Calculating population Growth
Using Chapter 53 on Population ecology and the equations for population growth
for exponential and logistic models
Do the following exercises:
1. Distinguish between exponential and logistic population growth. Give the equations for each.
2. What is carrying capacity? Why do populations fluctuate around some estimated value of K?
3. Using density independent growthdo the following: start with an initial population (N0) = 5,
K of 500 and r = 0.5, approximately how long does it take to reach K? What if you change r to r
= 0.05? Show your work.
4. Using continuous logistic growth, A population of deer with the following criteria;
N(0) = 5, K=500, and r = 0.2. What will the population be after a year?
Vary r to 0.5 and 1; Calculate the population size in a year for each of those values of r.Show
5. A population of Daphnia follows a logistic graph, if its N(0) = 5, K=500, r = 0.2, Calculate N
at T=2 ? Change r to the following: 0.5, 1, 2, 5. Discuss what changes if any, would occur using
T=2. What does this imply? Show your work.
6. A population of Spotted Fritillary butterflies exhibits logistic growth. If the carrying
capacity is 500 butterflies and r = 0.1 individuals/(individuals x month), what is the
maximum population growth rate for the population? (Hint: maximum population growth
rate occurs when N = K/2).
Fun with Water Potential!
Botanists use the term water potential when predicting the movement of water into and
out of plant cells. Remember, the movement of water across a semi-permeable
membrane as it follows its own concentration gradient is osmosis. But plants are a
unique case because they have a cell wall which prevents a plant cell from bursting if it
takes on too much water. If a plant cell is placed in a hypotonic environment, it will take
on water UNTIL water pressure inside the cell builds up to a point that it cannot take on
any more. This increase in water pressure will actually push water molecules back out
of the cell against water’s concentration gradient until the amount of water moving in
due to solute difference is equal to the water moving out due to water pressure—this is
a dynamic equilibrium!
Water potential is a measure of how likely water is to move from one location (say
outside the cell) to another (inside the cell). For example, in the case above….a plant
cell placed in a hypotonic solution…..water has a higher potential (tendency) to move
INTO the cell than it does to move OUT of it. Therefore, water potential is GREATER
outside the cell than inside the cell because the water outside the cell has the
GREATER POTENTIAL TO MOVE. Just like any solute will diffuse DOWN it’s
concentration gradient—from high to low concentration, water will always move from an
area of greater water potential to an area of lesser water potential.
Water potential is made up of 2 parts---solute potential and pressure potential. Add both
together to get the total water potential. See below.
Note: (we use the greek letter ―psi‖ or ―Ψ‖ to represent water potential.)
Solute potential + Pressure potential = Water potential
Ψs + Ψp = Ψ
Solute potential—( Ψs )—the greater the concentration of a solute, the lower the
waterpotential.—an inverse relationship. Think of it this way: if you place a plant cell in
very saltywater, water will leave the cell for the environment it’s in. Water had a greater
tendency tomove OUT than in (the cell). Therefore, water potential was lower in the
environment than inthe cell. This means that the water in the environment had low
tendency to move (into thecell) than the other way around. Said another way, water that
was in the cell had a greaterpotential to move (OUT) than the other way around. In
summary, solute potential is theeffect that solutes have on a solution’s overall water
Pressure potential—( Ψp )—physical pressure increases water potential—a direct
relationship. If you have a syringe filled with water and you press down on the plunger
(increasing pressure), water will leave the syringe through the needle (the only
opening).Plant cells work the same way, if water pressure increases inside the cell, that
pressure willdrive water back out. The cell wall will not break, but it is a little bit elastic
and will bulgeoutward. This is called TURGOR. The water pressure that causes turgor
is called TURGORPRESSURE. Lack of turgor is called WILTING!
Now let’s add some numbers to this:
Pure water has a water potential of ZERO.
Solutes added to pure water decrease water potential—negative numbers.
Pressure increases water potential.
AP BIOLOGY Created by Samantha Kayhart
Example:Plant cellin pure waterProblems:
1. The solute potential of pure water is _________________.
2. The solute potential of the plant cell is (greater/less than)pure water. Therefore the
greaterwater potential is (in the cell/in the solution). Circle your choice.
3. If solute potential in the plant cell above is –6.25 bars and pressure potential is 0,
what iswater potential of the plant cell? _________________________ What does this
indicate in terms of water movement?
4. If solute potential in the plant cell above is –6.25 bars and pressure potential is 6.25
bars,what is water potential of the plant cell? ________________________ What does
this indicate in terms of water movement?
5. A plant cell has a solute potential of –4.0 and a pressure potential of 1.0. It is then
placed ina solution with a water potential of –5.0. What will happen to this plant cell?
6. A plant cell has a solute potential of –2.0 and a pressure potential of 0.0. It is placed
in asolution with a water potential of –1.0. What will happen to this plant cell?
The Energy of Reactions
Energy input or energy
Anabolic or catabolic?
Increasing complexity or
Change in G positive or
Spontaneous or nonspontaneous?
Molecule complexity greatest
in product or reactant?
ATP coupled process, or ATP
Greater energy in the
reactants or products?
Dehydration or hydrolysis?
ATP formed, or ADP + P?
Entropy increased or
High energy bonds formed,
Decomposition or synthesis?
Energy of reactants vs
products same or different?
Atoms of reactants vs
products same or different?
Gibbs Free Energy
• Enthalpy is expressed in kJ (kilojoules)/mol, entropy in J/K (joules/kelvin), and
temperature in K. Cancel the Kelvins, and convert J to kJ by dividing by 1000 to find G in kJ.
• Standard temperature is 298K (25C), but some problems use 20C (293K)
• Free energy is calculated using Δ G = Δ H - T ( Δ S)
where a negative G value is
exergonic (spontaneous) and a positive is endergonic (non-spontanteous)
• Practice Problems:
A + B -> AB
CD -> C + D
CH4 + 2O2 -> CO2 +
N2 + 3H2 -> 2NH3
Hydrolysing ATP ->
ADP + Pi
Glucose (glucose + Pi)
* 2COCl2 + H2O ->
CO2 + 2HCl
Δ Free energy
Ender- or exergonic?
Spontaneous or not?
* Phosgene, COCl2, was used as a weaponized gas during World War I. It reacts with
moisture in the lungs to produce HCl, which causes the lungs to fill with fluid, leading to
death. Use the energy values above, at a body temp of 37C (310K) to see if this reaction is
spontaneous or not.
Genetics and Chi-square analysis
A student makes a dihybrid cross with Drosophila. She crosses two heterozygotes for the white
eye. Ww x Ww. She expects to see a 3:1 phenotypic ratio of Red eyes (WW and Ww) to white
eyes (ww), her null hypothesis. She rears the next generation through to adult flies and counts the
White eyes (ww) 210
Wild type (red) eyes (WW and Ww) 680
Perform a chi square analysis on these results and find out if it is close enough to 3:1 to fail or
reject her null hypothesis.
Shoppers have mobbed WalMart to buy Christmas Toys for their kids. In a bin of specials,
the following are chosen in one 10 minute interval:
Kaptain Marvel 30
Ninja Turtle 15
Are the toys taken at random or is there a preference? Do a chi square analysis.