Population Growth & Demography
Before 1700, human population growth averaged λ = 1.0004. What does this say about births compared with deaths? Where does this period fall in the demographic transition?
Births barely exceeded deaths. This is the pre-industrial stage: high birth and death rates, with the population at a true carrying capacity.
At equilibrium, 80% of meadows in a pika metapopulation are occupied, and the annual patch extinction probability is 0.1. What is the colonization rate?
Using:
p* = 1 − m/c: 0.8 = 1 − 0.1/c
so c = 0.5.
Princeton and a site in central Japan have similar mean annual temperature and rainfall. Would you expect them to share a biome? Would they share the same species?
They would share a biome (temperate forest), because climate predicts vegetation type. Their species would differ, because which species are present also depends on dispersal and history.
A pond has algae, snails that eat the algae, and crayfish that eat the snails. As nutrient input increases, which levels increase? What limits the algae?
Algae and crayfish increase, while snails stay roughly constant because crayfish control them. The algae are limited by resources.
Why do leaves look green?
Seedlings on a forest floor get light that has already passed through the canopy.
Which pigments help them capture what remains, and why?
Chlorophyll a and b absorb red and blue light and reflect green.
The canopy removes most of the red and blue, so carotenoids, which absorb more green light, help capture what’s left.
A population drops from 500 to 400 in one year, and its annual death rate is 30%. What is its per capita birth rate?
λ = 400/500 = 0.8.
Since λ = 1 + b − d
0.8 = 1 + b − 0.3
so b = 0.1.
A large spring-fed pond always has newts. Nearby small ponds lose their newts in dry years but are repeatedly recolonized.
Classify each type of pond, and predict what happens to the small ponds if the large one is drained.
The large pond is a source and the small ponds are sinks. Without immigration from the source, the sink populations go extinct.
A forester plants a pine 200 km north of its range edge. With no competitors nearby, it grows, flowers, and sets viable seed. What limits the pine’s northern range? Is its fundamental niche larger than, smaller than, or equal to its current range?
Its range is limited by dispersal. Its fundamental niche is larger than its current range.
A pond has algae, snails that eat the algae, and crayfish that eat the snails.
A fish that eats crayfish is then introduced. Predict what happens to the snails and the algae. What is this type of effect called?
Crayfish decline, snails increase, and algae decline, so the algae become limited by herbivory. This is a trophic cascade.
Why does a C3 crop’s carbon gain drop more than a C4 crop’s on hot afternoons? Where on Earth would you expect C4 grasses to dominate?
In heat, stomata close to save water, and O₂ builds up inside the leaf. Rubisco then grabs O₂ instead of CO₂ (photorespiration), losing fixed carbon. C4 grasses should dominate hot, sunny, dry regions.
Two lakes contain the same fish species, and each has K = 1,000. Lake 1 has 100 fish and Lake 2 has 500.
Which lake has the higher per capita growth rate? Which adds more fish per year?
Lake 1 has the higher per capita rate, because per capita growth declines with density.
Lake 2 adds more fish in total: 0.5r × 500 = 250r, versus 0.9r × 100 = 90r.
A large spring-fed pond always has newts.
Managers can either build corridors that double c or improve meadow quality so that m is halved. Which raises pika occupancy more?
They have the same effect. Both raise p* from 0.8 to 0.9, because p* depends only on the ratio m/c.
If succession followed the tolerance model, what would removing the early colonists do to later species? Which 1920s view of communities fits tolerance best?
Removing early colonists would have no effect on later species. Tolerance fits Gleason’s individualistic view.
A new drug halves the infectious period of a disease with R₀ = 3. What is the new R₀? Does that stop the disease? What vaccination level would have the same effect?
The new R₀ is 1.5. That is still above 1, so it does not stop the disease.
The effect equals vaccinating 50% of the population.
Bark beetles kill every tree in a watershed. Would you expect stream nitrate to spike as it did after clear-cutting at Hubbard Brook? Why?
Yes. With no live plants taking up nitrogen, decomposition keeps releasing it, and it leaches into streams.
A salamander’s life cycle works like this:
This year there are 50 larvae, 20 juveniles, and 10 adults. Project next year’s numbers. Would starting with 80 adults and nothing else change the long-run growth rate?
100 larvae, 18 juveniles, and 13 adults. The starting mix would not change the long-run growth rate, because λ is a property of the matrix. The starting vector only affects the early years.
Treat the mouth as the “mainland” and the lungs as the “island” for bacteria. Some patients’ lungs clear bacteria poorly, so bacterial populations persist longer. Which curve shifts, and how does lung microbial diversity compare with that of healthy lungs?
The extinction curve shifts down, so equilibrium diversity is higher.
For two diatoms, α_AA = 0.01, α_BB = 0.02, α_AB = 0.005, and α_BA = 0.04. Find each species’ carrying capacity. Can each species invade when the other is at its carrying capacity? What is the outcome?
K_A = 100 and K_B = 50.
B cannot invade A, because 1 − 0.04 × 100 < 0.
A can invade B, because 1 − 0.005 × 50 > 0. A excludes B.
Each infected deer transmits a pathogen to 0.5 susceptible deer per day and stays infectious for 6 days.
Calculate R₀ and the fraction of deer that must be vaccinated to prevent an outbreak.
R₀ = 0.5 × 6 = 3.
Preventing an outbreak requires:
v > 1 − 1/3 ≈ 0.67.
Plants produce 10,000 J of NPP. Caterpillars eat 1,000 J, assimilate 400 J, and convert 120 J into new biomass. Calculate production efficiency and trophic efficiency. Why do the two differ?
Production efficiency is 120 / 400 = 30%.
Trophic efficiency is 120 / 10,000 = 1.2%. Trophic efficiency is lower because most primary production is never eaten.
An elasticity analysis for a sturgeon population gives adult survival an elasticity of 0.6 and fecundity an elasticity of 0.05. A 10% increase in either costs the same. Which do you fund, and why might fecundity matter so little in this species?
Fund adult survival, because λ responds far more to proportional changes in it. Sturgeon are long-lived and almost no eggs survive, so extra eggs barely change λ.
The slides describe island biogeography as a multispecies source–sink metapopulation. What plays the role of source and of sink? Why doesn’t the island ever hold the mainland’s full species pool?
The mainland is the source and the island is the sink. Every island population is headed toward extinction without immigration, so the species count settles where extinction balances immigration, below the mainland total.
Two grasses compete for soil nitrogen. Grass X maintains zero growth at 1 mg N/kg, while grass Y needs 4 mg N/kg. Predict the outcome.
Then suppose Y’s deep roots reach nitrogen that X cannot. How could that change the outcome?
X wins, because it draws nitrogen below the level Y needs to persist. With deep roots, each species would be limited more by its own kind than by the other. That stabilizing niche difference, a form of resource partitioning, allows coexistence.
Three seaweeds grown alone yield 300, 500, and 400 g/m². A mixture of all three yields 700 g/m², with similar shares from each species. Is this a selection effect or complementarity? What mixture result would point to the other mechanism?
This is complementarity, because the mixture beats the best monoculture and every species contributes. A selection effect would show a mixture yield near 500 g/m², dominated by the top species.
A country plans to plant forests across its snowy northern grasslands to offset emissions. Predict the net climate effect, and explain the two opposing processes.
The forests store carbon, which cools the climate. But a dark forest absorbs more of the sun’s energy than snow-covered grassland, which warms it. The net effect could be warming.