he population of Japanese sika deer in central Japan was determined each year from 2005 to 2014. The sika deer population underwent logistic growth starting at 26,000 deer in 2005 and stabilized at 58,000 deer between 2012 and 2014. Based on these data, the rmax for this population was determined to be 0.57. Central Japan contains a variety of habitats, including forests and grasslands. Sika deer benefit from the resources in grasslands more than forests; if deforestation occurred, producing more grasslands in the region, the carrying capacity for sika deer population would increase. What would the population size of sika deer be one year after the carrying capacity increased to 70,000 as a result of deforestation

The population would grow to 63,667 deer in a year, and the growth rate would decrease the following year.

Explanation:

Sika deer population : starting at 26000 in 2005

                                     stabilized at 58000 between 2012 and 2014

                                      rmax = 0.57

The population size of Sika deer be one year after the carrying capacity increased to 70000 as a result of deforestation

carrying capacity (k) = 70000

population size ( N ) = 58000

max growth(rmax) = 0.57

To determine the growth

dN/dt = rmax N [ (K-N) / K ]   (1)

insert the given value into the formula above

dN / dt = 0.57 * 58000 [ 12000 / 70000 ]

           = 33060 [12000 / 70000 ]

           = 5667

The increase in population = 5667 + 58000 = 63667