environment. This carrying capacity, usually referred to by the letter K,is the maxi-
mum population size that can be regularly sustained by an environment. Change the
environment and Kchanges, for example, by such events as adding a predator, remov-
ing a competitor, or adding a parasite. The notation that follows (in the form of a dif-
ferential equation) represents a rate of population increase that is limited by interspe-
cific competition (see above):
in which Nis the population size, tis time, Kis the carrying capacity, and ris the
intrinsic rate of increase.
What are survivorship curves?
Survivorship curves record and plot the fate of the young, and their chances of sur-
vival in key age categories. Significant factors affecting all populations are birth rates,
death rates, and longevity. By recording the numbers of births and deaths over a peri-
od of time, researchers can determine the average longevity of organisms in each age
class; these numbers tell a great deal about a population.
There are three basic survivorship curves. Type I curves represent species that
have offspring with a high survival rate, with most living to a certain age and then
dying; humans are an example. Type II curves represent organisms with a steady death
rate from the time they are born or hatch until they die; their survivorship varies and
includes such species as deer, large birds, and fish. Type III curves include those
organisms that have a low survivorship shortly after being born, but with a high
longevity for the individual organisms
that survive; maple and oak trees can be
included in this category.
What is the air quality index?
Mathematics plays an important part in
the air quality index (AQI), a scale devel-
oped by the U.S. government to measure
how much pollution is in the air. The AQI
measures five specific pollutants: ozone,
particulate matter, carbon monoxide, sul-
fur dioxide, and nitrogen dioxide. The
levels range from 0 (good air quality) to
500 (hazardous air quality); the higher
the index, the higher the level of pollu-
tants and the greater the likelihood of
detrimental health effects.
dt
dN rN
K
= ]KN- g
320
In this sample graph of a survivorship curve, it is
easy to see how the survival rates of maple trees,
deer, and people vary greatly over time.
