AP BIOLOGY EQUATION LIST
I)
Chi-Square (used to determine whether a null hypothesis (H0) should be accepted or
rejected.)
-write a null hypothesis (example: “The application of heat will have no difference on the
reaction rate catalyzed by perioxidase.”)
-df= degrees of freedeom = n-1 (the number of categories of data-1).
-p-value provides chi-square values at different significant levels. Biology used p-value of 0.05,
that is, there is a 95% confidence that any data deviation are or are not achieved by chance
occurance.
-if the sum of the chi-square values are greater that the p-value at the 0.05 confidence interval,
than the hypothesis is rejected and there IS a difference between what you observed from what
you expected.
LINK TO Problem Steps: http://course1.winona.edu/sberg/Equation/chi-squa.htm
Past Free Response Essay with chi-square equation: GOOD ONE with answer:
http://apcentral.collegeboard.com/apc/members/repository/ap03_sg_biology_26426.pdf
2)
HARDY-WEINBURG EQUILIBRIUM: Used to determine if allele frequency in
population is changing.
p2 + 2pq + q2 = 1
and p + q = 1
p = frequency of the dominant allele in the population
q = frequency of the recessive allele in the population
p2 = percentage of homozygous dominant individuals
q2 = percentage of homozygous recessive individuals
2pq = percentage of heterozygous individuals
Link to worked problems: http://www.k-state.edu/parasitology/biology198/hardwein.html
3)
Water Potenial Equation:
 =
P
+
S
Or
Water = pressure + solute
Potential potential
potential
Water moves from high (less negative) to low (more negative) values. Pressure potential is ZERO in an
open system.
In a closed system, the solute potential (often called the osmotic pressure potential) must be cosnidered
since the solute affects water flow and can build pressure. Solute potential (ψs) can be calculated using the
following equation (R will be provided on test if asked)
 S = - iCRT
i = # particles molecule makes in water
C = Molar concentration
R = pressure constant 0.0831 liter bar
mole °K
T = temperature in degrees Kelvin
= 273 + °C
4)
POPULATION GROWTH EQUATIONS
a) RATE OF NATURAL INCREASE:
reproductive potential)
increase in population (not considering instrinsic
Birth rate (b) − death rate (d) = rate of natural increase (r).
-birth rate expressed as number of births per 1000 per year (currently 14 in the U.S.);
-death rate expressed as the number of deaths per 1000 per year (currently 8 in the U.S.);
-So the rate of natural increase is 6 per thousand (0.006 or 0.6%).
b) Exponential Growth Rates (NO LIMITING FACTORS
The rate of population growth at any instant is given by the equation
dN = rN
dt
where



r is the rate of natural increase in (genetically determined
reproductive rate)
t — some stated interval of time, and
N is the number of individuals in the population at a given
instant.
The algebraic solution of this differential equation is N = N0ert where




N0 is the starting population
N is the population after
a certain time, t, has elapsed, and
e is the constant 2.71828... (the base of natural logarithms).
Plotting the results gives this exponential growth curve, so-called because it reflects the growth of a
number raised to an exponent (rt).
Doubling Times…For you math enthusiasts…used in Bio for bacterial growth
equations.
When a population has doubled, N = N0 x 2.
Putting this in our exponential growth equation, 2N0 = N0ert
ert = 2
rt = ln (natural logarithm) of 2 = 0.69
doubling time, t = 0.69 / r
So Sri Lanka with an r of 1.3% (0.013) has a doubling time
t = 0.69/0.013 = 53.
(You can use the same equation to calculate how quickly an investment in, for example, a certificate of
deposit will enable you to double your money.)
c) LOGISTIC GROWTH (considers density-dependent factors = carrying capacity)
In this equation, the biotic potential (rN) is limited by environmental pressures which determines carrying
capacity (K). This is a more realistic curve.
FOR YOU CALCULUS ENTHUSIASTS, this is what would really be used in determining population
curves……….you can integrate the equation and provide instantaneous data:
WON’T BE ON TEST BUT GOOD TO KNOW IF YOU HAVE CALC!!!!
It is possible to use the rules of calculus to integrate the growth rate equation to calculate the population
size at a given time if the initial population size (N0 is known). We won't do the math here, but will give the
equation:
When you calculate growth rates with this equation and start with N near 0, you can plot a curve called a sigmoid
curve (x-axis is time, y-axis is population size), which grows quickly at first, but the rate of increase drops off
until it hits zero, at which there is no more increase in N. Due to the continuous nature of this equation, K is
actually an asymptote, a limiting value that the equation never actually reaches. This is where one is reminded that
the logistic is a model and will not behave exactly as a real population would, as a real population can grow by no
less than one individual and this equation predicts growth (when close to K) of fractional individuals.
5)
r-selected vs. K-selected species:
r-selected: rapid growth; short-lived
high reproductive rate; many offspring;
no care for young;pioneer species; rapid
growth following by crashes. J-Curve.
k-selected species: slower development;care of young;
excellent competitor; longer lived; larger body size;
limited dispersal;equilibrium species; S-curve
6)
Survivorship curves: