Problem in Understanding or "reading" a formula

[CasTern]

Good evening
For my Master Thesis I am calculating the daily Volume (possible number of birds at the site on the next day) on a daily basis.
after I have done my research I have a questions regarding the formula (attached) used in this paper :
regarding my work I try to estimate the daily volume of one day to another (so here from day 1 to day 2) . I assumed to work with

V=N(1)+(N(1)-N(i-1))* Phi(i-1)
I ridiculed the summing sign because the interval of my days is only 1 and no further summation takes place.
I used the first one of examples below, but I am not sure anymore because I do not know how to translate the N(i-1) ; while phi(i-1) means the stopover persistence between day 1 and 2.


To put in Numbers in
First day number of seen Individuals= N1 =11
Second daynumber of seen Individuals = N2= 7 (is N2 the same as N(i-1)??) or the difference between i-1 so day 2 minus day 1 = -4 (?)
And Phi is the stopover persitence (the proabbility an Indiviual stayed in the locality)
So which of these formula is the right one regarding this formula?

1.) V=11+(11-7)* Phi(i-1)
2.) V=7+(7-11)* Phi(i-1)
3.) V=11+(11-(-4))*Phi(i-1)

I would be very glad if you could help me out because I have searched for a lot of possible answers and after doing my statistics my mind is kind of blank.

Greetings Dennis

 

[blamocur]

V=N(1)+(N(1)-N(i-1))* Phi(i-1)

This looks wrong. For 2 days you get $k=2$ andV=N(1)+(N(1)-N(i-1))* Phi(i-1)
$$V = n_1 + \sum_{i=2}^2 [n_i - n_{i-1}\phi_{i-1}]$$Since you have only one value of $i$ in your sum, i.e. $i=2$ you get $$V = n_1 + n_2 - n_1\phi_1$$.
Did this help ?

 

[CasTern]

Good evening Blamcour!
It helped because now I understand the issue a lot better and which N is the right one for my variables!
Thank you very much.

 

[Dr.Peterson]

I try to estimate the daily volume of one day to another (so here from day 1 to day 2) . I assumed to work with

V=N(1)+(N(1)-N(i-1))* Phi(i-1)
I ridiculed the summing sign because the interval of my days is only 1 and no further summation takes place.
I used the first one of examples below, but I am not sure anymore because I do not know how to translate the N(i-1) ; while phi(i-1) means the stopover persistence between day 1 and 2.

To put in Numbers in
First day number of seen Individuals= N1 =11
Second daynumber of seen Individuals = N2= 7 (is N2 the same as N(i-1)??) or the difference between i-1 so day 2 minus day 1 = -4 (?)
And Phi is the stopover persitence (the proabbility an Indiviual stayed in the locality)
So which of these formula is the right one regarding this formula?

1.) V=11+(11-7)* Phi(i-1)
2.) V=7+(7-11)* Phi(i-1)
3.) V=11+(11-(-4))*Phi(i-1)

You have 2 days, so k = 2 and, as you say, you are summing over only one term (i=2), making the formula

$V=n_1+[n_2-n_1\phi_1]$​

since $i=2$ and $i-1=1$.

So with your numbers, $n_1=11$ and $n_2=7$, we get $V=11+[7-11\phi_1]=18-11\phi_1$.

None of your attempts are right. Besides needing to interpret the indices correctly, your parentheses are incorrect (phi is multiplied by only one number, not the difference), and you need to specify i.