Population Ecology (part 1) What causes populations to grow or decline? I. Demographic Rates II. Models of Population Growth III. Density Dependence 100 IV. Population Regulation 80 K 60 Population 40 20 0 0 20 40 60 80 100 Time I. Demographic Rates: II. Models of Population Growth • Births Gains (+) • Immigration -- movement into a population • discrete growth -- demographic events occur in discrete units of time (no overlap • Deaths Losses (-) of generations) • Emigration -- 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 - most organisms dont fit either type perfectly (e.g., population will grow, shrink, or stay the same seasonal reproduction in long-lived species) II. Models of Population Growth Discrete model: t Nt = N0R0 Exponential Growth -- growth in an unlimited environment N0 = initial population size • unrealistic, but a good starting point N = population size at time t t R = Net Reproductive Rate: # of offspring produced Discrete model: N = N R t 0 t 0 0 per individual alive at time 0 • includes probability of dying before reproducing rt Continuous model: Nt = N0e 1 Discrete model: Continuous model: 100 t rt Nt = N0R0 Nt = N0e 80 In continuously growing population, growth is given by: 60 dN/dt = rN 40 Population where: 20 dN/dt = instantaneous change in population size 0 0 20 40 60 80 100 Time N = population size (# of individuals) R0 = 1 -- population stays same size r = b - d: the intrinsic rate of increase or the R0 > 1 -- population grows Assumptions: instantaneous per capita rate of population growth R < 1 -- population shrinks 0 • no overlap of generations b = instantaneous per capita birth rate • constant environment • all individuals identical d = instantaneous per capita death rate • immigration = emigration e = base of natural logarithm (2.72) Continuous model: 100 But what about reality? rt 100 Nt = N0e 80 80 60 no population grows 60 40 without hitting some limit 40 Population 20 Population 20 0 0 20 40 60 80 100 0 Time 0 20 40 60 80 100 r = 0 -- population stays same size Time 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 Limited Growth capita growth rate (r) is unrelated to population size (N). This means: 1) Birth rates are unaffected by population size, and Assumptions: 2) Death rates are unaffected by population size 1) Resources become limited as populations increase Does this make sense? ) 2) Thus, per capita rate of growth must b decrease with increasing population ) r r = b - d Birth rate( ) r Population (N) ) d Per capita Resources growth rate( Per capita growth rate( Population (N) Population (N) Death rate( Population (N) Population (N) 2 Limited Growth – caused by changes to birth and death rates that are density dependent Limited Resources ) r 1. Food Per capita growth rate( 2. Space Population (N) b, birth rate 3. Shelter d, death rate 4. Others? Rate Population (N) Logistic Growth Model – limited growth Limited Growth – caused by changes to birth and death 100 rates that are density dependent 80 K ) r dN/dt = rN (K-N) r = 0 K 60 0 Per capita Population 40 growthrate( K K = carrying capacity; upper 20 Population (N) limit to population size; 0 b, birth rate equilibrium density 0 20 40 60 80 100 d, death rate Assumptions: Time r = 0 r = 0 r = 0 • K is constant In this model, r never changes, • all individuals identical but in nature, that is exactly what Rate • immigration = emigration happens: birth or death rates change as resources become • no time lags scarce K K K • relationship between r & N is linear Population (N) IV. Population Regulation Changes in K: Changes in r: Key consequence of density dependence: ⇒ increase population density ⇒ increase speed at which population reaches K Population regulation: when population 100 100 fluctuations are bounded so as not to increase indefinitely or decrease to extinction 80 80 60 60 Population 40 Population 40 20 20 0 0 abundance 0 20 40 60 80 100 0 20 40 60 80 100 Time Time time time 3 without regulation populations go extinct or increase to infinity Tight population regulation: return to K after perturbation K abundance time time abundance abundance time Ecological causes of population regulation Intraspecific Competition • Intraspecific Competition • resources become limited • Disease/Parasitism ⇒ mortality increases or birth/settlement declines • Predation Predators • can cause competition for shelter and density- dependent mortality, or Disease/Parasitism • 4 types of predatory responses cause density- dependent mortality: • increased rates of transmission at high densities 1. functional response ⇒ causes density-dependent mortality 2. aggregative response 3. developmental response 4. numerical response 4 .