Calculate population growth rate (lambda) at each time interval using the ratio

Question

Calculate population growth rate (lambda) at each time interval using the ratio method, and then calculate the mean of Use the mean(lambda) to then calculate the value of the per capita growth rate (r)

R Studio Help:

lynx data:

a) Calculate population growth rate (lambda) at each time interval using the ratio method, and then calculate the mean of Use the mean(lambda) to then calculate the value of the per capita growth rate (r).

lambda = Nt+1/Nt, lambda for each time step, r=ln(lambda), (in this case ln(mean(lambda))

Year, Population 1931,8454 1932,11932 1933,16799 1934,22812 1935,23901 1936,19993 1937,12784 1938,10403 1939,10613 1940,8410 1942,8032 1943,10937 1944,13340 1945,10326 1946,8816 1947,7539 1948,4137 1949,4626 1950,10345 1951,8399 1952,14034 1953,12297 1955,13192 1956,11281 1957,11027 1958,14808 1959,41246 1960,43136 1961,48829 1962,55819 1963,41596 1964,28767 1965, 21614 1967,17356 1968,22958 1969,37634 1970,43925 1971,56920 1972,59068 1973,45024 1974,24782 1975,13446 1976,17699 1977,23216 1978,32470 1979,37250 1980,37966 1981,48100

Explanation / Answer

yeart <- read.csv("year.csv")
yeart["lambda"] <- NA # creating a new column lambda
yeart$lambda[1]=1 # an assumption as we do not have previous year data

a=2:48
i=1
for (i in a)
{
yeart$lambda[i]=yeart$Population[i+1]/yeart$Population[i]
i=i+1
}
yeart$lambda # this column gives the value of lambda
a= yeart$lambda[2:47] # we do not choose 48 as we do not have the nxt year data and it gives the value NA
c=sum(a)
c=c/48
c=log(c)
# c is the answer of r =ln(mean(lambda))=0.04722

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