It seems they used modern human mutation rates, which vary by ~300%, to predict age at reproduction. Since the relationship between this rate in parents and the offspring even a few generations back does not seem to be particularly well understood, it seems they would have a hard time reaching back very far into history with this analysis and claiming any accuracy at all.
To me it reads like someone bought a cheap e.g. lux meter, realized it was highly thermally sensitive, and instead of throwing it out or making a better one, declared they could use it to sense both light levels and room temperature.
This point was already addressed in the research. It is tiring to see this low effort comments on every research thread, thinking that the researchers are idiots and there is no need to read the article to reject it.
Can you point to the text that addresses this? The closest thing I see in the article is this paragraph:
Children's DNA inherited from their parents contains roughly 25 to 75 new mutations, which allows scientists to compare the parents and offspring, and then to classify the kind of mutation that occurred. When looking at mutations in thousands of children, IU researchers noticed a pattern: The kinds of mutations that children get depend on the ages of the mother and the father.
Later: Hahn, Wang and their co-authors built a model that uses de novo mutations—a genetic alteration that is present for the first time in one family member as a result of a variant or mutation in a germ cell of one of the parents or that arises in the fertilized egg during early embryogenesis—to separately estimate the male and female generation times[...]
So, it is saying it can measure results for male and female parents separately. But can their analysis of the "kinds" of mutations tell the difference between e.g. "30yo mother, 45yo father" or "20yo mother, 30yo father, plus lots of environmental factors that increase mutations"? The article doesn't make that clear to me.
I skimmed the study around all the matches for the strings "mutat" and "environ", and this was the best I found: Estimates of the error in our model fit do not show increasing error with either genetic or geographic distance from Iceland (figs. S6 and S7), the origin of the pedigreed mutation data used to train our model. Such a trend may have been expected if differences in mutational spectra were driven by genetic or environmental differences among populations.
The last sentence is actually ambiguous, but I think it's saying "If environmental factors tended to mess with mutational spectra, then we might expect to see X, which we did not see." It's still not clear to me how possible it is for there to be environmental factors that generate the same mutational patterns as higher age. And the only other "environ" match is in a sentence about what affects the age at which people have children.
I’m personally tired of scientists who “address it” by dutifully calling out some subset of the problematic aspect of their approach, and then go ahead and publish low-quality results for the headline.
An analogy for this one could be saying something like “I know it sucks when people say unkind things, but I think you’re stupid.” Acknowledging the problem does nothing to prevent it or resolve it. It just means at some level the person knows what they’re doing is wrong, and they aren’t self-disciplined or integrated enough to stop.
It burdens the (numerous) other parties with the effort, in the same way scientific results like this do.
Not everyone subscribes to Science Advances. I can't even get their page to load. Humor us and try to explain your thoughts instead of complaining about the "effort" of the GP, please.
The answer to GP's objection is not explained in the linked article, as far as I can tell.
The writers of a research paper have a vested interest in seeming smart and displaying their findings as a novel contribution to the greater corpus of research. It's better to think skeptically and critically about any new research paper than to accept it as fact.
A lot to unpack (read - wildly speculate about) here.
10,000 generations ago. Like the next one but less of a "solved game".
1000 generations ago - Old men coupling with young women reads as small-scale tribal society to me. Polygamy, pride-of-lions. Groups are small enough that village elders control the, uh, means of production. The bottleneck on food is natural stocks.
200-300 generations ago lines up with the dawn of civilization and large-scale farming (5-7000 years ago). The bottleneck on food is human labour. Young people are encouraged to start (reasonably) self-sufficient farming families, and the surplus is traded for, taxed, or stolen.
0-50 generations ago (1000AD+)
??? Cultural escape velocity is reached. Women are having children later than ever before, pointing to less risky lives, greater food security, and increased autonomy, but also a heavier load of cultural baggage. Becoming elves isn't all it's cracked up to be.
Also, before someone else says it, blah blah blah average vs median.
I watch a lot of old movies (30s-40s-50s). A ton of them have a 40s-50s man marrying a 20s woman.
No idea if that was societal norm, mens fantasy, or whatever. I have to kind of believe movie execs would want the largest audience and so if 40s-50s men dating 20s women was not appealing to women of the time they'd been losing 1/2 the market. But, maybe these particular movies were the male equivalent of romance novels which seem to be written 99% for a female audience
Some examples:
The Girl Can't Help It (1956)
South Pacific (1958)
My Fair Lady (1964)
The Far Country (1954)
Casablanca (1942)
To Have and Have Not (1944)
Charade (1963)
There are literally 100s of them and I'm not recommending any of the movies above per-say, but it does stick out to me just how common that theme is of man, at least 15yrs older than woman which I believe is less common today
I wonder how many of the male protagonists in these movies are extraordinarily
or above-average rich, successful, handsome or charming.
I daresay you won't find a George from Seinfeld in there, rather a set of George Clooneys.
I don't doubt that there was an age difference, but we have/had plenty of living couples from that era and can look in the census records - were Spring/Fall marriages that common?
Afaik career of actress was considered to be dead by the time she was 40 or so for most. Younger are more sexy, basically. Male actors could play big roles later. It is not that older women did not existed in real life. They outnumbered old men in real life.
Plus, movies always operated in fashions. What was depicted was heavily limited by big studios policies and by mandated codes. These limited topics and the way things were shown.
Movies are not reality and never were. They don't depict real life now either.
There have been men in their 20s marrying women in their 50s too (especially when inheritances have been involved) but since they wouldn't get children in that case, they would be totally invisible in these kinds of genetic statistics.
Even if average age in a relationship was symmetric, men being fertile for longer would cause age at (child's) conception to be higher for men. That effect needs to be untangled before we can know just how much men preferred younger women in the past/vice versa.
There is a simpler explanation.
Those older men are known actors/stars
who have established some influence in the industry.
That or some people might buy tickets to watch movies because it has a familiar name in leading role.
The combination of the two above might be enough to explain why the older men can still play lead roles in movies.
Well, that leads to the question, why only men were famous actors past 40, which is where the arguments becomes tautological.
Because men can have attractive roles past 40 and women not, or only very rarely. I don't remember the name of the movie, but it was about greek and a female character that was 40, but the cast was not offered to a 40 year old, but a 30 year old.
Because 40 year old women are not supposed to look like 40 year olds, which is where we are back to the fantasy thing.
Biology is a real thing, though, men can become fathers with over 50, but women cannot. So I am not judging btw. But those fantasies are real and strong, even though they are taboo nowdays.
Biased age disparity in marriage is hardly a "fantasy" or even "taboo". I suspect if you looked at e.g. the top quintile of male earners, or those who married more than once, you're liable to see an even more pronounced gap over the aggregate median. Equally as interesting, how do wealthy divorced/widowed women marry afterwards?
Poking at US presidents that stood out (i.e. more than 5 years):
This shortlist includes the two oldest (Biden, Trump) and youngest (Kennedy) presidents voted into office. A relevant quote attributed to Jacqueline Kennedy[1], whose second marriage was to a businessman 23 years her senior:
> The first time you marry for love, the second for money, and the third for companionship.
Well yes, there is this image, that the successful older men, has a younger wife (and even younger affairs). But the average men has not. Hence serving the "fantasy" of the target audience.
But as far as I observe, this is frowned upon today. It still exists of course, many of the hollywood heros regulary change their 20 year old models for partner, but there is increasing criticism about it. I mean, my partner is 7 years younger and even this was met with criticism.
Criticism from whom? If it's your friends, get better friends. Other than that, it might be family - which is easily explained as jealousy (any success at all tends to get that response). Am I missing some hypothetical case where someone criticises you about the age of your partner and their opinion somehow matters?
> Well, that leads to the question, why only men were famous actors past 40, which is where the arguments becomes tautological.
It was well known that Hollywood had an age discrimination problem for women up until the mid or late 80s or so.
Like a really well known problem where women couldn’t get leading roles after a certain age. It was a well publicized thing and just kind of common knowledge.
Why would you want a 20 year old wife at age 50. The maturity gap would be almost unbridgeable. The only benefits are sexual and even then the maturity aspect might play a part. Even in my late 20s, the idea of someone who has just left their teens would be deal breaker
If a man at 50 wants to marry, it is usually because he wants kids, otherwise there is no reason to get married at that age. If he wants kids, the woman must be in the fertility age, which is 15 to 35, with the best bet in the 20-30 interval. Just biology. Yes, the maturity gap is big, but if that is the price to pay to have kids ...
As they say, if you have dirty thoughts about 14 year old girl, and want do get rid of them, just spend some time with a 14 year old girl.
Same thing with 50 year old men with 20 year old wives. I am in my early 40s and there is no way I will marry woman in her early 20s, unless she is very special. Sure, 20 year old bodies are attractive, but maturity difference is too great. The movies are fantasies, showing off women at the age of peak physical attractiveness, with just enough immaturity to make the man feel more responsible by contrast, but without any of the quirks of actual immaturity.
Having a 20 year old sex partner is another story. And many women are willing to let you live your fantasy, for a time, for a price...
Those are all before birth control and before the maturation of fields like sports, entertainment and computers where young men could command as much money and influence as old industrialists. That probably shifted cultural ideals.
Also those movies are from the days where only a handful of movies were made every year, so the lack of competition meant you could write anything and jam it down people's throats, rather than needing to follow demand.
You know this hasn't stopped, ie Tom Cruise is 60 and you won't see him having female partners above 40, that look like 30. Sure he doesn't look his age, be it genes, good lifestyle, laser treatments etc. but he always looks much older than his partners.
It happens in real life too - successful older men being with much younger females is normalized by society and a common sight. The opposite not so much though.
Top Gun: Maverick came out last year, and features Jennifer Connolly (52) as his love interest. That’s still an age gap, but she certainly isn’t under 40.
women in their 20's wanting someone close to their age is a recent phenomena and only in the western world. Go to Africa, Asia, South Smerica or even eastern Europe and wonen in their late teens to early 20's will regularly express an interest in guys in their 30's or 40's.
tldr: America is a woman's dating market but the odds are better stacked for men once you leave the country.
If a woman bears many children throughout her life, you can still have a situation where the first pregnancy occurs much earlier than today's average yet the overall conception average is roughly same as nowadays.
These numbers also reflect the children that survived.
If men were begetting from a young age 100k years ago, and most of their children died until they were older and more experienced, those early children are lost from the DNA record.
According to the book Sapiens it depended on resources, but women often breast fed for 4 or 5 years partly as a way to spread out and reduce number of children. The need for lots of children was a consequence of farming and industrialisation and exponential growth.
If you can survive to menopause.
The average of 24+ years old appears way too high, as it was common in the old extant cultures to bear from age 14 or even less.
In the past the age of female fertility was higher than today, mostly due to nutrition. Age of 14 was more of an exception than a rule, it used to be 16 or more. Also even 24 is a right average for 14 and 34, most women even today can have children at 34.
Breastfeeding works as a natural contraceptive, so I highly doubt it - babies would need to be on solid foods without breastfeeding, and that was much harder in the past then it is now.
It's weird—the link in the article body goes to some sketchy IP address, but the "More information" section after the article has what looks to be the real link: https://www.science.org/doi/10.1126/sciadv.abm7047
It is indeed an unusual assertion, but it does bring up some interesting ideas - it seems obvious that the speed of evolutionary change in species is highest whenever the environment changes (especially after various great extinction events associated with drastic change) but in any particular place would settle up in some local optimum (or Nash equilibrium between the related species) after some time of no significant change, so in some way one might say that the evolution is "completed" at that point.
Of course, even for this definition human evolution is absolutely not "completed" at the moment, since however fit/adapted homo sapiens were to the conditions of Africa 200 000 years ago, the last few thousand years have seen enormous changes in our environment to which we definitely haven't adapted yet in the insignificantly small span of 100 or so generations; If the major changes in our social and physical environment would stop today, perhaps we might reach some evolutionary "stable spot" in a 100 000 years (or much more), but right now we haven't even fully adapted to agriculture, much less modern conditions.
Yes, the relatively novel adaptation to process lactose is a great example of an adaptation to agriculture and animal husbandry that started to happen but didn't even yet have the time to properly spread out until the environment changed again so much to make it not as relevant due to wide and easy availability of all kinds of arbitrary dietary choices. We could consider our "evolutionary adaption to modern agriculture" to be completed only after probably hundreds of such and larger effects have had enough time to both occur as a mutation and either spread across all the population or stabilizing to some equilibrium state.
Not parent commenter, but what can be argued is that evolutions “rules” are way different to us then to any other animal (except the ones we closely handle ourselves). E.g. healing people, far smaller infant death rates, no basically no food scarcity from natural causes, etc. Our selection process is societal, not “natural”.
But the point is, evolution is not a “thing”, it is an observation explained by selection pressures, an emergent property if you will. The characteristics/statistics for people are way different than any other wild animal, so I think it is fair to attribute that to society vs nature.
Is our weak culled by predators, or are we pressured towards some change (e.g. more efficient digestive track) due to food scarcity?
Those would be some natural selection processes, and they don’t apply to us in any significant way since.. I would say the agricultural revolution at least, but maybe even sooner (the very reason we can “feed” such a hungry organ as our brains is due to our efficiency at hunting/processing food even back then thanks to tools/fire)
Anything that has some effect on the number of children one has, and their probability to survive until they can have their own children, would be a natural selection process. Nobody actually has to die, or even to remain childless.
I don't know if any science that takes this as a tenet. In fact, since our population is growing so much, it's likely that the rate of human evolution has accelerated quite a bit.
I guess it was derived from the old (or layman?) definition of evolution as survival of the fittest as in human society the unfit survive with the help of medicine, technology and charity.
I was watching some random show where they were talking about the reproduction rates in the former Soviet Union and large events (like world wars) have lasting effects on birth rates that echo through time approximately every twenty years.
The perennial older male age is because men are fertile longer than women so statistics would tend to this pattern over a large enough population.
There's power asymmetry, people are monsters and sexual predation is rampant but there's also biological feasibility at play here.
To demonstrate, let's say that we have an imaginary equalityville where for every age pairing and sex act, there is an exactly equal one with the ages swapped - as in mathematically perfect equality.
In equalityville occasionally 45 year old men sleep with 35 year old woman. But every time, a 45 year old woman sleeps with a 35 year old man, coincidentally, at the exact same time, doing equal things, in another part of town.
However, 45 year old woman give birth rarely. Let's say it's 1/99th the rate of the 35 year olds.
So there's
1000 45 year old women with 35 year old men resulting in 10 births
1000 45 year old men with 35 year old women resulting in 990 births
Now we're going to calculate the average age based on the babies.
Women (990 * 35 + 10 * 45)/1000 = 35.1
Men (990 * 45 + 10 * 35)/1000 = 44.9
And thus we get our paradox because we're counting by live births. So long as there are age delta pairings past some set of constraints, the male average will drift upward.
It'd be interesting to normalize for that. This is probably doable since actual fertility statistics are well studied.
Older men have had time to climb the social ladder and amass resources and status, a corollary for power. These equal higher odds of survival for offspring.
Younger women are more fertile.
There's nothing more to it than that. This dynamic has existed for so long it's part of our DNA now via sexual selection.
That assumes nuclear families raising children under capitalism - that's a culturally specific western view of the past maybe 200 years. There's many other modalities over the entire globe and 250,000 years. The premise and the conclusion of your statement is unsupported unless you can demonstrate those assumptions consistently holding in most societies over a quarter million years.
Now you're assuming there's a social hierarchy where someone can exercise sexual indiscretion as some kind of reward and where the social customs encourage such a behavior, which also must be demonstrated. Again, if we aren't talking about hard biology like menopause, puberty, fertility and stillbirth rates, things get dicey. Things can dip into eisegesis quickly.
One were women were treated as sexual resources to be taken and controlled
Another with more free will.
In both cases, sexual selection would lead the offspring of those that aligned with the dominant male and his group, through free will or coercion, to have greater survival odds due to the dominant male's ability to control or capture resources, or fend off danger.
If you're aware that a majority of stone-age societies practiced communism without hierarchies for several tens of thousands of years to offset this sexual selection, I'd be interested to hear about that period of history.
Regardless what you think of the text, even the most stubborn critics agree the classical claims lack critical support.
You don't have to assume communism. A world requiring lots of labor to do basic things with lots of diseases and death being common is alien to us. I don't realistically need to worry about wild animals, water access, food availability, or succumbing to unfortunate weather.
DNA studies show that human population may have been as low as 2,000, on the brink of extinction 70,000 years ago.
This time period is so vast we're talking neanderthals and a bunch of other hominids.
It's a wildly different structure. There was lots of diversity. I assumed no social structure in my claims and showed that regardless of social structure, that pattern would arise as an artefact of the biology of childbirth.
If you can demonstrate the delta is larger than biologically expected, then you have something to back structural claims. But that's you know, actual academic work that would take a month or twenty. We aren't going to resolve that here. The childbirth argument was the easy one.
Those metrics are culturally specific and the dataset of okcupid is limited to people who go on okcupid and volunteer answers to such questions. It's a classic case of participation bias: https://en.wikipedia.org/wiki/Participation_bias (see "Alf Landon wins in a landslide" for the famous example).
The takeaway here is that straight single middle aged men who chase after woman, are on ok cupid looking for them, and who fill out this survey, are on average, looking for younger women.
Those results cannot be seen as representative of the general population based on the methodology used here.
It gets worse. Similar to the Alf Landon flaw, this could simply be exposing the demographic makeup of the site. Perhaps men think there's a promise on okcupid of younger women so it self-selects for those proclivities. Perhaps women think there's a different promise so they come accordingly.
You have to extricate that. Otherwise, it'd be like going to a gay dating site, running a survey and then come out with some earth-shattering ground-breaking claim of 100% of men saying they prefer intimacy with other men. I mean, duh, look who you're asking.
That's not to say these results don't hold generally, they might. But this is not evidence supporting that.
Where's the paradox? Live births drive evolution afterall. Wouldn't such a massive survival difference start to show up in mate age preferences getting "coded" into our genes?
Amazing that, just a century after Einstein, modern science has progressed to the point of not only having developed time travel, but also the means to get a not-yet-blastocyst to reliably communicate “you’re about nine months early, genius” in untold numbers of dead and/or dying languages.
Somewhat grim, but this has to be disregarding the humans who never reach the reproductive age or the ones who cannot keep their offspring alive. So there is some survivorship bias baked into the methodology.
It frustrates me that people on HN, an intelligent crowd, draw conclusions without a serious basis. Why not ask,
'Is this study disregarding the humans who never reach the reproductive age or the ones who cannot keep their offspring alive?Is there is some survivorship bias baked into the methodology?'
You might find out - we might find out - rather than you guess wrong, never find out, and we all carry the error with us.
As I understand it, what the OP is saying is not something any study could ever control for without perfectly preserved DNA from a statistically significant sample of DNA from human populations going back to old generations. Any study that uses DNA collected from modern humans will weed out the DNA of humans whose descendants are not living today. Hence survivorship bias.
The problem is turning your 2 minute analysis into a conclusion instead of an informed question. The Internet is filled with such conclusions; another adds nothing.
>>The Internet is filled with such conclusions; another adds nothing.
reply
Problem is, the internet is also filled with studies that prove or disprove anything you want, best to be skeptical.
I personally don't put much credence into any studies that seriously thinks they can make any factual accurate statements about things that may or may not have happened 250,000 years ago. Science is never settled.
The study seems to look exclusively at the outcome in the contemporary gene pool. And not at archeological DNA samples, because then the x axis would be in years not in generations. There's nothing to compensate for or disregard, the study simply does not claim to describe anything it cannot (very indirectly) see.
If anything, more intelligent people might be more suspectible to these kind of errors -- assuming their intelligence applies and extends to fields they have little knowledge of. And also just enjoy intellectual speculation as such.
From the comments, it is pretty clear to me that people lack understanding of biology/modern computational genomics, and the models used and their limitations.
"Average age of people who gave birth include people who never give birth?" or "Is a selection bias to include only people who gave birth in the selection of people who gave birth" sound completely different if asked this way, right?
If I understand the method correctly, they are actually determining the age that the sample's parents generated dna material that went on to create them.
So everyone who has a parent is included - which is everyone who ever lived.
They can't possibly be working with genomes spanning the past 250k years--- the oldest known human remains are only estimated to be ~230k years old, and I doubt they have parent/child trios nicely spanning the intervening few hundred thousand years. So they have to be working on mutation rate inferences.
From a non-expert reading of the article, their pipeline is more like: modern human population genomes -> estimates of modern mutations' ages -> estimate of average historical parental ages.
The first estimation (genome -> mutation ages) was carried out in a prior study "GEVA" [1], and this paper's contribution seems to be estimating the average parental ages based on those previously estimated historical mutation rates.
I couldn't find any mention of using old DNA samples. The GEVA study pulls from two genome databases, TGP [2] and SGDP [3], both of which seem to be entirely modern genomes. I'm not an expert in the field, so maybe it's obvious to a population geneticist that these databases do include old genomes.
Given that they're only using modern (surviving) genomes, the critique of survivorship bias seems valid.
> Furthermore, fathers were consistently older, at 30.7 years on average, than mothers, at 23.2 years on average, but the age gap has shrunk in the past 5,000 years
If 10 generations == 250 years, that sounds very debatable to me. Looking at e.g. Joseon-era Korea, did it really become a different civilization between 1500 and 1750?
With "conceive" (when used as a transitive verb), the subject is the parent(s) and the object is the child. There's potential for confusion because of some ambiguity but the only reading that makes sense in the context is the one intended by the author. IMO the grammar is not bad.
To my understanding, if one mother birthed 3 children at ages 15, 20, and 25, then her age of conception would be 20. So it could be the case that women did become mothers in their teens if they also continued bearing children into their late 20s.
And if they got more successful at bringing those children to adulthood with each try (a pattern frequently seen in animals), the visible average resulting from that 15, 20, 25 example would even be higher than 20.
I know that's a common conception about the past, but what's the actual evidence for it?
There are plenty of social and religious norms even today that keep people from getting together too young.
There's also no reason not to think people at the time understood how sex and pregnancy worked. They didn't have the internet but they were as intelligent as we are today. I'm sure they could figure out how to have "fun" without always having kids.
The Bible and plenty similarly old texts refers to marriage of such young women to usually older men, but even Romeo and Juliet is about 14 years olds.
Biological fertility as a baseline only slightly modified by social norms seems to be a good guess.
And Juliet was considered way to young to marry (we don’t really know how old exactly Romeo was).
While mid-teens was acceptable age in many cultures to marry and have children by the 17th century that wasn’t really the case. e.g. the average age at first marriage for women was 24 in England in the 1600s
I just mentioned it as a much later example for early marriages, but my other example(s) wasn’t refuted.
Also, I think quite a lot can be reconstructed from even primitive drawings, let alone a whole dvd we know got popular and thus even more relevant for an age.
The only "other example(s)" I could find from you was "The Bible". I (respectfully) avoided questioning it.
I do agree with you about getting information from even primitive drawings. I think we differ in our views about the degree and type of information we can get.
I would hazard that they are accounted for. People had very many children, only some children survived, some of those reproduced again, I would also guess that the mothers who would die during pregnancy or during childbirth would encounter that at one of the earlier in life pregnancies, and no longer be contributing to the average. I could see all that together supporting the average age of 23.
Also, today at least, miscarriages are relatively elevated in very young mothers, then decrease, and then increase again. IIRC, the lowest rates of miscarriage are in the early 20 to mid 20s or something like that.
At least for other mammals like elephants, primates and lions, breeding doesn’t start with sexual maturity, at least for males.
Older, higher ranked males control the breeding rights. Males often have to either fight for status or separate from the group and create their own breeding pool.
Wouldn’t be surprised that humans do something similar in early cultures since they tend to have highly organized societies, even for females?
The linked paper doesn't obviously support the claim you're making here. Maybe I've missed something?
"The median age at menarche was 14.5 years (95% CI=14–15; Nindividuals=128; Nobservations=199), which is within the range of variation of modern populations."
Sexual maturity means that an organism as reached the capability of to reproduce.
Looked around in the literature. Apparently consensus is that paleolithic hunter-gathers had menarche earlier than agricultural groups. Around the same age as the current averages in developed countries.
Having menarche and having the capability to bring a child to term are different. Pregnancies at early age have a higher rate of miscarriage. It seems there is a question of definition of sexual maturity - for me it is the age of reliably giving birth, for you the capability of getting pregnant. I am fine with either as long as it is clear what we use.
A few points, female fertility declines steeply past 40, but males not so much, so older males could conceivably father children with other females.
Dare I say it, and this may just be not right, Genghis Khan is purportedly supposed to have fathered thousands of children it is said he had 500 or so secondary wives (citation needed).
Since average (mean) income is famously a bit pointless due to a few very rich people, wouldn’t father’s age at conception be similarly effected?
To me it reads like someone bought a cheap e.g. lux meter, realized it was highly thermally sensitive, and instead of throwing it out or making a better one, declared they could use it to sense both light levels and room temperature.