Lecture 3 - Density dependence Flashcards
F3 for
0 - 1 - 2 - 3
s0 s1 s2
counting babies (0 yrs) - just after reproduction
- number conditional on parent survival
F3 = survival 2-3 * fecundity age 3
s2 * m3
F3 for
1 - 2 - 3
s1 s2
counting 1 yr olds - before reproduction
- counting fledglings
F3 = s0 * m3
Leslie matrix
Fx = Sx * Mx
row x column
what is λ
pop growth rate λ = 1 births = deaths - proportion of indvs in each age class is constant
fecundity + growth + survival = λ
schedule of deaths
survival curves
schedule of births
fertility
uses of leslie matrix
- derive finite rate of pop change λ and stable age distribution
- perturbation analyses = identify main age-specific vital rates that affect abundance + age structure
- modify analyses to include density dependence
perturbation analyses
measures importance of system and components on productivity
sensitivity
how small changes affect λ when others are constant
- identify stage that contributes most to pop growth
elasticity
estimate effects of proportional change on λ
exponential growth
simplest model
idealised pop in unlimited resources environment - doesn’t exist
- few indvs, no limiting factors = pop increase in proportion to births and death rates
births during time interval - deaths
e.g. sea otters - low, reintroduced, 30 fold increase
exponential growth calculate
dN/dt = rN
N = pop size t = time dN = change in pop size dt = change in time r = B - D
density dependence = negative feedback
crowding, resource limitation affects growth
insufficient resources = less births, more deaths
- negative feedback prevents unlimited pop growth
- intraspecific
carrying capacity K
max stable pop supported over long time period
- as density increases, per capita resources decrease
when equilibrium b=d K = 0 growth rate
K (limitation) is stable equilibrium, by density dependence regulation
