14.2: Measuring and Modeling Population Change p. 660
Definitions:
Carrying Capacity: the maximum number of organisms that can be
sustained by available resources over a given period of time.
Population dynamics: are changes in population characteristics determined
by natality mortality, immigration, and emigration.
Fecundity: is the potential for a species to produce large numbers of
offspring in one lifetime.
Geometric Growth
The Carrying Capacity of an ecosystem is the maximum number of
organisms that can be sustained by available resources over a limited period
of time. The carrying capacity is said to be dynamic, because it can change
over time, and is dependent on environmental changes, which are
continuous. The variations in the environment; maybe abiotic or biotic
factors.
When populations increase in size, then the resources available to them
would decrease in availability. As population density increases the
availability of resources decrease and competition for resources increases,
due to the ecosystems carrying capacity.
Factors That Affect Population Growth
Population size may increase or decrease, depending on the number of
Births or Deaths within the population.
Population size may also change based on Migration. Immigration occurs
when more individuals move into a particular habitat and emigrations occurs
when they move out of the habitat. Changes in population characteristics, is
known as, Population Dynamics.
The main natural determinants, measure per unit time, are Natality (the
number of births) and mortality (the number of deaths), immigration (the
number of individuals that move into an existing population), and emigration
(the number of individuals that move away from a population).
Fecundity: the potential for a species to produce offspring in one lifetime.
The potential to produce a large number of offspring in their lifetimes,
express a high fecundity. Females that live longer, have the potential to
complete more reproductive cycles, increase in fecundity, but produce fewer
offspring per cycle.
There are 3 recognizable patterns of survivorship.
Type I: has a very low mortality rate until the females are beyond their
reproductive years, but produce a relatively small number of offspring.
Type III: has a very high mortality rate when they are young, and they often
produce a large number of offspring.
Type II: species are intermediate between these forms and tend to show a
uniform risk of mortality throughout their life.
Figure 3: The survivorship curves (red) of many organisms, such as; (a) the Dall
mountain sheep, (b) the five-lined skink, and (c) the perennial dessert shrub, roughly
match one of three idealized patterns (blue).
Calculating Changes in Population Size
The population growth of any given population is calculated mathematically
using the following formula:
Population Change = [(births + immigration) – (deaths + emigration)]
Initial population size (n)
x 100
The solution is expressed on a percentage (%).
Biologists use this formula to determine population size changes over time.
Open Population: a population in which change in number and density is
determined by births, deaths, immigration, and emigration.
Closed Population: is a population in which change in size and density is
determined by natality and mortality alone.
Biotic Potential
The maximum rate a population can increase under ideal conditions.
For any organism the maximum reproductive rate that could be achieved
under ideal conditions.
Population Growth Curves (Geometric Growth)
Geometric Growth: is a pattern of population growth where organisms
reproduce at fixed intervals at a constant rate.
When birth rates and death rates per individual remain constant, populations
grow at a fixed rate in a fixed time intervals. Population growth is expressed
in a growth per unit time. (ratio or percent)
Usually there are specific breeding seasons for some species, yet deaths can
occur throughout the year. In such cases, the population typically grows
rapidly during the breeding season and then declines throughout the
remainder of the year until next breeding season begins. Their growth rate is
constant and can be determined by comparing the population size in one
year to the population size at the same time the previous year. This ratio is
the geometric growth rate and is symbolized by the Greek letter lsmbda (λ)
λ = N(t + 1)
N(t)
1. A nesting colony of gannets on Isle Bonaventure exhibits geometric
growth. During the year a initial population of
50 000 birds had 32 000 births and 29 000 deaths.
a) Calculate the geometric growth rate (λ).
b) Estimate the population sizes after 2 and 10 years.