Chapter 12 – Temporal and Spatial Dynamics of Populations
(253-255, A; 257-263, A and B; remainder, C)
Populations vary over time. Density dependant factors usually encourage population towards its carrying capacity, but equally
important are environmental conditions which can affect birth and death rates and intrinsic biological systems of a population (i.e.
some populations are inherently unstable and tend towards oscillation in their numbers).
Species can vary in their size fluctuations/cycles based on their sensitivity to environmental change (generally greater in smaller
organisms) and their lifespan. Species which are resistant o environmental change and have a long lifespan re generally relatively
stable intrinsically; species which experience a rapid overturn of the population may be less so as their numbers depend on continued
reproduction which is sensitive to the environment. Periodic cycles: when one can observe regular intervals between a population’s
highs and lows (in numbers).
Temporal variation can have an effect on age structure and affect population growth (imagine an illness wipes out all individuals in
the human population between the age of 5-25).
Despite irregularity in environmental conditions, population cycling seems to be very regular for most populations. This is reflective
of intrinsic qualities of a population. Some populations, for example, are extremely sensitive to environment fluctuations and can
oscillate wildly when such affected. Populations have an intrinsic tendency towards periodicity, much like a pendulum. One can
generally observe time delays in a population’s increases or decreases due to fluctuations in the environment or other factors. These
factors impart momentum which may cause a population to either overshoot or undershoot its carrying capacity.
Populations modeled on the logistic equation can be used to study population cycles. Time delays are especially apparent in
populations with discrete generations as birth and death are associated with breeding episodes. These populations can oscillate
between overshoots and undershoots due to the fact that they can’t continuously readjust their growth rates. One model a population’s
periodic cycles due to intrinsic growth rate by the equation: ΔN(t) = RN(t)/K[K –N(t)]; where ΔN(t) is the change in population size
from one time interval to the next; where R is the proportional increase or decrease in N per time unit; K is the carrying capacity; [K
–N(t)] serves to make R density-dependant by a factor of 1 – N(t)/K. R can be used to predict population oscillations: when R is < 1
the population approaches, but does not exceed the carrying capacity; when R is >1 but <2, it approaches and overshoots the carrying
capacity, but becomes closer with every subsequent generation (damped oscillation); when R >2, the population gets farther and
farther from the carrying capacity with every generation (may assume limit cycle, regular cycling of high and low or become chaotic
Continuous-time populations have no built-in delays as response to a changing environment, instead delays result from time which
separates reproductive episodes. This can be modeled: dN(t)/dt = rN(t)[1 – N(t – )/K]ț; where t is a response to density-influenced
birth and death rates at țtime units in the past; whether or not oscillation occurs depends on the product of rț, (intrinsic growth rate x
time units); damped oscillations are seen at a product of π/2; the population approaches the carrying capacity at 1/e; a limit cycle is
formed with the product > π/2.
Population cycling can be observed in laboratory settings. By manipulating “environment factors/fluctuations” (temperature) and with
knowledge of the intervals between reproductive episodes between generations, population cycling can be modeled and observed quite
Metapopulations are populations of individuals from the same species made up of subpopulations spread over areas. This spread is
generally due to habitat patches. These populations are governed by two processes: the growth and regulation of subpopulation
within their patch (in extreme cases, with no migration, they may operate independently; extinction is, in this instance, common) and
migration of individuals to form new subpopulations/extinction of established subpopulations. Due to their small size, such
populations are very sensitive to chance fluctuations; however, these fluctuations are buffered due to the fact that individuals can
usually move between subpopulations.
Rescue effect: the maintenance of small, dwindling subpopulations due to migration of individuals from large, productive
There exist three types of randomness that can affect populations: catastrophe, can cause extinct or low numbers due to fire, disease,
predation, etc.; environmental variability; stochastic, change is numbers due to random chance, e.g. patterns of probability dictate
that between 1 and 2 individuals will die every year; flip a to determine whether it’s one or two for each year; if there are frequent
repeats of ‘2’ the result can be devastating to small population; this random walk system can result in the extinction of a population
due to pure chance. Instances of Stochastic extinction become very rare with larger populations or density-dependant changes in birth