Question

The color with the greatest survival reproduces at a rate of 5 offspring per pair per year, the next highest survival color reproduces at the rate of 4 offspring per year, then 3, 2 and 1 for the remaining phenotypes. Assume that the survival pattern continues indefinitely. Determine how many generations it would take for the population of the most stressed phenotype to drop below 5% of its original portion of the population. The five colors are Red, Turquoise, Dark blue, black, and sage green. For example lets say that sage green was the highest surviving worm phenotype. How would you even

Answer 1

Only looking for a process here.

Answer 2

what process are you even looking for though? like wow thats a lot of words.

Answer 3

Trying to see how to calculate when each of the populations would stress out and fall below their original population. So for example lets say that the original population was 203.

Answer 4

It's more a mathematical question I think tbh although this is for biology haha.
Yes I mean what generation it would take till each phenotype dies off.

Answer 5

Dw, I and my peers are extremely confuzzled rn

Answer 6

dont we need to know how many pairs of each colour are there to begin with?

Answer 7

just to clarify, nothing is dying right? only its percentage share of the population is dropping

Answer 8

you could try this:

write a differential equation to model population at any time

\[dx/dt = k \frac{x}{2}\]

x= total population
x/2= no of pairs
K= growth rate (offsprings per pair per year)

solve it

\[x_1=C_1e^{k_1 t/2}\]

Answer 9

i've added the subscript 1 to indicate that we are looking at one particular colour

Answer 10

In my investigation turquoise is the number that is stressed.
So we have an original pop of 200
and birds are practically eating the population of worms

Answer 11

wait im confused you have two equations?

Answer 12

poor poor worms

Answer 13

and things are dying, the birds are eating.

Answer 14

i'm sorry, i dont follow the bio part... are there members of the population dying? if so... at what rate?

Answer 15

well baru the thing is that our original pop is 200
but for turquoise an average of 57 are picked up by the birds. The birds are the predators so the worms gotta die.

Answer 16

:( BUT WORMY WAS MY FRIEND...lol

Answer 17

isnt this what you are doing?

Answer 18

@karatechopper this is def bio...but i dont remember how to do it

Answer 19

Lol that paper you attached is what my lab is

Answer 20

hmm.... i dont know any bio. but this looks like a differential equations problem.
i dont think you have given all the details in the question.
you need to mention what is growing and what is dying at what rate... and how many of each are there to begin with

i know only the basics of diff. equations... but if you can make the question more general, i think a lot of people here will help

Answer 21

what is d?

Answer 22

frequency dying is .42

Answer 23

solved by using hardy weinberg

Answer 24

so if its dying at .42, the pop would grow at .58 right

Answer 25

and we are trying to see when the population will fall below 10. (5% of original populaiton)

Answer 26

then it wil be an inequality.
\[x^y<10\] and x is how many die out to the power of time(y) idk this is a guess...but its an idea...its def an inequality though

Answer 27

idk 🙅🙅🙅

Answer 28

so you gotta find out the number of generations after which the population of weakest one falls below 5% of its original portion of the population
okaay
The five colors are Red, Turquoise, Dark blue, black, and sage green.
green is the best
and lets say red is the weakest

and lets say the population distribution is like this(arranged from weakest to strongest)->

green= \(e\) members
black= \(d\) members
blue= \(c\) members
turquoise = \(b\) members
red= \(a\) members



% of red in this population= \(\Large \frac{a}{a+b+c+d+e} \times 100\)
5% of this portion is-> \(\Large \frac{5a}{a+b+c+d+e}\)

now we will derive some equation for population at \(n^{th}\) generation

so if a species "s" has "x" members and each member gives "y" offsprings then total offsprings of 1st generation will be=\(x (y)\) and for second generation it will be-> \((xy)(y)\)
so in general we can write that the \(n^{th}\) generation wil have \(x (y)^n\) people

note that i have assumed that the older generation die when new generation comes
lets say that percentage of red that we want comes in \(n^{th}\) generation
so now total population after \(n{th}\) generation will be-\(e(5)^n +d(4)^n+c(3)^n+b(2)^n+a(1)^n\)

the percentage of \(red\) is-> \(\Large \frac{a}{d(4)^n+c(3)^n+b(2)^n +e(5)^n} \times 100\)

and
\(\Large \frac{a}{d(4)^n+c(3)^n+b(2)^n +e(5)^n} \times 100 < \frac{5a}{a+b+c+d+e}\)
we can find \(n\) from here
but finding n from here might get tedious depending upon the values a,b,..