In Memory of Bill Hamilton

Stories with Bill Hamilton in them

By Mike Orlove

I first met Bill in February 1971. I had recently written an undergraduate paper on Kin Theory having been interested in it not onloy because of its relevance but because of a long-standing interest in accualtes since I was eight years oold, especially Polistine wasps and Xylocopine bees.

Ross Crozier was then a Grad or post-doc ant Cornell in Brown's lab and Ros liked my paper, and took a copy to Georgia where he an hamilton were convention goers togerther. Hamilton changed his travel palns to return to Britain not directly from Georgia via Washington D.C., but to Travel to Ithaca to meet me, and then to to New York and fly back to England from there.

During our visit in Ithaca in GeorgeEickwort's lab, I showed him computer printouts from my simulation model with graphas demonstraiting clearly that equilibrium K was les than 4/3 between sibs for wasps when alturism was dominant, and greater than 4/3 when selfishness was dominant, and only euql to 4/3 during half-dominance.

De decided to invite me to Imperial college as soon as possible to do graduate work with him.

We correspnded during and throughout the Spring and Early Summer, and with sadness becaue I would be not onlyh leaving friends and family, but Xylocopa and Polsites behind, I arived at heathrow Airport on 31 July 1971.

Please understand that it is painful to recall these things because of the way we lost Bill last March. My own Father passed away in November of 1992, and it is avery similar experince all over again. No doublt you feel some of the same things I do and you don't have to work hard to immagine what it is like for me.

I will not go through everything chronologically but only tel you some highlights now.

Woverver my arival at Heathrow is somewhat commical. What probably happened is bill was in a hurry as he was leaving for 2 weeks holiday in Ireland on 1 August, the next day. He was in fact in a hurry. One explanation for the debackle was he may have told the airline that he needed to collect me quicly. As the "ship" as they called it landed, it was allegedly the prototype speciemn of the Bowing 747 (it flew flawlessly one could feel no mition it was like being in a large building that showed no inertail sogns of tilting)., they announced on the P A system please stand in place and remain standing until told to do ohterwise. An ariline attenedent came to me adn whispered in my ear, "Are you Michael Orlvoe?", "Yes" was my reply, she took me by the arm with my small duffle bag (allI brought) and took me all the way to the edexit of the plane. As I was lead off, a mddle-aged guy siad to his companion (wife/) "Look Ethel, they got one for drugs." No folloong! that it funny because of the stereotype for American tourists beginnign sentences with "Lok Ethel...". When i got to the door another lady asked "Are you Michael Love?". I corrected her saying "I am Michael Orlove", thinking she would realize she was the one with the mistake if it was a mistake at all. but she thought she was right and figured I must be the wong perosn, so I was supposed to be the first one off, but ended up the last one off much to bill's disappointment.

I found my duffle bag in time it hd to go thoruh some kind of thing so it was with the colleced things as if I hadn't carrie it on ard. It rooled aroun on a great turntable, and then i went into a galss both with two customs men to be cleared.

I knew nothing of the abundance of Scarlet Runner (Phaseolus coccineus) in Britain and took a seed of it with me, I asl oknew nothing of how susceptible to inbreeding depression it is, and only had one seed.

I also had a canister of Brine Shrimp eggs (Artemea salina) which I wanted to study, having been toold that all female populations can thrive using thelytoky, and I was intersted in observing a male "invade" such a population, to see if there was selection for mating with him or his descendants.

I was escorted into a small booth with two customs men. the queeriedd waht I had to declar, and the first and formost thing on my short list was a carton of Holerith cards (IBM punch cards) with my genetics simulation programs on them.

they asked whether these were of any value. In short they wanted to know if it was a comercial enterprise, for if it were, i.e. I had something that could cause private gain to one business but not to its competitor(s) it woudl either be illegal or highly taxed.

I was clueless as to what they meant. To me they were my inspired creations, and I said they were of great value, but they grasped that I didn't understand their menaing.

they asked what is it exactly. I aid "simulations of populations of wasps, and programs for doing algebra with the results of the simulations.

they said are they of any benefit to you. I ansered, "I will learn agreat deal about the way the world works.." "We mean are they of any monitary benefit to you,!" "Yes said i, in the sense that Thjey will lead me to earning a doctorate, and a population geneticist earns more than a street sweeper." "At that time Bill entered, a little peeved at the time that has transpired. A few words rapidly transpired and I was out of there. I asked them if I coudl keep my Scarlet runner Bean seed, and a canister of Artemia eggs, and they laughed and siad that was no progblem. i asked them if Scarlet runners were already in England, and both bill and they thought I was a bit odd. Of course they are common in Britain and somewhat rare in the States.

I had onl seen them except for the picture of the vine on a packet orf sees wwhen I was eleven, only months ago and was impressed by the size and exquisite appearance of the blossoms, as wel as the Polistes and Xyulocopa on the blossoms.

bill had trouble believing I didn't understand their indirect questioning, however all traces of negativity evaporated in the car on the way to Silwood. He asked me what i predicted woudl be the really big thing in Population Genetics in the near future that hasn't made surface yet. I told him that though the futre people woudl see we were right, they would question our notion of randomness, and see that the really good theories we had wodl be robust enough to withstand the illusiary nature of randomness. Howefer, they would discover new things we missed through an awareness of such. He agreed with me wholeheartedly.

He left me at the field station for 2 weeks on myh own, I made new friends, wrote to old ones back home. i illustrated a litter to my sister showing a jet on fire on a neighboring runway duirng my take off. i was afraid she woud thingk i burned up and wanted her to know it wasn't myu plane. the pilot said it was a test on a cipher plane and no real disaster.

The fit student I ment was Jillian Hickling, doing her Ph. d. in nematology.

Upon his return Bill saw I had trained a worker of Paravespula germanica to fly through my window (barely opened a crack) to access a feeder all the way through my room. He told me interesting stories about moving wasp nests in tropical America a bit at a time, and how if the wasp becaem confused, she would often go to the original location before the move before continuing her search at the business end of the trajectory of the nest. A similar incident had occured wit the feeder.

One of the highlights of my life was Bill's showing me one of the highlights of his creations. this was a stroke of genius equal to or surpassing the "K-R rule", in sheer genius, though not as sweeping in relevance. come on! the K-R Rule is a hard act rto follow, or preceed for that mater!

This mystery object was a board game, called "Incstuous Arthropods", though it was orniginally named by Bill as "Incestuous Insects". I like the 2nd mentioned name better, but he was one to avoid cutsiness, and indeed questioned a poster i drew for an exhibit ofthe game at an open house scince fair at Silwood, because the beetles depicted in the cartoon playing the game on a tree stump were "four-legged". I too as a 3 - year old hated toy insects with four limbs, or antennae springing from the tops of their heads instead of the location of their nostrils, for their inaccuracy.

When Creatinve Computing published my "Wasps and the Impossible Elevator" tehir cartons, and even regular depictions had the was looking "four-legged". They had redrawall my picgtures, turjning ny Polistes fuscatus wasps into Tripoxylon polites ones! Bill just aid "tehy are too four-legged". He had the same complaint about the beetles that batttled in a bottle in a puddle with a paddel in Dr. Suess's "Fox in Socks".

but Bill's game as was Bill himself, was marvelous!

The brilliance involved in the nomogram which did the calculations during the playing of the game, matches or maybe even surpasses the brilliance of the K-r "rule" but its relevance to understanding how the universe works is not as great, or at least obvously as great, but it did show how evolution works, and how to get into the neodarwinistic paradigm without getting lost first.

The game reflects reality in that there is a prisoner's dilema, if both females produce few males, and agree not to outdo each other in the male production, they can both do very well in producing losts fo female dispersers, but if one cheats while the other trie3s to "honour" such an agreement, she wil hurt her partner severely and gain at her expense.

I was able to demonstrate that the string and "Z" nomogram does accurately precict how many females eqch female's sons wil fertilize. I immagine many players will have to take Bill's word for it, much as they trust their personal computer to give the right answer without understanding how it got it. Many people will get an intuitive acceptance of he nomogram by testing it under extreme conditions, like one female makes no males or one female makes 12 of them.

Another titelating story involves a conundrum he set me.:

The conundrum involved certain flies of the family heteropezidae (spelling?). They have paediogenetic larvae. These larvae produce eggs which develope by parthenogenesis. Ceertain chironomids do that much ovipositing as larvae or pupae, but the heteropezid eggs, hatch inside the mother maggot, who is litterally eaten alive by her offspring who burst and burgeon forth to continue consuming the hostwhich may be another insect, or a mushroom, or mushroom spawn.

When the host is almost completely consumed and the maggots feel pangs of hunger, some of them become males and all of them pupate and the adulsts leave, mate, and find new hosts or die.

Now Bill's conundrum stated out as a statement that a blackbird might have an optimum clutch size of 4. If one of these birds laid 5 eggs, she woudl have more offspring but the survivorship of all of them would be so diminished that she wouedl have less surviving offspring than if he hd laid 4. If she laid 3 eggs, each offspring woudl have more survivorship than members of a clutch of 4, but the increase would not be great enough, to make their mother's number of surviving offspring as great as with 4.

Given this logic, one might be tempted to say:

"It's a good thing optimum clutch sizes aren't 1 or 2, for if they were think of all the species tht woudl go extinct!".

Now these heteropezids, especially ones in th eenus Heteropezia, which live in mushrooms, in their dispersal stage which exists as an adult fly, have only one egg inside them and that is all they lay in a lifetime. The question is since evolution is non teleological, how is it that the parts of the genome that code for an optimum clutch size of 1 "know" that there is a compensating part of the genome that allows the larvae to be paedeogenetic to "compensatge" for the tiny optimum?".

The solution i cam up with was the one Bill had hoped I would here it is:

The life-cycle of Heteropezia probably evolved from that of a "normal" fly through many intermediate stages. At one of these one might expect a life cycle in shich all maggots metamorphosed into the adult stage, but there were two phenotypes, and maybe even intermediates between them. One of the two woudl be a stay-at-home fly ready to exploit the same host it grew up in, and the other would head for the hills ihn search of a new host.

The two phenotyupes in this "polyphenism" could evolve seperately, wiht differetn parts of the genome controlling the distinguishing characters between them. the clutch size of the dispersers could be free to evolve to be smaller and smaller. maybe flies with fewer eggs can fly farther without eating, either because thy have less of a payload, or less of a perishable cargo to feed, or have smaller size, and so do to scalijg phenomina can fly on less energy per miligram of body weight.

Genotpes with snmaller clutch sizes in their dispersers, might not lay as many eggs per fly on average, but woud successfull, or more successfully found new colonies.

I told this story to George C. Williams, whose response whetn, "You wnat to start 2ith 30,000 drosophila, and select for a clutch size that is smaller and smaller, until yo hae one fly that lays one egg, and then sell her for $50,000.".

Bill and Goerge are very similar in teh deseigns of their minds, and Bill's humour was very much like Georges. Their similarity is more than superficial.

Bill who always apreciated good humour, was somewhat stayed as is accpetable in Britain, but he gave a hearety roar to that story. I told hit to him to illustraite to him thier similarity, of which he was, however, very much aware.

Equally vehiment was a negative reaction I got out of him whn telling heim a story because I was unawares of all of the ramificatons:

Nova (Horizon) did a program for BBC television on sociobiology. Bill never used that word, nor did he use "Kin Selection". He used "social biology" and "Kin Theory" or "Inclusive Fitness Theory". He was like the reupted Martin Luther who siad: I am glad to be Luther and not a Lutheran, or Karl Jung who was glad to be Jung and not a Jungian, or Wittgenstein who was glad to be Wittgenstein and not a logical posativist.

The television program begins with the narator reciting the opening words of Bill's paper "Geometry for the Selfish Herd":

Consider a perfiectly circular lily pond."

A population of frogs liges on the shore of the pond and they distribute themsleves in a pattern resulting from each frog's minimizing its risk of being eaten by a water snake that rises up out of the pond and then choses one as its next meal.

for the model to work and not be indeterminate, if the snake makes its appearance in the exact middle of the pond. Assymetry is essential.

In the cartoon, tha tillustrated the narator's speaking, the snake reared its head right in the middle!

I learned how litteral the term "livid" can be. He wasn't mad it me butobviously affected. His face was Dark red almost dark purple. His eyes glowed bright whit against the dark background. I knew he was upset they got it wrong.

Unawares of the full ramificatons of this incident I repeat this story so far to John Maynard Smith shortly after. John's reaction was as unexpected and as strong, though quite different:

He grabbed my shoulders and shook them gently and said "Tell me it isn't true!"

It turned out that John was the author of the TV program, but left for a visit to the States for a spell, and trusted the editors to get it right. He siad "That will teach me to give anyhone some work to do and then rush off to America.".

A scientific American Article he did at the same time on Kin Theory, wasmessed up for the same reason, they got worng a diagram with chromosomes showing whow haplodipload organisms' relatednesses to their siblings are different to those for diplodiploids.

John and Bill had some bad blood between them in that John coined the term "kin Selection" while refereeing, or having refereed Bill's famous 1964 two papers.

This was exacerbated by the claim of John and others that J. B. S. Haldane was asked in a pub, way back in the thirties, if he lived his life by Natural Selection.

The answer he allegedly gave, after taking some time to think or calculate on the back of a napkin for a moment, was "Wellif I did I would be willing to lay down my life to rescue more than one of my identical twins, more than two of my brothers, or more than eight of my first cousins.".

When John put this in print around 1978, Bill was unhappy because he siad that if Haldnae had discovered teh K - r rule that explicitly, it woudl have made a bigger splash on society than it did. It is conceivable that might have taken V. C. Wyhne-Edwards' book in 1962 Dispersion and the Evolution of Social Behaviour, to digust peopel with group selection to prepare us for the reception Bill so diservedly got.

One when a visitor in his home, I asked him in front of his family whether the reference to turnip blossoms and cabbage blossoms spring from different branches on the same tree, in GAMPBLERS SINCD TIME BEGAN was in reference to the phylogenetic tree, or the woody ancestor of the now herbacious cabbage and turnip. His answer, as expected, was "Both". This is wonderful and attests to his skipp as an exceptionally engenious writer as well as scientist. this applies ot Dawkins as well.

I expressed this sentiemnt to his children wanting them to realize his excellence a sa writer as well. I feel very sad for them, and especially Rowie because she was onoy 22 when he died.

This my last story for this letter, but attests to his wonderful humour.

In 1978 I was working on my paper "A reconciliation of Inclusive Fitness and Personal Fitness Approaches: a proposed correcting term for the Inclusive Fitness Formula". the omision of this correcting term was not so much an oversight, but had certain good reasons to reccomend it. Howewever its inclusion has certaqin realdelights too!

While this was being considerd by the Journal of Theoryetical Biology, Lewis Walpert was a t a loss as to whom it woudl go for refereeing, and there was really only one choice, namely, Bill Hamilton.

He actually relly liked it, and some int3eresting correspondances spawned out of it.

It one time before I handed in the Galley proofs, I wondered if I might be upstaging Poor Old Bill too much, or at all for that matter, so I phoned him and asked him if I shold call the new formula Inclusive Gitness, or just Gitness, instead of Corrected Inclusive Fitness. He asked me as to why I would worry about such a thing. I told him I din't wnat to intrude on his territory, his answer waws "Welll you always could call it Intrusive Fitness!".

I miss him emensely, and feel bad for him those of us howevernumerous who logved him, and know it was his own altruism that made him assume the risk that killed him. he was more like George Price than most of us realized. A major reason for George letting go of life, was his losing a home where he allowed homeless people to live, and he coudl no longer provide for them.

thsi was not played up so much in Narrow Roads, but was very much in Bill's awareness of the situation at the time.

Well I must go now, please stay in touch,

Please forgive my typos, it si not so much my segvere visual impairment, as a nerve pinch in the nerve in my neck going to the left ahnd.

I have fallen out wiht myh new landlord and the sherrifs could come to evict me any time after 2:00 p.m local time. That is 32 minutes from now.

i have foudn nowhere to live suitable for my life threatening allergies, but am continueing my search. Hopefully the Sherrifs will not come til tomorrow morning it being Sunday and all.

So I will get this off to you, please forgive the crude un proofed stae of things.

The reconciliation paper was in the JTB 1979 v 81, pp577-586.

I will include a URL for the computer program used to do that paper, and some essays in there may be helpful.

Two other URLs for support software are included. i will aslo include an essay which wws gong to go into th epackage, but gotsaved for the next verison.

I hve not been able to upload that yet. sorry.

I hope this is helpful to you.


Sometimes a word has a slightly different meaning in Science than in common usage. Thus a "force" in physics has a different meaning from that implied in "forcing yourself to give up smoking" or an evil "force".

In its everyday sense "altruism" donotes an act which results in the actor making some kind of a sacrifice to help someone else. It is inherent in this definition that the actor is aware of these costs and benefits and to whom they acrue, while choosing to act. To a sociobiologist who studies nonhuman organisms (birds, insects, etc.), such a definition would be useless since we cannot read the minds of these creatures and know what they think or feel for certain. Therefore a different definition for altruism was adopted by biologists. It is based on the outcome of the action not its intention. For example an animal wishing to help its neighbor, feeling discomfort in the process and continuing the process inspite of the discomfort but actually benefiting from the interaction at its neighbor's expense, would be altruistic by the first definition but not by the second one. Impressing someone by means of an expensive gift of an addictive drug would be an example of this.

Therefore, these gains and losses to the two interactant are not necessarily in pleasure, but rather in FITNESS. Here's another word! It might mean brute force or healthy condition in the gymnasium, but in evolutionary theory it is a measure of evolutionary sucess. There have been several definitions. They have each been tried one by one to preserve Darwin's theory as the picture became more complicated. The kind of fitness used in the definition of altruism is what is called "personal fitness" or "reproductive success" or simply "RS". It is measured as the number of offspring an animal or plant produces with its own reproductive system in its lifetime regardless who rears or rescues them. These are weighted by risks taken in their production. Thus a hypothetical bear may have twice as large a litter if she refuses to hibernate and carries on feeding. However, if there is a 50% probability she will die with the cubs before Spring if she tries this stunt, then bears who try will have the same RS as those who don't. Your RS like the other two kinds of fitness also takes into account "interest rates". A human who waits to be 50 years old to reproduce might have to have 5 kids to do as well as another who had 1 kid at age 14. This is because that 1 could be reproducing at an early age and a grandparent by the time the 5 were born. The 5 might not get born because their would-be parent might meet with an accident. So to simplify things biological models are often limited to semelparous organisms like corn plants or praying mantides who are all the same age , they all reproduce together at the ends of their lives and then all die together. In other words all have non-overlapping generations so RS is measuredas the number of offspring produced at the end of life (period).

RS takes into account extra offspring produced due to windfalls (e.g. a windstorm knocks down many persimons and ahungry wolf finds them) as well as extra help given a would be parent by others (e.g. a hungry pregnant wolf gets fed byher sister).

Classical fitness or Darwinian fitness doesnt take windfallsinto acount nor help from neighbors due to the thought that the animal's genes didnot earn the bonanza.

Your Inclusive Fitness, like classical fitness does not increase with bonanzas you experience from the help your kingive to you. But it does increase with the help you give to others! This is so because inclusive fitness is tallied up by counting "offspring equivalents" the individual rears or rescues regardless who their parents are.

Your grandchild would count as 1/2 of an offspring equivalent (i.e. 1/4 of a self equivalent because offspring are 1/2 self-equivalents). A niece or nephew is also half an offspring equivalent. Thus an act causing you to leave behind seven grandchildren and three nieces and nephews, as opposed to ten grandchildren and no nieces and nephews, would leave you no better or no worse off. This is so even though commioting the act would lower your classical and personal fitnessees. If commiting committing the act got you seven grandchildren and four nieces and nephews ans opposed to ten grandchildrenthen it would be the prefered strategy.In 1964 William D. Hamilton, then at the London School of Ecomomics, who discovered personal and inclusive fitnesses, predcicted that inclusive fitness would be the thing maximized by natural selection. Of course this is true of personal fitness too, and it is clear from the above example, that sometimes an animal's inclusive fitness is higher than its personal fitness, the point is that an animal has more control over its inclusive fitness and by maximizing that, it will maximize the expected value of its personal fitness. In other words cases where the animal suffers a low personal fitness due to sacrifices made will on average be compensated (sometimes over sometimes under but on average just right) with gifts from others. In the case of those species of ants with truly sterile workers thecompensation would go not to the worker but a queen somewhere in the population with her genotype.
This is not mystical but just a consequence of statistics. One can look at the offspring equivalents as good for their own sake as carriers of the actor's genes, or as prommises that the actor will be compensated. each system is an equally good predictor of evolution ary success. This is reminiscent of the concept used in Vedic cultures of "Karma"(Sanskrit for energy, motion, action) where an altruistic act lands the actor good karma which in turn can be looked at as good for its own sake (the satvasic approach) or a promise of a feture reward (the rojasic approach). Thus personal fitness is a rojassic (pertaining to selfishness) concept and inclusive fintess is a satvassic (pertaining to light, penetration, transparency, altruism) concept. The only reason for appealing to The Vedic Tradition (pertaining to cultures such as Hinduism and Buddhism) is to resolve an apparent discrepency in the apparent equivalencebetween the personal fitness and inclusive fitness approaches. This is taken care of in Vedic Philosophy by theconcept of "group karma". In Population Genetics theargumentgoes ss follows: if in my life I raised 10 nieces and nephews and had no own offspring, then I have increased the sum of all the inclusive fitneses in the population by 5 andthe some of all the personal fitnesses by 10. Shouldn't bothincrements equal each other? Well in fact they do, becase although each niece or nephew has 1/2 of an offspring equivalent in her/him, she/he also has 1/2 of a stranger equivalent too. So the 10 individauls I reared corespond to five offspring and five strangers. Hamilton put all the Stranger equivalents togrther in a catchall called "dilutingeffect". This is because strangers are made of on average representative samples of the gene pool. Parts of a relativemade of representative samples of the gene pool are thought of as a diluting agent diluting the genes which are replicasof the altruist. This is such a complex way of looking at itthat I prefer to think of the stranger equivalents as being meted out equally to every one in the population. This is the kind of "white lie" that might arise by saying I raisedone offspring and one stranger instead of saying I reared two nieces.

Then If I reasied the 10 nieces and nephews as above, my inclusive fitness would come out not as 5 but 5+C. Where C is the total number of stranger equivalents reared this generation divided by the population size. And every one gets a C tacked on to his inclusive fitness and C is the same for everyone in one generation. C is the "group karma" componentg. Thus in a world where mostley everyone is altruistic a mean individual would get more out of society than he/she puts in riding on a good group karma so to speak.