POPULATION DYNAMICS
Reproduction leads to growth in the number of interacting, interbreeding organisms of one species in a contiguous area--these form a population. (Distinguish between unitary and modular organisms: for unitary organisms, count numbers; for modular organisms, count modules? biomass?)
Exponential growth ("biotic potential","intrinsic rate of increase") Simplest assumptions for calculation of growth of population: environment (per individual organism) remains constant: constant resources, constant dangers every individual has equal and constant reproductive probability rate of increase (reproduction) is proportional to the number of individuals dn/dt = rn dn/n = r dt log e N = rt + C N = e C e rt N = number or density of organisms t = time r = rate constant (if r large, population is fast growing) C = integration constant N = N o e rt N o = e c = number of org's at time 0 N = N o 2 t/d D = constant "doubling time" = log e 2/r
Two ways of plotting exponential growth:
For cells like bacteria, D shows cell doubling time For populations of more complex organisms, D indicates population doubling, which depends on birth and death rate, D = log2/(b-d) (and in populations where it is permitted, on immigration and emigration rates, D = log2/(b-d+i-e)) potential growth rate is the exponential curve with the highest r or lowest D: rmax or Dmin = "biotic potential"
Dmin depends on species: bacteria (E. coli) housefly elephants Dmin 20 min 1.77 day 31 years Exponential growth at these rates leads to enormous population increases in short times For E. coli, 100 doubling times (33 hrs) gives N = 2100 = 1030 (1018 g or 1012 metric tons bacteria) Rabbits in Australia 1859 24 imported 1865 20,000 killed 1895 20,000,000 killed Environmental resistance limits population growth
Environmental resistance comes in two forms: Density-independent factors": constant for all population sizes (reduce r) Usually abiotic (temperature, rainfall, daylength, O 2, salinity) Density-dependent factors": change with population size Some abiotic (space, light) Mostly biotic (parasitism, predation, mating behavior, birth control, availability of prey, competition, mutualism): less food, less mating, more emigration, disease spread, mortality through competition (also positive effects, like civilization: disease control, agriculture) dn/dt = rn (1 N/K), where K = carrying capacity of the environment
Environmental resistance limits population growth: biotic potential density-independent resistance density-dependent resistance
Fluctuations: interacting environmental resistances lead to fluctuating population sizes: Abiotic, density-independent, time-dependent harsh environmental resistances fluctuate (fire, drought, flood, winter freezes) Biotic environmental resistances with long response time, fast and active response lead to overshoot, oscillations
What really causes the hare oscillations? Overpredation? Competition? Other suggestion: hares strip willow bark, willows produce salicin (phenolglycoside), lack of winter food crashes hare population Krebs et al. (Science 25 Aug 1995): Predator exclusion, food provision both increase hare peak densities, but don!t stop oscillations Hudson et al. (Science 18 Dec 1998): Red grouse oscillations stopped by treating population to remove helminth parasites, which affect fecundity Ranta et al. (Science 13 Aug 1999) Lynx oscillations: suggest a combination of interacting predator-prey and climate oscillation (North Atlantic Oscillation)
Summary Considering only reproductive rates, populations grow exponentially Population growth rate depends on birth, death, immigration, and emigration Density-dependent factors lead to logistic growth patterns Abiotic fluctuations and biotic interactions can lead to fluctuating population densities