weeks 1-4

Question 1

What is a population?

Answer 1

• group of individuals of same species that live in the same place.
• group of individuals that live close enough to find each other and reproduce.

Question 2

What is population ecology?

Answer 2

• Study of how/why populations change over time and space, in terms of distribution, abundance and composition.

Question 3

What’s the difference between a discrete and a continuous growth model?

Answer 3

• Discrete models track time in discrete steps (1 year, etc.), while conituous models track growth over a continuous, smooth curve.
• Discrete models use difference equations to model pop growth, while continuous models use differential equations.

Question 4

What types of species are best-suited to discrete population growth models, and what types are best suited to continuous models?

Answer 4

• DIscrete models: species with pulsed reproduction (seasonal repro) or species with non-overlapping generations (short-lived).
• Continuous models: species with overlapping generations and non-seasonal reproduction.

Question 5

What’s the difference between a stable population and a stationary population?

What characteristic of the population are you describing with a stable population and what are you describing with a stationary population?

Answer 5

• Stable populations have unchanging proportions of individuals in each demographic (i.e. adults vs. juveniles).
• Stationary populations are not growing are declining (λ=1).
• “Stable” described population distribution and “stationary” describes pop growth.

Question 6

What’s the equation to predict population size at time (t) with a discrete population model?

Answer 6

N_t = λ^t * N₀

Question 7

What is the equation for population growth using a continuous model?

Answer 7

dN/nt = rN, where r = b-d

Question 8

What is the equation to determine pop size at time (t) using a continuous growth model?

Answer 8

• N_t = N_o * e^rt, where r = b-d.

Question 9

Derive equations to express λ in terms of r, and r in terms of λ.

Answer 9

N_t =λ ^t * N_o N_t = N_o * e^rt

So…

λ = e^r and r = ln (λ)

Question 10

Derive the equation for doubling-time of a population using discrete growth.

Answer 10

N_t = λ^t * N_o

λ_t = N_t / N_o = 2

ln(λ_t) = ln(2)

t * ln(λ) = ln(2)

t = ln(2) / ln (λ)

Question 11

List 5 assumptions of an exponential growth model.

Answer 11

1. b and d are constant over time.
2. no differences in b and d by demographic group.
3. no e or i.
4. no time lags.
5. no genetic structure.

Question 12

Give 4 examples of populations that might be experiencing exponential growth.

Answer 12

1. Newly established pops with few predators.
2. Invasive species.
3. Pops recovering from catastrophic declines.
4. Humans.

Question 13

Describe how stochastic models differ from deterministic models in terms of:

1. predictability,
2. outcomes and
3. starting conditions.

Answer 13

1. may vary unpredictably
2. outcomes uncertain
3. different starting conditions can produce different outcomes.

Question 14

1. What kind of pattern of population growth do deterministic factors create?
2. Give 4 examples of deterministic factors.

Answer 14

1. directional, non-random growth patterns.
2. habitat loss
3. fragmentation
4. invasive species
5. overharvest

Question 15

Name 3 primary sources of variation in population growth.

Answer 15

1. Deterministic factors
2. Sampling error
3. Stochastic processes

Question 16

What is demographic stochasticity?

Answer 16

Chance variation in b and d in real populations (i.e. survival rate may be 0.726, but in any given year in a population of 10 individuals, you’re not going to have 7.26 survivors!) even when λ does not change.

Question 17

What is environmental stochasticity?

Answer 17

Uncertainty due to unpredictable changes in environmental stochasticity.

Question 18

What is the “funnel effect”?

Answer 18

Variance in N increases with time in a pop models with stochasticity.

Question 19

How do you calculate average growth rates in models with stochasticity?

Why?

Answer 19

1. Use geometric mean (multiply the t growth rates and then take the t-th root.
2. With no stochasticity, can just take average (arithmetic mean), but with stochasticity the arith mean will over estimate lambda.

Question 20

Describe how you would use past year’s estimates of λ to model stochasticity.

What is an assumption of this approach?

Answer 20

Run many (say 1000) replicates, eac taking a value of λ at random from previous years’ data.

Assumes future variation will be same as past.

Question 21

What is the effect of temporal autocorrelation on stochastic population growth estimates?

Answer 21

Causes underestimation of variability in growth rates (b/c you measured for a few years, and those years tend to be more similar than others).

Question 22

1. What is scramble competition?
2. What’s another term for it?

Answer 22

1. individuals have equal access to resources, so when shortages occur, everyone is equally affected.
2. “exploitative competition”

Question 23

1. What is contest competition?
2. What is another name for it?

Answer 23

1. Individuals have unequal access to resources, so those with less access suffer more when there are shortages.
2. “interference competition”

Question 24

What is the logistic growth equation for density dependence?

Answer 24

dN/dt = rN (1-N/K)

where K is the carrying capacity

Question 25

If a population is experiencing logistic growth, what is causing that?

Answer 25

Density-dependence.

Question 26

Graph r over N with exponential growth.

Answer 26

Question 27

Graph N over time with exponential growth.

Answer 27

Question 28

Graph r over N with logistic growth.

Answer 28

Question 29

Graph N over time with logistic growth.

Answer 29

Question 30

Graph growth over population size with logistic growth.

Answer 30

Question 31

Graph growth over N with exponential growth.

Answer 31

Question 32

What is a theta-logistic model? What is the equation?

Answer 32

Allows for non-linear relationship between pop growth rate and N. dN/dt = rn [(1-N/K)^Θ]

Question 33

What is Θ when there is a linear relationship between r and N?

Answer 33

Θ = 1

Question 34

What's the equation for logistic growth where density-dependence occurs with at time lag?

Answer 34

dN/dt = r (1 - N_t-L/K)

Question 35

When density-dependence occurs with a time lag in pop with logistic growth, what do graphs of N over t look like when: 1. rL is small 2. rL is medium 3. rL is large

Answer 35

1. similar to logistic growth with no lag 2. logistic growth with damped oscillations until K is reached. 3. stable limit cycle (continous uniform period and amplitude oscillations) around K.

Question 36

1. Graph N_t+1 over N_t for logistic growth with scramble competition. 2. When will population increase and when will population decline?

Answer 36

Pop will grow to left of exact replacement line, decline to right of it.

Question 37

Graph N_t+1/N_t over N_t for logistic growth model with scramble competition.

Answer 37

Question 38

What is the discrete growth model equation for scramble competition? What is this equation commonly called?

Answer 38

N_t+1 = N_t \* λ_max^{(1 - N/K)} "Ricker equation"

Question 39

What is the discrete growth model equation for contest competition? ## Footnote What is this equation commonly called?

Answer 39

N_t+1 = N_t [(R_max K) / (R_max N_t - N_t + K)] Beverton-Holt equation

Question 40

Recipe for chaos?

Answer 40

* Scramble competition * Very larger growth rates (r \> 2.7, λ \> 15)

Question 41

What 3 things did Andrewartha and Birch propose as limits on population size? Which is most important?

Answer 41

1. shortage of resources 2. inaccessability of resources 3. shortage of time when r is positive (weather, predators, etc.) Number 3 most important.

Question 42

What is density-vague population change?

Answer 42

Proposed by Don Strong as a more realistic (but less mathematically feasible) alternative to density dependence. At medium densities, that is not much change in growth rates relative to very high or very low densities.

Question 43

What 2 things might make you not notice density dependence in a population?

Answer 43

1. Data sets with short time series! 2. Time lags not taken into consideration.

Question 44

What might make you conclude there is density dependence, when there really isn't?

Answer 44

Spurious correlations (like correlations between N_t+1/N_t vs. N_t).

Question 45

What are population dynamics?

Answer 45

Analyses of causes of changes in population density, including both population regulation (process that returns pop to its equilibrium density) and population limitation (process that sets equilibrium density).

Question 46

What is population regulation?

Answer 46

Mechanism that returns a population to its equilibrium density (as determined by population limitation).

Question 47

What is population limitation?

Answer 47

Process that sets the equilibrium density of a population (which occurs via mechanism of population regulation).

Question 48

How do you calculate reproductive value?

Answer 48

Repro value = # offspring an ind of a given age class will produce relative t the first age class (first age class always = 1.0).

Question 49

How do you calculate fecundity in a pre-breeding census?

Answer 49

F_x = m_xS_o

Question 50

What does the Leslie matrix look like for a pre-breeding census?

Answer 50

Question 51

How do you calculate fecundity in a post-breeding census?

Answer 51

F_x = S_xm_x

Question 52

What does the Leslie matrix for a post-breeding census look like?

Answer 52

Question 53

What is a Lefkovitch matrix, and how does it differ from a Leslie matrix?

Answer 53

Just like a stage-structured Leslie matrix, but some individuals will stay in same stage, while others will move into next stage. So you get two survival values in the same row for each stage.

Question 54

What does a Lefkovitch matrix look like?

Answer 54

Question 55

Why do age and stage strucured models rarely include density dependence? (2 reasons)

Answer 55

* It's rare to know which parameters are affected, and how much, and by whom (is juv d-d only caused by # of other juv's, or everyone?) * It's a pain in the ass to calculate!

Question 56

How do you add demographic stochasticity to a stage-structured model?

Answer 56

Determine probability that each individual survives or reproduces using binomial (survival or repro of 1 offspring only) or Poisson (repro of \> 1 offspring) distribution for each matrix element (vital rate).

Question 57

How do you add environmental stochasticity to stage-structured models?

Answer 57

Determine the mean and standard deviation of each matrix element from years worth of field data. Replicates of model are run with random samples within those standard deviations.

Question 58

What is sensitivity analysis?

Answer 58

Determines how sensitive pop growth is to changes in each vital rate in a matrix.

Question 59

How is sensitivity calculated?

Answer 59

Sensitivity = Δλ / Δv where v = vital rate.

Question 60

The sensitivity of a matrix element depends on what 2 things?

Answer 60

1. reproductive value of that age class. 2. proportion of ind's in that class at Stable Age Distribution.

Question 61

What is elasticity, and how does it differ from sensitivity?

Answer 61

Rescales sensitivity values to represent the proportional change in lambda due to the proportional change in the vital rate. (Allows you to compare percent differences when vital rates are not anywhere near equal.)

Question 62

How do you calculate elasticity?

Answer 62

E_v = (Δλ/λ) / (Δv/v) where v = vital rate

Question 63

What are 2 assumptions of a cohort life table?

Answer 63

1. No yearly variation in vital rates. 2. Stable age distribution.

Question 64

What are 3 assumptions of a static life table?

Answer 64

1. No yearly variation in vital rates. 2. Stable age distribution. 3. Stationary population.

Question 65

How is survivorship different from survival?

Answer 65

Survivorship is the probability of an ind in age group x living to a given age in a life table (not a matrix).

Question 66

Name 3 useful life-history values you can calculate from life tables.

Answer 66

1. Net reproductive rate. 2. Generation time 3. Instantaneous rate of increase (r) (approximate)

Question 67

Name 4 key life-history tradeoffs.

Answer 67

1. Current repro vs. survival. 2. Current repro vs. future repro. 3. Repro vs. condition/growth 4. Number vs. quaity of offspring