Grizzly Models

Exercise A

1. Initial populaiton size has a huge effect. The smaller the population, the higher the probability of declining to 0, from which there’s no way back.

2. Demographic stochasticity would still be important, especially if the initial population were small.

3. Environmental stochasticity would certainly be important. Severe winters shouldn’t have a big effect, given that grizzlies hibernate. During the spring, summer, and fall, however, droughts and forest fires are two random factors that could certainly affect populations in negative ways.

4. Neither demographic or environmental stochasticity can be affected directly by management techniques. The effects of demographic stochasticity could be reduced by managing to keep populations as high as possible. Possible techniques might include creating or maintaining habitat corridors linking small populations.

Exercise B. Running multiple simulations

1. Running single simulations lets us track changes in a single population. When we run multiple replications, we only see the highs and lows at each time step, as well as the average, of course.

2. Running multiple replications gives us confidence in the results. Because of the random aspect of these simulations, one or two runs of the model could give us a misleading impression of the expected behavior of the model. If you flipped a coin five times, there is a very slight probability (about 3 times out of 100) that it would come up heads five times in a row. In the off chance that this actually happened, if we relied on that one run of the model, we would predict that the coin will always come us heads.

Red-cockaded Woodpeckers.     

Baseline Models

1. Abundance decreases over time.

2. 1 yr.

3. 117 after 20 yrs, 53 after 50.

Sensitivity Analysis      

1. Increasing survival rates increases the overall population size, but not equally for all age classes. The increase was greatest when survival of the 4+ age class was increased.

2. Given the chance to have an equal effect on any of the age classes, it would seem to be most effective to concentrate on adult survivorship.

Part 3 (more woodpeckers).

1. The 25% increase in the stage 0 age class had the biggest impact.

2. In this case, efforts at improving survivorship in the most recently fledged woodpeckers has the strongest impact on the population. While we needed to increase the survivorship more (a 25% increase), it is probably easier to have an effect on 1st year survivorship than that of the adults. Efforts at reducing predation on young in the nests could be a very effective means of achieving the desired increase in 1st yr survivorship.

Limits on Population Growth

Scramble Competition

1. 8 years

2. 3 years

3. It drops below K for the 1st 2 cycles and then gets back to K at t3.

4. They could be reducing available prey or fouling the environment with waste.

Contest Competition in Osprey

1. <6 years
2. <5 years
3. The population increases, obviously, but also increases faster in the early phases of growth because negative effects of being close to the carrying capacity aren’t felt when K is very large.
4. Yes. If K is set by available nest sites and very large numbers of nest sites are provided, the population might be affected by other limiting factors, probably related to food availability.
5. Duh! Put up more nest sites.

Barnacles and Ceiling Competition

1. < 2 yrs, 13.
2. It takes less time to reach the ceiling if growth rate is higher.
3. It takes longer under contest competition because the growth rate slows as the population nears K, whereas under the ceiling competition, the population is growing rapidly up to the moment it reaches the ceiling K.

Harvesting Tuna

1. Growing, you might guess that they could given the rapid growth rate.
2. Declining, no!
3. <6 time steps (12 years), <17 time steps (34 years)
4. .0391
5. Less
6. Between 10 and 20.
7. Sustainable

Management Options

1. about 18 steps
2. with 1% about 24 steps, with 3.9% it never doubles.
3. almost 50% higher with the 3.9% harvest
4. The numbers speak for themselves. If you harvest at the maximum sustainable rate, more tuna can be taken, more $$ for the fisherpeople.
5. Yes, we would reach the same conclusions. The rate might be slightly lower, or need to be adjusted when random effects drive the population to low numbers.
6. Limits mean that there will be a reduced income for the fishing fleet in the early years of a sustainable harvesting program. It all revolves around convincing people to curtail current consumption in order to get a greater yield in the long run. Current behavior suggests that this will always be a hard sell to our species.