140 likes | 371 Views
x = age at beginning of the time interval S x = Number of survivors at start of interval. d x = Number dying during interval l x = Proportion surviving at start of age interval = n x /n o.
E N D
x = age at beginning of the time interval Sx = Number of survivors at start of interval
dx = Number dying during interval lx = Proportion surviving at start of age interval = nx/no
px = sx = age specific survival rate (probability of surviving to the end of the period) = (nx+1)/nx; = 1- qx qx = mx = age specific mortality rate (probability of dying before the end of the period) = (nx-(nx+1)) / nx = dx/nx = 1 - px
Nx = Mean number of individuals alive during the period = (nx+nx+1)/2 Tx = sum of the time to be lived by the nx currently alive ex = age specific life expectancy
kx = Exponential mortality = ln sx sx = e-kt
lxbx = Number of female individuals born during interval x. Gross Reproductive Rate (potential number of offspring) = bx Net Reproductive Rate (average number)= Ro = lxbx = ( Fx)/no
G = cohort generation length = mean period elapsing between birth of parent and birth of offspring. G = [(lxbxx)]/[(lxbx)] = 2.1/1.2 = 1.75 = (xFx)/Fx (The time it takes) / (number produced)
Calculation of r Recall Nt = Noert; set t=G NG/No = erG = Ro r = ln(Ro)/G = ln(1.2)/1.75 = .104 r =(RolnRo)/ (lxbxx)
Reproductive value vx = [erx/lx][ (e-rxlyby)] ; where summation over range y = x → ∞