# MATLAB question regarding demographic stochasticity

• MATLAB
• chuy52506
In summary: I haven't done this in a while.In summary, the population follows a specific equation with given parameters and the initial population. To calculate the probability that the population will be greater than or equal to 10000 in 100 time steps, we need to find the parameters for the normal distribution of p(100) using the properties of random variables. After normalizing the distribution, we can use a computer routine to find the cumulative distribution function (CDF) and calculate the probability.
chuy52506
A population follows this equation:
x(n+1)= 0 if x(n)≤2 and p(n+1) = A*x(n)-B if P(n)>2
Where A=Normal(1.1,0.2) and B=Normal(100,20)
Let the initial population x(0)=1000

So far i created this mfile:
xlist = [];
x0=1000;
x=x0; xlist=x; N=100;
for n=1:N
R = 1.1+.2*rand(1); a = 100+20*rand(1);
x = R*x-a;
xlist = [xlist,x];
end
plot(0:N,xlist)

I ran it for 100 time steps

The question is,
What is the probability that x(100)≥10000?
I have no idea how to calculate the probability of this using matlab, any ideas?

chuy52506 said:
A population follows this equation:
x(n+1)= 0 if x(n)≤2 and p(n+1) = A*x(n)-B if P(n)>2
Where A=Normal(1.1,0.2) and B=Normal(100,20)
Let the initial population x(0)=1000

So far i created this mfile:
xlist = [];
x0=1000;
x=x0; xlist=x; N=100;
for n=1:N
R = 1.1+.2*rand(1); a = 100+20*rand(1);
x = R*x-a;
xlist = [xlist,x];
end
plot(0:N,xlist)

I ran it for 100 time steps

The question is,
What is the probability that x(100)≥10000?
I have no idea how to calculate the probability of this using matlab, any ideas?

Hey chuy52506.

The key thing to take note of is p(100).

What you will have to do is find the parameters of the normal distribution for p(100). Just in case you are wondering it has to be normal since a normal + another normal = a normal.

So basically if we want to get the parameters: we use the properties of Random Variables:

E[aX+bY] = aE[X] + bE[Y]
VAR(aX + bY) = a^2Var(X) + b^2VAR(Y)

E[Ax(n)] = 1.1x(n)
VAR(Ax(n)) = [x(n)]^2 x 0.2

E = 100, Var(B) = 20

By adding the means and variances we get our p(n) variable being:

p(n) = Normal [ 1.1x(n) - 100, [x(n)]^2 x 0.2 + 20 ]

Now you normalize the distribution and use a computer routine to find the CDF corresponding to p(n >= 10000) = 1 - p(n < 10000).

Also make sure you double check my work just in case.

## 1. What is demographic stochasticity in MATLAB?

Demographic stochasticity in MATLAB refers to the randomness or uncertainty in population dynamics caused by fluctuations in birth and death rates. It is an important concept in population ecology and is often studied using mathematical models in MATLAB.

## 2. How is demographic stochasticity incorporated in MATLAB models?

Demographic stochasticity can be incorporated in MATLAB models by using random number generators to simulate fluctuations in birth and death rates, or by adding stochastic terms to the equations that describe population dynamics. This allows for the modeling of realistic and unpredictable population changes over time.

## 3. What are the advantages of using MATLAB for studying demographic stochasticity?

MATLAB is a powerful and versatile tool for modeling and analyzing complex systems, such as population dynamics. It allows for the incorporation of demographic stochasticity in models, making them more realistic and applicable to real-world scenarios. Additionally, MATLAB has a user-friendly interface and a wide range of built-in functions and tools that make it easier to analyze and interpret data.

## 4. Can MATLAB be used to study demographic stochasticity in different species?

Yes, MATLAB can be used to study demographic stochasticity in various species. The principles and methods of incorporating demographic stochasticity in models are similar across different species, and MATLAB allows for the flexibility to adjust and customize models for specific species or populations.

## 5. How can demographic stochasticity be accounted for in data analysis using MATLAB?

To account for demographic stochasticity in data analysis using MATLAB, statistical methods such as Monte Carlo simulations or bootstrapping can be used to incorporate randomness in the data. This allows for a more accurate analysis and interpretation of results, especially when dealing with small or fluctuating population sizes.

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