Ecology Notes – Oct. 11/12
- Population dynamics are the ways in which populations change in abundance over time. Population
size changes as a result of four processes – birth, death, immigration, and emigration.
Nt+1 = Nt+B-D+I-E, where Nt is population size at time t.
- Patterns of population growth: Populations exhibit a wide range of growth patterns, including
exponential growth, logistic growth, fluctuations, and regular cycles. These four patterns are not
mutually exclusive. A single population can experience each of them at different times.
- Exponential growth: The population increases by a constant proportion at each point in time. When
conditions are favourable, a population can increase exponentially for a limited time. When a species
reaches a new area, exponential growth can occur if conditions are favourable. The population may
grow exponentially until density-dependent factors regulate its numbers. Species such as the cattle
egret colonize new regions by long-distance or jump dispersal events. Local populations then expand
by short-distance dispersal events.
- Logistic growth: These populations first increase, then fluctuate by a small amount around the
carrying capacity. Plots of real populations rarely match the logistic curve exactly. Logistic growth is
used broadly to indicate any population that increases initially, then levels off at the carrying
- For K (carrying capacity) to be constant, birth rates and death rates must be constant over time at
any given density. This rarely happens in nature. Birth and death rates do vary over time, thus we
expect carrying capacity to fluctuate. K on a graph is the point where birth and death rates intersect.
- Population fluctuations: In all populations, numbers rise and fall over time. Fluctuations can be
deviations from a growth pattern (ex. is Tasmanian sheep population) or erratic. In lake erie
phytoplankton populations, fluctuating abundance could reflect changes in environmental factors
such as nutrient supplies, temperature, or predator abundance.
- Population outbreak is when the number individuals increases rapidly. An ongoing outbreak of the
mountain pine beetle has killed hundreds of millions of trees across BC. This has altered forest
composition, and CO2 is released as the trees decay (17.6 megatons every year).
- Population cycles: Some populations have alternating periods of high and low abundance at regular
intervals. Populations of small rodents, such as lemmings and voles, typically reach a peak every 3-5
years. Different factors may drive population cycles in rodents. For collared lemmings in Greenland,
field studies and modeling indicated that the 4-year cycle is driven by predators, such as the stoat. In
other studies, predator removal had no effect on population cycles (so may be driven by food
supply). Factors driving population cycles may vary by place/species. Some population cycles may
stop if certain environmental factors change. Warmer winter temperatures affect snow conditions at
high latitudes, making it more difficult for lemmings to feed and avoid predators. Their populations
have stopped cycling every 3-4 years.
- Delayed density dependence are delays in the effect that density has on population size. Commonly,
the number of individuals born in a given time period is influenced by population densities that were
present several time periods ago. Delayed density dependence can cause populations to fluctuate in
size. Example – A predator reproduces more slowly than its prey. If predator population is small,
prey population may increase, then the predators will increase, but with a time lag. Many predators
may reduce the prey population, and then the predator population will decrease again. The logistic
equation can be modified to include time lags (τ). Depending on the values of the population growth
rate (r) and the time lag, adding delayed density dependence to the logistic equation can result in
different graphs. When rτ is small, the population exhibits logistic growth. Intermediate values of rτ
can result in fluctuations about the carrying capacity that become smaller over time (dampened oscillations). When rτ is large, the population exhibits a stable limit cycle (regular cycle of ongoing
fluctuation about the carrying capacity).
- AJ Nicholson studied density dependence in sheep blowflies using laboratory experiments. In the
first experiment, adults were given unlimited food, but larvae were restricted to 50g of liver per day.
With abundant food, females laid enormous numbers of eggs, but when the eggs hatched, most larvae
died because of lack of food. This resulted in an adult population size that fluctuated dramatically. So
when adult densities were high, few eggs survived to produce adults, leading to population
fluctuations. In the second experiment, both adults and larvae were given unlimited food. The adult
population size no longer showed repeated fluctuations.
- Population extinction: The risk of extinction increases greatly in small populations. Fluctuations in
growth rate, population size, and chance events can affect a population’s risk of extinction.
- The geometric growth equation can include random variation in the finite rate of increase (λ).
Random variation in environmental conditions can cause λ to change from year to year (good years
and bad years for growth). Computer simulations for three populations allowed λ to fluctuate at
random. Two of the populations recovered from low numbers, but one went extinct. Fluctuations
increase the risk of extinction, and the degree of fluctuation is important. The range of variation in λ
is measured by the standard deviation (ϭ). Ϭ=0.2, 0.3% of populations went extinct in 70 years.
Ϭ=0.4, 17% of populations went extinct. Ϭ=0.8, 53% of populations went extinct. When variable
environmental conditions result in large fluctuations in growth rate, the risk of extinction increases.
Small populations are at greatest risk. If the simulations are repeated using larger initial population
sizes, there are fewer extinctions. These patterns ha