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
N = number or density of organisms
dN/N = r dt
t = time
logeN = rt + C
r = rate constant
(if r large, population is fast growing)
N = eC ert
C = integration constant
N = No ert
No = ec = number of org's at time 0
N = No 2t/D
D = constant "doubling time" = loge2/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, O2, 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