Question

By mid 1900s black footed ferrets had declined to virutal extinction because their primary prey (prairie dogs > 95% of the diet of these ferrets) has disappeared (due to disease and hunting). Starting >30 years ago, the ferrets were reintroduced to a series of sites int he nrothern US where prairie dog populations were restored to natural levels. Betty Biologist is assigned the task of understanding population dynamics at several of the reintroduction sites. Below is a summary of the sites of reintroduction she is monitoring -- they include two "new ferret reintroduction sites" just about 10 years old (where prairie dogs are now hyperabundant ) and two "old ferret reintroduction sites" where prairie dog populations are at much lower densities (approximating historical abundances).

Betty conducts a snapshot census in one of her sites. She finds the following information: there are 500 new females in the cohort, 200 1 year old individuals, 150 2 year old individuals, 100 3 year old individuals, 50 4 year old individuals and no individuals older than 4. What survival profile do ferrets in this site have? She also learns that ferrets can't reproduce in their first year of life, but otherwise at this site have constant birth rates (consistent with the average rates she found in literature, described above).

A. Calculate gross and net reproductive rates and explain the difference in words

B. If the total population in plot B is now 1000 ferrets, how many ferrets would you expect in the old site in 10 years? Why?

Answer 1

Age class	Number in age class	Survivorship from birth	Age-specific survival	Fecundity
x	Nx	lx	Sx	mx	lxmx	xlxmx	?xlxmx / ?lxmx
0	500	1.00 (500/500)	0.4 (200/500)	0	0	0
1	200	0.40 (200/500)	0.75 (150/200)	2	0.8	0.8
2	150	0.30 (150/500)	0.66 (100/150)	3	0.9	1.8
3	100	0.20 (100/500)	0.5 (50/100)	1	0.2	0.6
4	50	0.10 (50/500)	0 (0/50)	0	0	0
		sum		6	1.9	3.2	1.684(3.2/1.9)
				GRR	R0		T

Survivorship from birth to age-class x, is denoted lx. (l for life)
lx = Nx/N0 (N for number)
here, N0 = 500

Age-specific survival is denoted sx. (s for survival)
sx = N_x+1/Nx (= l_x+1/lx) lx decreases continually through age classes.

Fecundity

mx is usually measured as female offspring per female of age x (m for maternity).

mx = 1/2 number of offspring born to parent of age x

Gross reproductive rate = ?mx

Net reproductive rate, R0 = ? lxmx.

generation time, T = ?xlxmx / ?lxmx

Gross reproductive rate: 6

(number of females produced per female without considering the survival rate of immature stages) Total lifetime reproduction in the absence of mortality. This is the average lifetime reproduction of an individual that lives to senescence, useful in considering potential population growth if all ecological limits were removed for a population. GRR is rarely if ever attained in nature, but useful to consider how far below this a population is held by ecological limits.

Net reproductive rate: 1.9

(number of females produced per female during its life) Average number of offspring produced by an individual in its lifetime, taking normal mortality into account.