): helping relatives can be favoured
even at a cost to oneself when b.r > c

This inequality is known as the relative inclusive fitness
effect. It is the partial effect of the actor’s trait on the
actor’s own direct fitness (-c) plus the partial effect of the actor’s trait
on the fitness of relatives (b), weighted by relatedness (r).

Puts the individual actor at the center of the analysis, and allows
one to predict behaviour on the basis of which strategy maximises the
individual’s expected inclusive fitness

W.D. Hamilton (1964) The genetical evolution of social behaviour. Pt I & II. J. Theor. Biol. 7: 1-52. Cited nearly 7,000 times.
Wilson Social Research 2005
Edward O. Wilson: tries to
denounce kin selection and
reinstate group selection as
the appropriate framework to
study social evolution
Wilson & Hölldobler PNAS 2005
Foster, Wenseleers & Ratnieks Trends in Ecol. Evol. 2006
Wilson & Wilson New Scientist 2007
Wilson & Wilson
Q. Rev. Biol. 2007
Wilson & Wilson Amer. Scientist 2007
Wilson BioScience 2007
"It is often said in research reports on social insects that
some particular set of empirical data is “consistent with kin
selection theory.” But the same can be said of almost any
other imaginable result, and the particular connection of
data to the theory remains unclear. Hence, kin selection
theory is not wrong. It is instead constructed to arrive at
almost any imaginable result, and as a result is largely
empty of content. Its abstract parameters can be juryrigged to fit any set of empirical data, but not built to
predict them in any detail, nor have they been able to
guide research in profitable new directions."
"the theory has contributed little or nothing not already
understood from field and experimental studies“
(E.O. Wilson BioScience 2008)
Wilson (1975) Sociobiology: The New Synthesis:
discusses Hamilton’s rule as a special case of group selection and
mentions that “Hamilton’s viewpoint is unstructured. The convential parameters of population genetics, allele frequencies,
mutation rates, epistasis, migration, group size, and so forth, are
mostly omitted from the equations. As a result, Hamilton’s mode
of reasoning can be only loosely coupled with the remainder of
genetic theory, and the number of predictions it can make is unnecessarily limited.”
Hölldobler & Wilson (1990) The Ants, p. 182:
better treatment of inclusive fitness theory and mentions that
“Hamilton’s rule is robust as a theoretical prediction”
Hölldobler & Wilson (2009) The Superorganism: authors criticize kin selection theory
in one place, support it in others, at one stage admit that kin and group selection
are simply alternative bookkeeping methods to measure gene frequency change,
but elsewhere maintain that they are not
Martin Nowak: found 5
supposedly fundamental rules
for the evolution of
cooperation
Laurent Lehmann: not a
fundamental classification
scheme – all the rules
ultimately reduce to
Hamilton’s rule
Ohtsuki et al. (2006): “Natural selection favours
cooperation, if the benefit of the altruistic act, b, divided
by the cost, c, exceeds the average number of
neighbours, k, which means b/c > k. ... We note the
beautiful similarity of our finding with Hamilton’s rule...”
Lehmann et al. (2007): it is Hamilton’s rule!!!
Martin Nowak, Corina Tarnita, Ed Wilson:
IF theory is limited in scope and traditional
population genetics and game theory are
better frameworks to study social evolution
The New York Times: “The scientists argue that studies on animals since Dr. Hamilton’s day
have failed to support it.The scientists write that a close look at the underlying math reveals
that Dr. Hamilton’s theory is superfluous. It’s precisely like an ancient epicycle in the solar
system, said Martin Nowak. The world is much simpler without it.”
Others disagree: “This paper, far from showing shortcomings in inclusive fitness theory,
shows the shortcomings of the authors”, said Francis Ratnieks of the University of Sussex.
“Rather than saying the paper is wrong, it would be
more fruitful if critics also went back to basics: state
model assumptions, derive predictions, test
empirically. Such a return to rigour would help the
field advance to the next level.”
Matthijs van Veelen: statistical
derivations of Hamilton’s rule based on
the Price equation are no good
Arne Traulsen: Hamilton’s
rule cannot do evolutionary
dynamics and requires
weak selection
A series of deaths have started occurring in New York; Some are
being found mutilated while others have an equation wΔz =
Cov (w,z) carved onto their skin. As police investigate they
discover each victim was forced to choose between sacrificing
their own life or a loved ones' life. Before long it becomes clear
that this perpetrator has suffered just such a similar fate...so now
is coping by seeking a way of solving this philosophical enigma.
Can Captain Maclean and his officers such as Eddie Argo and his
new partner Helen Westcott stop this suspect, because he will not
until he gets to the end of this equation.
Rated R for strong brutal violence including a rape, gruesome
images and pervasive language.
Abbot et al. (2010) Nature, in press : “Is there a sharp
distinction between IF theory and ‘standard natural
selection theory’? No. Natural selection explains the
appearance of design in the living world, and IF theory
explains what this design is for. Specifically, natural
selection leads organisms to become adapted as if they
were trying to maximize their IF. IF theory is based on population
genetics, and is used to make falsifiable predictions about how
natural selection shapes phenotypes, and so it is not surprising that it
generates identical predictions to those obtained using other
methods.”
The power of IF theory is that it led to an increadibly powerful
strategic way of thinking about animal behaviour.

Nowak et al.(2010): IF theory
 requires weak selection (gradual evolution)
 cannot deal with synergistic, nonadditive
fitness effects
 can only deal with pairwise interactions
 cannot take into account details of genetic
inheritance (e.g. arbitrary dominance)
Corina Tarnita, from
http://smartbabesaresexy.blogspot.com/

Each of these claims is manifestly wrong!




Original version of IF theory (the “gradient” version) was
indeed derived in the limit of weak selection
Hamilton (1964) was actually explicit about this:
“Considering that, the present use of the coefficients of
reIationships is only valid when selection is slow”
The “gradient” version of IF theory was further extended
in the ESS IF maximisation methods of Peter Taylor &
Steve Frank (1996) and the IF methods of François
Rousset (2004), it is also this version that is used by NWT
But there is also a more general, statistical version of IF
theory, first derived from the Price equation by Hamilton
(1970), which also works under strong selection

Simplest gradient version of Hamilton’s rule:
w / g  w' / g.r  0
relatedness
-c
b
 w = fitness of actor, w’ = fitness of recipient
g = breeding value for actor’s level of cooperation
 E.g. with additive fitness effects :
w = 1-C.g + B.g’, w’=1-C.g’ + B.g
→ increase in level of cooperation when -C + B.r > 0
 E.g. with nonadditive fitness effects:
w = 1-C.g + B.g’ + D.g.g’, w’=1-C.g’ + B.g + D.g.g’
→ increase in level of cooperation when (-C+D.g) + (B+D.g).r > 0
ESS level of cooperation g*=(C-B.r)/(D(1+r))
Frank 1997, Wenseleers et al. 2010






Can deal with nonadditive fitness interactions since weak
selection linearises all nonlinearities + extensions for dominance
Can easily be extended to interactions between > 2 individuals by
adding more terms for additional relatives that are affected
Realistic model for continuous traits, probabilistically expressed
traits or discrete traits with strong selective effect that are only
rarely expressed (low penetrance)
Weak selection is usually realistic since distribution of fitness
effects of new mutations usually follows an exponential
distribution (most mutants only deviate slightly from wild type)
Also good (1st order) approximation for when selection is strong
IF theory provides an easier, more powerful & general method for
finding ESS’s than traditional population genetic theory
W.D. Hamilton (1995): “...my confidence that I had proved maximisation
of inclusive fitness, with or without multiple alleles under weak selection
was important to me. I was and still am a Darwinian gradualist for most
of the issues of evolutionary change. Most change comes, I believe,
through selected alleles that make small modifications to existing structure and behaviour. If one could understand just this case in social situations, who cared much what might happen in the rare cases where the
gene changes were great and happened not be disastrous? Whether under social or
classical selection, defeat and disappearance would, as always, be the usual outcome
for genes that cause large changes. I think that a lot of the objection to so-called
'reductionism' and 'bean-bag reasoning' directed at Neodarwinist theory comes from
people, who, whether through inscrutable private agendas or ignorance, are not
gradualists, being instead inhabitants of some imagined world of super-fast progress.
Big changes, strong interlocus interactions, hopeful monsters, mutations so abundant
and so hopeful that several may be under selection at one time -- these have to be the
stuff of their dreams if their criticisms are to make sense. ...”
~
~
z  cov( z a , D a )  ave((z)da )  cov( z d , Pd )
Hamilton (1970) also derived a more general version of
his rule based on a population genetic theorem known
as the Price equation (also see Queller 1992, Frank 1997,
Gardner et al. 2007, Wenseleers et al. 2010)

Trait (e.g. gene for altruism) will spread in a population
~, g )  ave ( wg )  0
when g  cov( w

George Price
Covariance between relative fitness and individual
allele frequency (or breeding value)
+ mean fitness-weighted change across inheritance paths
(transmission biases, e.g. due to meiotic drive or biased mutation)
~
 No transmission biases → cov( w, g )   ~ .V  0

wg
g
~
~
z  cov( z a , D a )  ave((z)da )  cov( z d , Pd )
The expected neighbour-modulated fitness of a random individual
can be written in an additive way as

wˆ  w   w~g . g ' .( g  g )   w~g '. g .( g ' g )  w  c.( g  g )  b.( g ' g )
β‘s: average effect of being more cooperative than average and of
interacting with an individual that is more cooperative than average,
defined in terms of partial least-square regressions



 w~g .Vg  0 when  w~g   w~g . g '   w~g '. g . g ' g  c  b.r  0
(neighbour-modulated fitness condition)
This is identical to the inclusive fitness condition
 w~g . g '   w~ ' g . g ' . g ' g  c  b.r  0
since normally  w~g '. g   w~ ' g . g '
~
~
z  cov( z a , D a )  ave((z)da )  cov( z d , Pd )
That the expected neighbour-modulated fitness is written in an
additive way doesn’t mean that fitness has to be frequency
independent and that you can’t have synergy, since the costs &
benefits can be a function of the behaviour of the other individual(s)


E.g. w( X , Y )  1  C. X  B.Y  D. X .Y
with discrete strategies (X=Y=0: defect, X=Y=1: cooperate)
Gardner et al. (2007) and Wenseleers et al. (2010):
under haploidy average costs & benefits can be calculated using
least-square regression calculus as
r  (1  r ). p
 w~g . g '  c  C 
D
1 r
r  (1  r ). p
 w~ ' g . g '  b  B 
D
1 r
~
~
z  cov( z a , D a )  ave((z)da )  cov( z d , Pd )

Cooperation spreads when –c + b.r > 0
i.e. when –C + B.r + D.(r+(1-r).p) > 0, pure ESS p*=(C-(B+D)r)/(D(1-r))
The Price equation and Hamilton’s rule are dynamically sufficient
and can do evolutionary dynamics provided that explicit model
assumptions are made, e.g. about the fitness function and how
genotypes form, etc...

Costs, benefits & relatedness may change from generation to
generation but split in direct & indirect fitness effects always possible


E.g. in the absence of relatedness, cost=-C+p.D
No surprise that cost of cooperating is frequency dependent!!
If you work with breeding values the approach also works for
arbitrary dominance






Late 1800's and early 1900's: debate between
Mendelian geneticists (e.g. Bateson) and
biometrical (i.e. statistical) geneticists (e.g. Pearson)
R.A. Fisher (1918): showed how to integrate both
approaches by resort to least-square regression
methods
Showed that one can define the average effect of an allele
Generalised Hamilton’s rule: defines costs & benefits in terms
of the average effect of an allele (or strategy) on yourself and
on your partners’ fitness using least-square regression calculus
Just as with the average effect, costs & benefits may then
become “ecology-dependent”
Research
Area
Sex allocation
Policing
Conflict resolution
Cooperation
Altruism
Spite
Kin discrimination
Parasite virulence
Parent-offspring conflict
Sibling conflict
Selfish genetic elements
Genomic imprinting
Cannibalism
Dispersal
Alarm calls
Eusociality
Correlational
studies?
Experimental
studies?
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Interplay
between theory
and data?
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Abbot et al. (2010) Nature
Correlational Experimental
studies?
studies?
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Interplay
between theory
and data?
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Trait examined
Explanatory
variables
Altruistic helping
Worker egg laying
Caste determination
Policing
Level of cooperation
Work rate
Haploidiploidy vs diploidy
Costs, benefits and relatedness
Relatedness
Relatedness
Costs, benefits and relatedness
Need for work and probability
of becoming queen
Relatedness asymmetries due
to variation in queen survival,
queen number & mating
frequency
Resource availability
Competition for mates between
related males
Presence of old queens
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Presence of workers,
reproductives or other queens
Colony membership
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Sex allocation
Nr. of individuals trying
to become reproductive
Workers killing queens
Exclusion of non-kin
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Abbot et al. (2010) Nature
Melipona stingless bees
greatly overproduce queens: ca.
10%-20% of all female larvae
develop as queens, most are killed
soon after eclosion
Why? Mystery for >50 years.
IF theory: becoming a queen with
a probability of 14-20% is the
individual IF optimum of
developing larvae.
z*=(1-Rf)/(1+Rm)
Wenseleers et al. J. Evol. Biol. 2003; Ratnieks & Wenseleers Science 2006
A priori prediction: workers should be
selected to prevent or ‘police’ each
others’ reproduction particularly in
species with multiple mated queens
(Starr 1984, Ratnieks 1988)
Ratnieks & Visscher Nature 1989:
experimental confirmating of the
occurrence of worker policing in the
polyandrous honeybee
Wenseleers & Ratnieks Am. Nat. 2006:
meta-analysis of data from 100
species of ants, bees and wasps
showing that worker policing occurs
more frequently in species with
multiple mated queens
Starr 1984, Ratnieks Am. Nat. 1988, Ratnieks & Visscher Nature 1989; Wenseleers & Ratnieks Am. Nat. 2006
30
saxon wasp
red wesp
10
tree wasp
Norwegian wesp
median wesp
5
hornet
German wasp
common wasp
honeybee
0
30 50
70 80
90
95
98 99
level of selfishness
% of egg-laying workers
Asian paper wasp
A priori prediction: in colonies with a
queen: when policing is more effective
fewer workers should try to reproduce
in the first place, in queenless
colonies: species with low sister-sister
relatedness shold have more
reproductive workers (Wenseleers et
al. 2004)
IF optimum percentage of egg-laying
workers derived in terms in
parameters such as sister-sister
relatedness, avg. colony size, policing
effectiveness, queen fecundity, etc...
100
effectiveness of the policing
Wenseleers & Ratnieks Nature 2006:
both predictions empirically
confirmed!
Wenseleers et al. J. Evol. Biol. 2004, Wenseleers & Ratnieks Nature 2006, Ratnieks & Wenseleers TREE 2008
% males workers' sons
100
Stingless bee colonies: no
variation in relatedness structure
(single once-mated queen) but
huge variation in % of males that
are workers’ sons (0-95%).
M. favosa
n=8 species
Spearman R=0.95, p=0.0003
80
Parameters:
0.04 new cells built/day/worker (n=8 sp.)
worker life expectancy: 46.5 days (n=4 sp.)
M. quadrifasciata
Why the variation?
60
ESS
M. marginata
40
M. bicolor
M. subnitida
M. asilvai
20
M. scutellaris
M. beecheii
0
70
75
80
85
90
95
% female eggs laid by queen
100
Inclusive fitness model: due to
variation in the benefit of
replacing an average queen-laid
egg with a son caused by
variation in the % of the queen’s
eggs that are female, i.e.
variation in costs & benefits.
Cost in terms of reduced colony
productivity calculated using a
differential equation model.




T. Wenseleers, A. Gardner & K. R. Foster (2010) Social evolution theory: a
review of methods and approaches. In: Social behaviour: genes, ecology and
evolution (T. Szekely, A. J. Moore & J. Komdeur, eds). Cambridge University
Press.
P. Abbot, ... , T. Wenseleers, S.A. West, ...., J.A. Zeh & A. Zink (2010) Inclusive
fitness theory and eusociality. Nature, in press.
F.L.W. Ratnieks & T. Wenseleers (2008) Altruism in insect societies and
beyond: voluntary or enforced? Trends in Ecology and Evolution 23: 45-52.
F.L.W. Ratnieks, K.R. Foster & T. Wenseleers (2006) Conflict resolution in
insect societies. Annual Review of Entomology 51: 581-608.