Reproduction Issue: Polynomial or Exponential?

In summary, the conversation discusses a scenario where there is a parameter n and a exponentially large universe of organisms, with a given subset that is polynomially large. The organisms can only perform one action, which is to join with another compatible organism to create a new one. Each organism is compatible with a polynomial number of other organisms. The question at hand is whether the given organisms, when allowed to reproduce, can result in an exponentially large number of organisms. The discussion also touches on the concepts of exponential growth, polynomial growth, and time flowing independently of n. Ultimately, it is concluded that the subset of organisms can indeed end up with an exponentially large number, even if the total population remains fixed.
  • #1
twoflower
368
0
Hello,

let's have this scenario. We have a parameter n and a exponentially large (in n) universe of organisms. We are given a subset of this universe, which is only polynomially large. The only action which the organisms are able to do is that two compatible organisms join together and a new organism is created (the two original organisms remain there as well). The fact is that each organism is compatible with polynomially many other organisms from the universe and this polynom is the same for all the organisms.

The question is: if we let the given organisms reproduce as long as they are able to, may it happen that we end up with exponentially many organisms?
 
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  • #2
What do you mean by "exponentially large in n", "polynomially large", and "compatible"?
 
  • #3
  • #4
twoflower said:
The question is: if we let the given organisms reproduce as long as they are able to, may it happen that we end up with exponentially many organisms?

You need to re-think your question. Does time flow independently of n?
 
  • #5
Dragonfall said:
You need to re-think your question. Does time flow independently of n?

As I'm thinking about it again, now it seems clear to me that yes, we can end up with exponentially many organisms. I'm not sure what you mean for time to flow "independently of n", but we can imagine that time "happens" in discrete moments and only one thing can happen in each moment: two organisms join together and a new one emerge.
 
  • #6
"Time flows independently of n" means that the total population does not grow. This is as opposed to the total population growing wrt time. If the total population grows exponentially wrt time, then the subpopulation will never catch up.
 
  • #7
Dragonfall said:
"Time flows independently of n" means that the total population does not grow. This is as opposed to the total population growing wrt time. If the total population grows exponentially wrt time, then the subpopulation will never catch up.

I see. The universe (total population) is fixed and of the same size the whole time. It's only the subset which is growing.
 
  • #8
If the total population is fixed, then you can't talk about "exponential growth". And it's obvious that in this case, even if 1 new specimen appears every 500 years, eventually the subpopulation will eclipse the total population.
 
  • #9
Dragonfall said:
If the total population is fixed, then you can't talk about "exponential growth".

Why not? I can, indeed, end up with exponentially many organisms (exponentially many in n) - that was my concern.

Dragonfall said:
And it's obvious that in this case, even if 1 new specimen appears every 500 years, eventually the subpopulation will eclipse the total population.

Is it really so obvious even if we take into account the limitation that each organism can reproduce only with polynomial (in n) amount of other organisms?
 
  • #10
twoflower said:
Is it really so obvious even if we take into account the limitation that each organism can reproduce only with polynomial (in n) amount of other organisms?

Since the original organisms remain, all you need is for tow to find each other... right?
 

1. What is the difference between a polynomial and an exponential reproduction issue?

A polynomial reproduction issue is one in which the population growth rate is determined by a polynomial function, where the population changes by a constant amount over a given time period. An exponential reproduction issue is one in which the population growth rate is determined by an exponential function, where the population changes by a constant percentage over a given time period.

2. Which type of reproduction issue is more common in nature?

This can vary depending on the specific species and environmental conditions. However, in general, exponential reproduction issues are more common in nature as they allow for faster population growth and can lead to larger populations in a shorter amount of time.

3. How do scientists predict the growth of a population with a polynomial or exponential reproduction issue?

To predict the growth of a population with a polynomial reproduction issue, scientists may use mathematical models such as the logistic growth model. To predict the growth of a population with an exponential reproduction issue, scientists may use the exponential growth model.

4. Can a population experience both polynomial and exponential reproduction issues?

Yes, a population can experience both polynomial and exponential reproduction issues at different points in time. For example, a population may experience exponential growth when resources are abundant, but then switch to polynomial growth when resources become limited.

5. How do reproductive strategies impact the type of reproduction issue a species may experience?

A species' reproductive strategy, such as the number of offspring produced or the frequency of reproduction, can have a significant impact on the type of reproduction issue it experiences. Species with a high reproductive rate, such as many insects, are more likely to experience exponential growth, while species with a lower reproductive rate, such as elephants, are more likely to experience polynomial growth.

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