Happy Galton Day!

http://www.theguardian.com/books/2009/jan/31/evolution-darwin-books

The authors set out to establish not only the centrality of race relations, and specifically slavery, in Darwin’s investigations, but to demonstrate that he formed the concept of sexual selection much earlier than is often thought and that it owes much to these racial controversies. The Descent of Man thus becomes all about sexual selection rather than this idea being loosely added at the end.

.. plumage development in the male, and sexual preference for such developments in the female, must thus advance together, and so long as the process is unchecked by severe counterselection, will advance with ever-increasing speed. In the total absence of such checks, it is easy to see that the speed of development will be proportional to the development already attained, which will therefore increase with time exponentially, or in geometric progression. —Ronald Fisher, 1930

Fisher stated that the development of sexual selection was “more favourable” in humans (Fisher, R. A. (1915). “The evolution of sexual preference”. Eugenic Review 7 (3): 188. PMC 2987134. PMID 21259607.)

Darwin was attracted to understanding human evolution through a sexual selection hypothesis because he felt it upheld the unity of humankind against pro-slavery demagoguery by explaining how black people and white people had come to look unalike, while emphasizing they did not stem from separate original stocks were not separate species.

Was Darwin wrong, and do ideals of beauty, in fact, vary around the world? If so that would certainly explain why sub saharan Africans look so very unlike Europeans.

But, I’m a bit concerned that only ~8 percent have read The Genetical Theory of Natural Selection

Fixed (soon), just ordered your recommendation. I got The Structure on your last recommendation, and checked “read” because I’m more than halfway thru it, so I cheated a bit, maybe.

I thank you for pushing my lazy butt to fix my background on my work field; I started in computer-medicine cross applications from the computer side (applying AI techniques to selecting MRI protocols for a given set of possible diagnostics), then went full computer industry, then back into computer support for life science research, but somehow never got to formally teach myself some of the basics of what the guys I help work on.

(although biology was always a fascination for me. Less than computers, but I got 21 out of 20 once in high school here in France – we score on a 0-20 scale)

Read Fisher? Easier said than done. I have a doctorate in a humanities subject and I know elementary statistics, but my mathematical education was limited and it takes me an hour to get through a page of Fisher. I have to work through the algebra before I can even get anywhere near seeing what the actual insight is.

If it comes to that, would Darwin have understood Fisher? I doubt if he was in that league as a mathematician. The Origin of Species is a pleasure to read, but it is not a particularly difficult book in the sense that The Genetical Theory of Natural Selection is.

This sort of genetics text is more up my alley in terms of my engineering training: http://www.boente.eti.br/fuzzy/ebook-fuzzy-mitchell.pdf

Useful in traffic planning believe it or not.

If I can join the crowd of fellow non-specialists in biology, I have to say that neither I read most of the scientific books recommended by Razib. I’am a humanities PhD who comes here to see how our host links exact science with historical knowledge. That is, I believe, the real force of this blog, this dialogue of biology and historiography. You don’t find it often on the web or even in print.

Is Nick Lane’s, The Vital Question, http://www.amazon.com/Vital-Question-Evolution-Origins-Complex/dp/0393088812, worth reading?

You shouldn’t necessarily be concerned. I’m guessing you’re making the assumption here that most of your readers are mostly interested genetics in a deep way? That may be the case to be honest but personally I have a lot more interest in your political/cultural and especially historical themes. So I wasn’t likely to be interested in genetics anyway.

I’m pretty much in the same boat. I’m a science type, but not a biologist. The genetics stuff is interesting — but not enough for me personally to make the effort to delve into textbooks for fun — it’s the historical stuff that keeps me coming back.

Agree with your point.

I am here for pure intellectual curiosity (fun). For fun, I might never read articles or books from cover to cover. Once some thing becomes a task, it is boring. I have plenty of tasks in my professional life, which need me to be responsible and study them from cover to cover despite of boredom. My professional mistake can have severe consequence which is the best motivator to be responsible and learn. Fear is the greatest motivator to do thing you might not enjoy very much. Well that is how life is.

Actually I did bought a lot of books (some recommended by Razib). But I only read some of them partially. Well, for fun, that is how fun is.

For example, math question is fun. I really enjoy solve math question. Never felt math is a task for me. History and science are like puzzle solving process which are fun. It is really exciting to figure out on your own without learning any thing first, which is confirmed by evidences and established knowledge. That is how I learn most about history and science. Just put idea and hypothesis first based on rational reasoning, then find both pro and con evidences to test your hypothesis. If not supported by evidences, then figure out where the mistake is and form the better new idea until all evidences fit. Well, that is how science works anyway. If you have PhD training, you know how it is.

Okay, okay! I’ll read it.

Following up on my previous comment, do you have any recommendations for a good modern treatment of evolutionary theory? (Math doesn’t scare me — it’s a bonus.)

For understanding the material discussed here, wouldn’t we be better off reading modern work, rather than Darwin *or* Fisher? Sure, the classics have the occasional gem, and are interesting from an intellectual history perspective; but for content, surely the accumulated wisdom of the last century counts for something?

But, I’m a bit concerned that only ~8 percent have read The Genetical Theory of Natural Selection (though one more than The Structure of Evolutionary Theory).

You shouldn’t necessarily be concerned. I’m guessing you’re making the assumption here that most of your readers are mostly interested genetics in a deep way? That may be the case to be honest but personally I have a lot more interest in your political/cultural and especially historical themes. So I wasn’t likely to be interested in genetics anyway. You could have added a question asking whether the reader was primarily interested in genetics or not to avoid people like me diluting the poll.I may be an exception, I doubt it, but I imagine a good fraction come for your non-genetic posts.

I posted this over on Sandwalk but all Larry could manage was “Get off my lawn” so I’ll try here!

I have two questions about the paper, pertaining to the species selected. Maybe three.

There are a lot of domestic species (or quasi domestic) in the data base, and thus, species with strong artificial selection.

My gut feeling is that there is a disproportionate number of species that tend to have larger than average changes in population size (boom/bust). This would mean that larger population size would be associated with relatively low diversity (initially) because of founder effects.

Third (maybe) I’m not sure if mixing entirely different reproductive patterns together is wise (i.e., looking at bees alongside bighorn sheep. Seems like you could get stung (or butted) that way.

Judging by the genome, humanity has an effective population size of about 20,000. This is due both to the possible bottleneck ending around 70,000 BP and, I should think, strong selective pressures before and since.

I am not sure I follow what your last sentence said, Razib. I think I agree with you that heterogeneity may not necessarily confer much variation in reproductive fitness, especially in the cases of alleles that have relatively small effects even in homozygous condition. MHC might have larger effects in the presence of a new pathogen, but in a stable environment might not represent more than a kind of placeholder for a larger set of small differences across lots of loci. Mating preferences based on sensing of difference, and thus mate preference for differences, could work to increase population heterogeneity for many polymorphisms of small effect, and this would be especially important in targeting phenotype tissues with extremely complex functioning. This might be significant in genes effecting cognition, for example.

Interesting essay, Razib. One of the things that has not so far been added to the model of balancing selection is the value, of simply having heterogeneity, in mate selection. We know all sorts of things now about how important this is in the case of the major Histro-Compatibility Complex, but I don’t think there has has been all much research to see if animals can sense other differences? If the sensing of differences at the MHC is just the tip of the iceberg? If it is, then many polymorphisms can be maintained simply non-random breeding , and need not entail high death rates to remain at HW equilibrium.

Interesting experiment, but I am puzzled by the takeaway some people seem to be getting that contingency is somehow shown to be less important now. Take the experiment one step further by mixing all these strains together and what happens? They did not do this experiment, but I will guess that nothing really interesting happens, because they have all converged on a similar phenotype. They all compete on a fairly equal basis.

Now, change the environment. Again, the experimenters did not do this, but I can make a reasonable speculation about what happens. Because the yeast cells have similar phenotypes, but different genotypes, some genotypes will be faster at mutating to take advantage of the new environment than others. The losers could have led perfectly virtuous yeast lives, with no drug tests and no pre-marital cloning, but their lines will perish. From my understanding, this sort of thing is precisely what people have in mind when they use the word “contingency.”

I don’t think that 640 populations in a very simple, homogeneous environment, without interactions with other populations, monitored for only 500 generations, can capture the kind of tail events that profoundly influence the course of evolution.

no, but i just learned what they are! i will if i ever get a chance to.

Brings to mind the great cilantro debate. I don’t know about the specifics of the genetics but there was an article in Nature last year.

http://www.nature.com/news/soapy-taste-of-coriander-linked-to-genetic-variants-1.11398

I have many friends who claim cilantro tastes like dishwater. I quite like it.

Have you tried bitter melon?

Also this African selection might be related to plant evolution of toxicity in the region?

Taste for different food seems quite persistent in families or immigrants. If genes identified, no surprise.
At end, it is always gene expression with different degrees of enviromental influence.

brussel sprouts are one of my favorites for sure! The other day my wife made some with lemon juice and I wanted to just dive into the bowl and start swimming around. here are a couple of somewhat related links this post reminded me of:
http://www.pbs.org/wgbh/nova/body/reed-taste.html
http://learn.genetics.utah.edu/content/begin/traits/ptc/

Minor side topic:

“they did not even consider the results of Pagani et al. (in the same journal!) from last year ”

Given the way academic publishing works, is it possible that they submitted before Pagani, et al. were published?

Publication lead times of half a year or more seem rather problematic in fast-moving fields (like genetics), especially if the use of a pre-print service like ArXiv isn’t standard.

If tuberculosis has differentiated in about the same manner as humans, does that mean there are differential risks from tuberculosis exposure when one is traveling in an area where the tuberculosis bacterium is somewhat different than in one’s home region?

I could see there being effects either direction – unfamiliarity may mean the bacterium has a harder time infecting you, or that your immune system has a harder time fighting it off.

How could that be tested given the dramatic differences in public health across regions which would much more significantly affect the probability of being exposed?

In their pdf, Enard et al say:
“…although signals of positive selection are detectable in all tested populations, these signals are systematically stronger in the out-of-Africa populations.”

Is this result consistent with saying that sub-Saharan Africans as a whole have a greater, richer genome set than, say Europeans and Asians, who in their various exoduses out of Africa, underwent ‘bottlenecks’? Due apparently to adaptive requirements and additionally were initially fairly small population samples to begin with?

Regarding MrJones’ comment… it seems to me
that part of the ‘constraint’ would be the finite
range in the population’s genome content. Ie:
In that sense, mama nature has by definition
a limited palette to play with in any given species,
regardless of the environments. Not to downplay
the clear genius of evolution by any means.

“does evolution result in an infinitely creative assortment due to chance events, or does it drive toward a finite set of idealized forms which populate the possible parameter space?*”

I may be misunderstanding but I’d imagine a bit of both i.e. a *potentially* infinite creative assortment due to chance events but in reality constrained to fit a finite set of environments (or broad categories of environment) which filter the range of possibilities.

Conjugation is very, very different from what we typically think of as sex, and is not an essential part of any bacterial species’ life style, that I am aware of. In my opinion, it’s better to think of conjugation as a method of replication of the plasmid or other mobile element that generally codes for the conjugation machinery. Transfer of genes other than the conjugation element is basically a side effect, and a fairly uncommon one at that.

OTOH, the problem that sex is supposed to solve, at least according to the argument Razib mentions here, is ameliorated in bacteria by conjugation, natural competence (uptake of extracellular DNA), transducing phages, and other forms of horizontal gene transfer.

Bacteria do not have sex, and they’re quite successful

Lots of bacteria do of course have sex. It’s called conjugation and a whole complex apparatus was evolved for it. Conversely, lots of fungi lost sexual stage and are quite successful without it.

There are Plants with XY and ZW sex determining systems. The key factor is as Razib said, which is the heterogametic sex.

X chromosome in drosophila?!! Who knew (certainly not I)? I thought this was strictly mammals. Birds have ZW, in (some?) reptiles and amphibians sex depends on gestational temperatures. And so on. Maybe there really was something to The Fly 😉

Rivers tend to divide apes and unite humans.

It seems that gorillas are sort of intermediate in this regard, though. While the rivers have been enough of a barrier to promote some level of speciation, there is also quite recent interbreeding. Is there a reason river boundaries are less problematic for them than for chimpanzees?

Or is this due to a single instance of one relatively late eastward migration of western gorillas? I recall a paper on Cross River gorillas where they pointed out some morphological anomalies (e.g., supernumerary teeth) that indicated recent hybridization.

There are lots of different swim strokes. The crawl was invented by American Indians, and so probably not what African ancestors used.

Do you think the human race will even be around in 10 million yrs? and even if we are around we can’t over come that problem?

I’m not a genetic anthropologist, or an anthropologist, but I’ll put my two cents in here.

I think the reason our ancestors were not afraid of water was simple. Once we stood and walked upright there were physiological changes to our bodies that gave an additional benefit: we could also swim. If you look at pictures of apes crossing water they wade, they don’t swim. Apes therefore know that falling into water that is over their heads will result in drowning and certain death. Of course they’re afraid.

If you think about your body position when swimming the legs are extended and the head cocked back to see where you are going. I don’t think any of the apes can do this (except us). You have to consider the planer kinesthetics of swimming, as early as australopithecus (Lucy) we could clearly manage the mechanics of swimming. Water was therefore no barrier to early humans–except for aquatic predators.

This doesn’t explain why we lost our fur coat.

One question to the assembled multitude that has crossed my mind, can any of the other great apes sweat, or are we the only ones that do?

P

You have a lot of hostility. You say to ignore the aquatic hypothesis, and then you discuss this new paper. Is it evidence for or against? I am just asking you to clarify.

Apes were unable to cross rivers. Humans were not so limited. So how is this an argument against human ancestors being aquatic?

Seems fairly inane considering that keeping (more) mutations in check is part of the explanation for the maintenance of sexual reproduction. Y’s shrunk to the essentials because it’s a dangerous place to be in the genome (not just because it does not recombine, mitochondrial DNA doesn’t do that either, it’s also the much higher male mutation rate).

Of course the evolutionary process does not proceed in a linear fashion on the Y chromosome? Seems irrelevant or strangely formulated here to me.

… human males would disappear within ~10 million years due to this process working its inevitable logic.

Why is this limited to human males? Why not mammalian males? But then, mammalian males have been around for nearly a quarter billion years, so that begins to raise some questions about the prediction. This issue is obviously implied in the fact of this paper’s existence (& of course in your discussion of it), but did nobody raise it as a serious objection to the hypothesis when the prediction of male extinction first appeared? I must be missing something, but I don’t know what it is. Please enlighten.

And let’s not forget that Darwin himself, as well as some other maverick biologists today believe that animals other than humans do in fact have a sense for the aesthetic, which contradicts all the “good genes” and indicator theories of sexual selection. David Rothenberg’s book, Survival of the Beautiful, is a great review of these ideas.

“But progress is being made, and in concert with fields like game theory and computer science I suspect that the future is going to be bright.”
LMAO

More on sexual selection here — new study from NIMBioS http://www.nimbios.org/press/FS_matechoice

This might interest you too, by some authors who argue that the diversity of models is somewhat bewildering and some distinctions are spurious (esp. relevant Fisherian runaway & “good genes”):

Kokko, H., Jennions, M. D., & Brooks, R. (2013). Unifying and Testing Models of Sexual Selection. Annual Review of Ecology, Evolution, and Systematics, 37, 43–66. doi:10.2307/annurev.ecolsys.37.091305.30000004

Imagine that …. and I thought this article was going to be about why geeks can never get laid.

Enjoyed your discourse. Now I know why I call myself “doglady”.Didn’t get my first dog until I finally lived in a house and wrote a letter to Pets and Pals of Oakland, CA ,(years ago)My mother put me up to writing the letter. I always felt I won because it may have been the only letter. But small world connection. One of the judges, unknowingly, was married to a distant cousin of mine. I have had several dogs, all best friends. Can hardly take care of myself these days, or I’d get a “labradoodle.” Cats are o.k., but my heart belongs to the pooch.Today I am very supportive of specialty working dogs.One can have no better friend than her dog.

I am thrilled that this progress researching the history of dogs has been made. I have intuitively “known” the truth for some time now, though it is based on my background as an athropologist, so I’m going say what we will all soon learn. The human-dog link-up actually starts back about 50,000 years ago (or more) and is part and parcel to the last great expansion of modern humans out of and away from Africa. The “wolf” involved probably looked a lot more like an Ethiopian Wolf or a Dingo than a Timber Wolf, thus explaining some of the differences in basal behaviors. I suspect all the different wild and domestic “yellow dogs” of today are closer to the final dog-human “product” than a modern wolf. Dogs evolved to feed off of Rodentia, thus the elongated “capture and hold” jaw and dentition composition and the from-birth “instinctive” ability to shake their head violently, rendering death in a small victim in a millisecond; not the sloppy, slow and unnatural pack slaughter seen in modern wolves and some wild dogs. The “where” of the human-dog link-up is much less important to me, because it clearly is something that took a little time and humans were moving pretty fast back then. So I suppose it may have actually started in Africa and developed through the middle east, the caucasus, India, and southeast Asia. This, to me, makes sense. I also feel we will learn more about the shared biomes, that is, the shared microscopic flora and fauna that have influenced the development of both animals, us and them. There is at least one study that indicates that babies raised in a house with a dog, on average, are healthier babies. Dogs were absolutely invaluable to early humans for several key reasons, which is important because they have always been “expensive” to maintain in terms of caloric consumption, which otherwise might be feeding the humans. But in acient times, they largely fed themselves, ridding the immediate area of rodents, which retained its value after humans started farming. That is reason #1. Reason #2 is that they were our first “early warning system”. Their senses, so much better than ours, could detect the pending presence of other humans and sound the alarm. Since these “other humans” probably meant to kill us, that was a very, very good thing. Reason #3 is that, quite simply, dogs were our emergency fall-back food source. They were our first domesticated farm animal, so to speak. The plains indians had a expression for when times that were really, really bad: they would refer to them as “when we eat our dogs”. This explains much of our own behavior to this day: there is no other animal on earth that we will adore so much in one moment and treat with such horrific coldness the next. Our best friend, indeed.

Why are inferred mutational rates higher? I would have thought they would be lower. Or maybe I’m confused about the use of the word ‘floor’. Why is there a ‘floor’ on how many mutations viable offspring can carry? Isn’t it a ‘ceiling’?

Here’s a nice map of dog/wolf mitochondrial haplotypes, with a focus on dingos. Interesting to note that haplogroup d is found in putative ancient European dogs like the elkhound and the lapphund, which does seem to place them somewhat apart, and suggests either a unique domestication event or more recent cross-breeding with wolves.

Moderate bottlenecks would skew allele frequencies and make PCs somewhat less useful? And the greater diversity / more root-like quality of the Asian breeds may be a mere result of the past admixture from wild canine subspecies, some possibly extinct?

Thank you. This is why I nitpick. Often, what appears even to me to be nitpicking is actually reflective of my ignorance: so I learn something when my nitpicking is corrected.

The second aspect is that the coalescence of the dog vs. wolf lineage is pushed further back in time than earlier genetic work, by a factor of three.

Um… 3 possibilities: (1) that word does not mean what you think it means (least likely), (2) I do not understand what is going on here (more likely), or (3) you meant to type divergence.

Please elucidate (or correct if that is called for).

Didn’t Bokyo already demonstrated African and Middle Eastern village dogs are just as genetically diverse as the Southeast Asian village dogs? For some reason, those who hold on strongly to the Southeast Asian origin theory tries to debunk the African village-dog discovery by citing the major trade routes in Africa and Middle East. True, their point may be valid, but no one ever seem to question the dog-consumption culture in East Asia: dogs are raised like livestock en mass which would preserve the genetic diversity. At least comparatively to the pedigreed dogs of Europe.

I think John McCarthy, of Lisp fame, was correct when he said those who are incapable of doing Math are doomed to failure.

Linear algebra is extremely useful for a quantitative geneticist, particularly for one who is interested in working on GWAS or NextGen sequence data in an intelligent manner (ie: more than just looking at additive genetic variation for a single gene at a time). It seems reasonable that if someone wants to study the missing heritability question (or just address it in their work), they should be thinking about more than just methods of examining rare variant effects, they should also be thinking about genetic architecture (ie: epistasis, haplotypes (sort of assumed in the rare variant hypothesis, but not by everyone who studies that part of the question, unfortunately), and possibly even some effects from imprinting that can be mathematically modeled). For that, you almost have to do your own programming, especially if you’ve got a complicated pedigree structure to your population.

also, it would be nice if all biologists stopped using excel and just moved to R. but i’m biased

For most sophisticated statistics and modeling the go to program is Matlab. R has been introduced to the community and discussed, but as most models are already in Matlab, it is of questionable cost effectiveness to switch.

It seems to me that a lot of the most important questions around in genetics at least are essentially abstract and quantitative in nature: we are still trying to find out how complex traits work and what we can do with the genetic information we have. Lab work is an essential part of the investigation, but you need to have statistical training to even understand some of the questions (the problem of missing heritability for example) properly.

J.M.S. scooped Hamilton on his top idea (kin selection) while blocking publication of Hamilton’s own paper on the topic. That’s more than just a “percieved” slight, methinks!

“i think macro is a lot of hand waiving” – so do I.

“is this micro-rooted-macro capable of non-trivial prediction?” – I’ve dealt a little with that kind of micro-macro and my answer would be no. Which is part of why I’m no longer working with that stuff.

I actually have no problem understanding that sentiment and I should point out I’m hardly the only soon-to-be economist who don’t think very highly of macroeconomics. At this point I only do work at the intersection of econometrics and microeconomics – where the general approach is quite different. Most of this stuff is just applied stats on individual-level data handling questions economists might ask themselves. I know you’ve talked about twin studies before here on your blog, and I should perhaps point out that these are often used in some areas of applied micro.

You know this but it bears repeating: Economics isn’t just macro. Some other areas within economics handle the science much better.

“contemporary economics does seem to have a problem where extremely powerful quantitative methods have become somewhat decoupled from the empirical questions at hand.”

I don’t know much about what’s going on in the field of biology, but I’m curious if you could elaborate a bit on that part? In which way – are you thinking about classical ‘excessive formalism’? Black-boxing? Or about requirements that researchers use new and complicated methods rather than simple ones in order to get published, even though sometimes the results may be very similar? Something else?

I ask because whereas I’d wholeheartedly agree that excessive formalism is a problem in economics as a whole and that there’s a huge amount of ‘math for math’s sake’ in the field, it’s not my impression that ‘applied math’/stats for ‘applied math’/stats own sake is that much of a problem. Although ‘theoreticians’ do exist in that subfield at least my impression is that the type of people working actively with new quantitative methods tend to be very focused on actually using the methods to deal with specific problems at hand in order to better approach the empirical questions they desire to answer – they mostly seem to use the methods because they solve problems that could not otherwise be overcome. Actually the kind of people who take up actively applying new and powerful quantitative methods tend to be quite interested in doing ‘actual science’, so all else equal I’d certainly assume them to be less ‘decoupled from the empirical questions at hand” than many others in the field (like, say, the economists who don’t feel the need to deal with the messy world of real data and who thus constrain their use of mathematical methods to complicated theoretical and often untestable models. Those guys are way more likely to ‘math up’ their stuff.).

Wrt. new quantitative methods it’s important to have in mind that there’s both a question to ask regarding whether it’s appropriate to use ‘a fancy’ method, and a question to ask about how to handle the situation in case you do. Black-boxing is a major concern, so some degree of formalism is required if new methods are applied. And sometimes the ‘non-fancy’ method may simply no longer be an option, because it’s been recognized that that approach to the empirical problem is deeply flawed.

i don’t know if you still need to go much beyond calc and stats if you are working mostly on the bench

Well, my current boss is a social scientist working in a field where things like Bayesian analysis and re-sampling methods are becoming the norm. And I’m having to explain these and other statistics topics to him from an Analysis level for him to be able to compete for funding.

So for a growing set of “bench” scientists knowing the math (and not just the equations and algorithms) is critical.

While the traditional methods of physiology have taught us much, they rely on either leaving most of the underlying processes responsible for a phenomena as black boxes or isolating part of a system. Neither approach can give us a detailed understanding of how multiple biological systems interact. Until we do have such a fine understanding, we’re left with the equivalent of sledge hammers for treating our maladies.

To really understand a system you have to be able to model it and modeling requires math.

Wilson is of the (last?) generation where significant discoveries could be made by stamp-collecting.

If one includes formal logic as a branch of math, then he’s wrong, even about himself, most likely.

Is this with older scientists or with the new younger ones? or? Besides math many do not have the broad background of knowledge like the ww2 generation did many r hired in due to some connection other then being great at biology. AM surprised how much people do not know these days…do to internet addictions minds going down stream…

Wilson makes a similar point in his recent ‘Letters to a Young Scientist’. he adds that if you don’t have the skills, you need to partner with folks who do know their Math. He gives some examples taken from his own research projects

The subtitle of Wilson’s piece talks about number-crunching and I think that goes to the heart of the matter. Being good at calculation is just one aspect of mathematical ability. At higher levels conceptualizing is more important and no one can be a good scientist who is not a good conceptualizer.

I think you hit the nail on the head re: programming–it’s a skill that is very useful and not very hard to grasp.

There’s also something to be said for ‘mathematical thinking.’ Understanding and doing complex mathematics is one thing, but developing good quantitative intuition is another. I found that taking courses in topics like linear algebra and formal logic and set theory to be incredibly helpful in getting me to think abstractly and analytically, even though I haven’t proved a theorem or corollary since I took those classes years ago. I would say, even you’re not mathematically inclined, a biology student could benefit from struggling through a course in higher mathematics, if only to engage intellectual muscles that don’t often get a workout in bio classes.

The question, or rather, question(s) are:

1. Just how high of a mathematical knowledge should be the bare minimum required for the average “biologist” (or rather life scientist) nowadays? A decade ago I remembered it was expected standard introductory college statistics and calculus would suffice, but it seems to be much, much higher nowadays.

2. And assuming the general quantitative requirements for the life sciences are continually increasing at a substantial rate (aka computational programming as recently as a decade ago wouldn’t even been mentioned in a conversation about necessary, general skillsets vs being touted as a potential career buffer/saver these days) , are most current or aspiring biologists/life scientists capable of even gaining basic proficiency, let alone mastery, of those increasingly difficult concepts?

PhD student here. I wish I knew MORE math(mainly stats). And I wish I knew more scripting!!