# How can a species switch from r to K - reproductive strategy in a single generation?

I ask because it seems as though humanity is in the midst of doing exactly this. Only a few decades ago, human population was growing exponentially, and it seemed destined to keep growing until hitting constraints of food supply, at which point we would devolve into resource wars and famine. But then it didn't happen -- over the last few decades, fertility rates in the developed and developing world have plummeted and the world population is expected to stabilize in the second half of this century around 10-11 billion people. Demographers list a number of reasons for this -- education and empowerment of women, urbanization, decreased child mortality and increased life expectancy, availability of safe and effective contraception, etc. The common thread is that these trends encourage people to invest more into fewer offspring. It's as though our entire species is spontaneously deciding to switch from an r-strategy of reproduction to a K-strategy.

My question is whether this is unprecedented or not. I had the impression that r or K strategy was typically a function of species, but here we have a case where humans seem to be switching between the two strategies in a single generation. Are there other species which can change their entire reproductive strategy when the population approaches its carrying capacity? If so, what kinds of environmental cues or epigenetic factors trigger the switch? How do they manifest themselves in the case of humanity's current switch?

The issue in your reasoning is to associate a $r$ or $K$ as being a property intrinsic of the species which, while not entirely wrong, is rather misleading.

The classical and simplistic model of population growth is the model of logistic growth

$$n(t+1) = n(t) + rn(t)\left(1-\frac{n(t)}{K}\right)$$

, where $n(t)$ is the population size (number of individuals in the population) at time $t$, $r$ is the growth rate and $K$ is the carrying capacity. Of course, there exist also continuous time equivalent of this discrete time recursion equation. Here is a quick and dirty R code to compute this recursion equation

r = 0.0004
K = 1e4
f = function(n) {return(n + r * n * (1-(n/K)))}

nbGenerations = 1e5
n = numeric(nbGenerations)
n[1] = 1
for (t in 2:nbGenerations)
{
n[t] = f(n[t-1])
}

plot(y=n,x=1:nbGenerations)


If you want to compute such function fast you can look for the general solution of the recursion equation (it is a good exercice if you are a little uneasy with recursion equations).

As you can see, the population grows exponentially until some point and then the growth is slower and slower until reaching the carrying capacity. If you look at this species at $t=2000$, then you will deduce that it is a r-strategy species because its growth is dictated by the parameter $r$ (the growth rate). If you look at the same species at generation $t=6000$, then you will deduce that it is a K-strategy species as the population dynamic is dictated by the parameter $K$. Yet, the species has not changed so much.

Being r or K strategic is not a intrinsic characteristic of the species as much as it is a characteristic of the species population size in a given environment.

Now, in my example I chose $r=0.0004$, just pick some greater $r$ value and you'll see that such change from being a r- to being a K- strategy species can change very quickly. Consider for example

r = 0.02 # growth rate
K = 1e10 # carrying capacity
f = function(n) {return(n + r * n * (1-(n/K)))} # recursion function

nbGenerations = 1e3    # number of generations to computer
n = numeric(nbGenerations)
n[1] = 1e7             # starting population size
for (t in 2:nbGenerations)
{
n[t] = f(n[t-1])
}

plot(y=n,x=1:nbGenerations)


You can now look for realistic estimates of $r$ and $K$ for humans (data from after the industrial revolution), plug them in this equation and see what you get! You can also try to estimate $r$ and $K$ from data (from after the industrial revolution only) of population size over time.

If you play with high values of $r$, you can get overshooting and you can even get chaotic population dynamic.

Are there other species which can change their entire reproductive strategy when the population approaches its carrying capacity?

Of course, this change in a conscious. It is not a decision of the species. It is not either so much an evolutionary process. It is just a consequence of their environment. Yes, all species follow some kind of model of population growth. The famous example of logistic population growth comes from daphnia which growth dynamic has been highly studied. Daphnia can have quite a high $r$ value (depending on the environment) and they can typically show overshooting behaviour of the carrying capacity before settling down back to the carrying capacity.

• If you enjoyed this simple models, you'll find another model of population growth with a predator in the post What prevents predator overpopulation? Commented Jun 9, 2017 at 21:35
• I see your point -- a simple logistic growth model with constant $r$ and $K$ does seem to fit human population growth pretty well after all. So I think I misstated my question. The logistic growth model doesn't say anything about birth and death rates -- just an overall growth rate. The simplest interpretation of the logistic model is that the birth rate remains constant but the death rate increases as the population approaches the carrying capacity. My question is why that doesn't seem to be the case currently with humans -- for some reason, the birth rates are changing drastically. Commented Jun 9, 2017 at 21:51
• $r$ is simply $r = b - d$, where $b$is birth rate and $d$ is death rate as measured at the carrying capacity at which the population growth is maximal (the steepest part of the graph). The realized growth rate at any time is of course simply $b - d$ at that time. Commented Jun 9, 2017 at 21:57
• Typically, individuals just fail to get enough ressource to produce or feed more youngs. That logic does not really hold for humans though. Many people have asked the question why rich humans tend to produce fewer children than poor humans. I am not sure of what the consensus is if any consensus has been reached. Commented Jun 10, 2017 at 2:18
• Okay, maybe that's a better way to frame the paradox I outlined in the first paragraph of my question: it seems that human population dynamics are essentially following a very simple logistic pattern, but not via the simple mechanism motivating the logistic model. As I pointed out, some things are known about the sociology leading to the flattening of the growth rate. But from a biological perspective, it seems very odd that humans and dahlias do the same thing for very different reasons... Commented Jun 10, 2017 at 2:55