Relationship between lifespan and reproductive age?

Question

I remember reading a while ago that there is a "general rule" in biology between an animals lifespan and when they reach reproductive age.

In other words, an organism that reaches sexual maturity after a short amount of time (for example, less than a year) will have a short lifespan (for example, 2-3 years) and an animal that reaches sexual maturity after a long time (elephant, 10-12 years) will have a much longer lifespan (40-60 years in case of elephant).

Is there a special name for this "law" or "rule"? Are there any major papers/theories supporting it that also attempt to propose why (perhaps from an evolutionary perspective) this trend exists?

Some quick supplemental questions:

1.) Is there also a trend between lifespan and animal size?

2.) Is there also a trend between lifespan and base metabolic rate?

3.) Do the two aforementioned "trends" or "rules" have technical names that I could look up as well?

Answer 1

The sort of thing you're talking about would be called a Life History Invariant: a dimensionless ratio between two life history traits $A$ and $B$, such that although the traits themselves vary widely between species, the ratio $\frac{A}{B}$ is relatively constant.

Eric Charnov has written a lot about this, including a book.

One of the invariants which has been suggested is the ratio of age of maturity $\alpha$ to adult lifespan $E$. Charnov claims that it is relatively invariant within taxa, but has a different value for eg. fish vs. mammals vs. birds vs. reptiles.

From Charnov and Berrigan, "Dimensionless Numbers and Life History Evolution: Age of Maturity Versus the Adult Lifespan", Evolutionary Ecology (1990).

(If the ratio $\frac{A}{B}$ is invariant, then plotting $A$ vs. $B$ for different species on a regular graph will give you a straight line passing through the origin. The slope of the line gives you the value of the invariant.

Sometimes, in looking for an invariant researchers will instead graph the quantities on a log-log plot: they then look for whether the curve is a straight line with slope 1 (whose height gives the value of the invariant), with a good fit. This method has been criticized: the fact that some quantities are just about necessarily a fraction of other quantities (eg. you can't really lay an egg bigger than yourself), together with the fact that log-log plots "squish down" variance about the regression, opens the possibility of observing artifactual yesses. I tried to give an intuitive explanation of this criticism in a quora answer. Charnov and company have dismissed it as not applying to the invariants they found, however.)

This invariant is slightly different than the one you describe, in that they deliberately ignore pre-maturity deaths. (If infant mortality were high enough then it would be possible for average lifespan to be less than the age of maturity.) Also, they measure the ratio of pre-maturity lifespan to post-maturity lifespan $(\frac{\alpha}{E})$ instead of the the ratio of pre-maturity lifespan to total lifespan $(\frac{\alpha}{\alpha+E})$. These are just two different ways of talking about the same thing, but the former has an upper bound of 1, while the latter has no upper bound.

Finally, it's important to note that even if a quantity is relatively invariant, it can't be expected to be perfect; you have to decide how much noise you want to allow while still finding an approximate invariant interesting.

Answer 2

There certainly is a general trend of later reproductive age and longer lifespan. This is simply because the organisms need to live at least until their reproductive age to be able to reproduce. However, other than that I think there is no definitive correlation that animals normally live approximately eight times as long as their reproductive age (as your Elephant example seems to suggest). For example, many Insects such as the Mayfly only live until they reproduce and then die quickly (speaking of a "magical first time").

To your supplementary questions:

1) Similar to the above there is a general trend of larger body mass and longer lifespan. This is because a larger body requires longer to grow. Again, beyond this very basic correlation, I would be careful of trying to find rules there as you will find very different lifespans in animals of similar size. Take for example the mole (lifespan 6 years) and the naked mole-rat (31 years).

2) No there is no general correlation between body size and metabolic rate. Metabolic rates vary greatly with habitat, warm blooded/cold blooded animals etc. If you restrict yourself to a certain family of species, such as mammals, you may find a weak correlation. For example, many smaller mammals have a higher metabolic rate, because their larger surface to volume rate requires a fast metabolism to keep their body temperature up. However also here you will find many exceptions (think of hibernation).

To summarize: It is tempting to try to find "general rules" in biology. However, while you will find many trends and correlations, particularly within certain families of species, calling them a rule is dangerous as it may lead people to believe they are generally true which is usually not the case because you will find exceptions everywhere. This is also the reason why you will not find names for such "rules" in reputable scientific literature.

Answer 3

I can't find a very fine writings/documents to support this or satisfy your question.

I think, it's related somehow. Let's take a sample: (It's not super accurate but you can make a search)

 ------------------------------------------------------------
|  Creature        Lifespan              Reproductive Age    |
 ------------------------------------------------------------
  Butterfly        7 week           Until become a butterfly
     Dog        around 14 yrs            around 9 months
    Human       around 80 yrs            around 10 yrs
   Whale        around 80 yrs             around 8 yrs
  Jellyfish    can be immortal        depends on a situation

The data above is some-kind the "usual" but still it's not the 100% of proof. There are other factors that affects the lifespan and reproductive age relationships like:

• Usual/Common ability to produce no. of offspring/s --- Like whales or elephants, they can't produce a ton of offspring in one shot so their lifespan can be longer. Or those cockroaches, they have short lifespan but they can produce a ton of baby roaches in one egg.
• Environment Capability --- If one can survive longer in one place, then there's a possibility of late reproduction maturity but when a creature has less of percent of survival in one place then there's a possibility of early production of offsprings. It all depends on the environment.
• Lifestyle --- Bad habits and unhealthy foods can shorten ourlives but good habits and healthy foods can help use for longer lives.