Population Ecology

Population Ecology (part 1) What causes populations to grow or decline? I. Demographic Rates II. Models of Population Growth III. Density Dependence 100 Population IV. Population Regulation K 80 60 40 20 0 0 20 40 60 80 100 Time I. Demographic Rates: II. Models of Population Growth • Births • Immigration • Deaths • Emigration Gains (+) -- movement into a population • discrete growth -- demographic events occur in discrete units of time (no overlap of generations) Losses (-) -- movement out of a population • continuous growth -- demographic events occur continuously - expressed as rates per individual (per capita) ⇒ the balance of these 4 rates determines whether a population will grow, shrink, or stay the same II. Models of Population Growth - most organisms don t fit either type perfectly (e.g., seasonal reproduction in long-lived species) Discrete model: N t = N 0R 0t Exponential Growth -- growth in an unlimited environment • unrealistic, but a good starting point N0 = initial population size Nt = population size at time t Discrete model: N t = N 0R 0t R0 = Net Reproductive Rate : # of offspring produced per individual alive at time 0 • includes probability of dying before reproducing Continuous model: Nt = N0ert 1 Discrete model: Nt = N0ert 80 Population In continuously growing population, growth is given by: 60 dN/dt = rN 40 where: 20 0 R0 = 1 -- population stays same size dN/dt = instantaneous change in population size 0 R0 > 1 -- population grows 20 40 60 Time 80 100 N = population size (# of individuals) r = b - d: the intrinsic rate of increase or the instantaneous per capita rate of population growth Assumptions: R0 < 1 -- population shrinks • no overlap of generations b = instantaneous per capita birth rate • constant environment Continuous model: • all individuals identical d = instantaneous per capita death rate • immigration = emigration e = base of natural logarithm (2.72) But what about reality? 100 Nt = N0ert 100 Population 80 80 60 no population grows without hitting some limit 40 20 0 Population N t = N 0R 0 Continuous model: 100 t 60 40 20 0 20 r = 0 -- population stays same size 40 60 Time 80 100 0 0 20 40 60 Time 80 100 r > 0 -- population grows r < 0 -- population shrinks Assumptions: • constant environment • all individuals identical • immigration = emigration Exponential Growth -- why is growth unlimited? III. Density Dependence The assumption of these models is that the per capita growth rate (r) is unrelated to population size (N). This means: Limited Growth Assumptions: 1) Birth rates are unaffected by population size, and 2) Death rates are unaffected by population size 1) Resources become limited as populations increase Per capita growth rate (r) Population (N) Resources Birth rate (b) r=b-d 2) Thus, per capita rate of growth must decrease with increasing population Death rate (d) Per capita growth rate (r) Does this make sense? Population (N) Population (N) Population (N) Population (N) 2 Limited Resources Per capita growth rate (r) Limited Growth – caused by changes to birth and death rates that are density dependent 1. Food 2. Space Population (N) 3. Shelter b, birth rate d, death rate Rate 4. Others? Population (N) Logistic Growth Model – limited growth Limited Growth – caused by changes to birth and death rates that are density dependent 100 K = carrying capacity; upper limit to population size; equilibrium density K 80 Per capita growth rate (r) Population 60 40 0 Population (N) 0 20 40 60 80 100 Time Assumptions: • K is constant In this model, r never changes, but in nature, that is exactly what happens: birth or death rates change as resources become scarce • all individuals identical • immigration = emigration • no time lags r=0 0 K 20 b, birth rate d, death rate r=0 Rate dN/dt = rN (K-N) K K • relationship between r & N is linear r=0 r=0 K K Population (N) IV. Population Regulation Changes in r: ⇒ increase population density ⇒ increase speed at which population reaches K 100 80 80 60 40 0 0 20 40 60 Time 80 100 when population fluctuations are bounded so as not to increase indefinitely or decrease to extinction 60 40 20 20 Population regulation: abundance Population 100 Population Key consequence of density dependence: Changes in K: 0 0 20 40 60 Time 80 100 time time 3 abundance without regulation populations go extinct or increase to infinity Tight population regulation: return to K after perturbation time time abundance K time Ecological causes of population regulation • Intraspecific Competition • Disease/Parasitism Intraspecific Competition • resources become limited ⇒ mortality increases or birth/settlement declines • Predation Predators Disease/Parasitism • increased rates of transmission at high densities ⇒ causes density-dependent mortality • can cause competition for shelter and densitydependent mortality, or • 4 types of predatory responses cause densitydependent mortality: 1. functional response 2. aggregative response 3. developmental response 4. numerical response 4