Ch.4

Question 1

Biological organisms are set up to

Answer 1

reproduce.
Our species has experienced dramatic growth

Question 2

Population Growth Models ( 2 types)

Answer 2

Unlimited resources (exponential growth model)
Limited resources (logistic growth model)

Question 3

Compensatory dynamics

Answer 3

the idea that in a resource-limited community, an increase in the density of same species should be balanced by a decrease in the density of other, interacting species-is the basis for most theories of community stability and ecosystem resilience.

Question 4

Exponential Population Growth: unlimited resources

Answer 4

Nt = number of individuals in a population at time t
Nt+1 = the size of the population at the end of the next time interval
B = number of individuals born
D = number of individuals that die
I = number of individuals that immigrate into the population
E = number of individuals that emigrate from the population

At time t +1 the population size can be estimated by:
Nt+1 = Nt + B + I + - D - E

see slide for more

Question 5

Exponential Population Growth: unlimited resources
to determine the difference between one time point to the next one must:

Answer 5

Nt+1 - Nt = B + I - D - E

Question 6

unlimited resources
to determine the difference between one time point to the next ( closed population) E = 0 & I = 0

Answer 6

Nt+1 - Nt = B - D

B and D will be dependent on the
number of individuals in the population.

Question 7

population size vs time - J curve

Answer 7

all you need to recognize is that the change in the number of individuals with regard to time is: dN/dt

Question 8

dN/dt = B - D

What does b and d stand for

Answer 8

we will use b as the per capita birth rate and d as the per capital death rate. And this will yield:

dN/dt = bN – dN
Or
dN/dt = (b-d)N

Question 9

r =

Answer 9

Instantaneous rate of increase, the population growth
is governed by this constant

Question 10

the population growth
is governed by which constant

Answer 10

r = Instantaneous rate of increase

Question 11

When resources are unlimited, r, is at

Answer 11

its maximum value
for a species and this is referred to the species’
intrinsic rate of increase.

max = 1.0

Question 12

intrinsic rate of increase

Answer 12

the number of births minus the number of deaths per generation time—in other words, the reproduction rate less the death rate

Question 13

K is representative of

Answer 13

the carrying capacity
the number of individuals the environment can support indefinitely, given fluctuations in resources in the environment

Question 14

carrying capacity

Answer 14

the number of individuals the environment can support indefinitely, given fluctuations in resources in the environment

Question 15

Logistic Population Growth

as a population grows, and its density increases, a number of things can happen: DACA

Answer 15

Depletion of resources
Accumulation of waste products
Aggression between individuals
Competition for mating opportunities

Question 16

Density Dependence

Answer 16

Depletion of resources
Accumulation of waste products
Aggression between individuals
Competition for mating opportunities
All of these negative feedback inputs between population size and per capita growth rate has been termed density dependence.

Question 17

b’ and d’ now represent

Answer 17

the per capita density-dependent birth rate and per capita density-dependent death rate, respectively.

Question 18

logistic equation
describe the curve

Answer 18

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

S curve the levels off at K

Question 19

carrying capacity graph

Answer 19

Increased birth and decreased death
decreased birth and increased death
^ shift back to equilibrium of K

Question 20

exponential curve looks like a

Answer 20

J curve

Question 21

How does the population growth rate vary as a function of population size?

Answer 21

when the population is at 1/2 its (K) carrying capacity it has the most growth ( dN/dt)

Question 22

What about the per capita population growth rate with respect to population size (N)?

Answer 22

Negative Slope
linear decreease

Question 23

Assumptions of the Logistic Growth Model
( rarely met in nature)

Answer 23

1. The per capita growth rate is a linear function of N.
2. The population growth rate responds instantly to changes in N. (no time lags)
3. The external environment has no influence on the rate of population growth.
4. All individuals in the population are equal (No effects of individual age or size).

Question 24

Logistic Growth Model is difficult to meet but is still taught bc

Answer 24

It simply shows that population density can alter the growth rate of populations.

Also because it can be modified to relax the assumptions

Question 25

Woiwod & Hanski (1992)

Answer 25

studied density dependence Found density dependence in 69% of aphid and 29% of moth time series data sets. BUT, when short time series (<20 years) are removed from the analysis, the percentage of studies showing significant density dependence increased: 84% of aphid, 57% of moth

Question 26

Turchin and Taylor (2006)

Answer 26

Found density dependence in 18 of 19 forest insect populations and 19 of 22 vertebrate populations Also observed cyclic, chaotic, and stable dynamics

Question 27

Brook and Bradshaw (2006)

Answer 27

Found “convincing evidence for pervasive density dependence in the time series data” and “little discernible difference across major taxonomic groups” They also found a trend toward zero net growth (implying equilibrium) as the number of generations in the time series increased.

Question 28

Brook and Bradshaw, 2006 graphs

Answer 28

In (A) density dependence increases with the length of time series data collected In (B) as the number of generations monitored increases net rate of population change tends toward zero (equilibrium)

Question 29

the evidence for density dependence is

Answer 29

consistent and overwhelming for many different types of species.

Question 30

Density dependence is important for

Answer 30

population regulation

Question 31

Allee Effects

Answer 31

at low population densities animals have issues with things like finding a mate allee effects are a positive association between fitness and population size.

Question 32

Two manifestations of allee effects

Answer 32

1. Component Allee Effects – positive association between a fitness component (i.e. survivorship, fecundity) and population size 2. Demographic Allee Effects – when component allee effects cause a positive association between population size and per capita growth rate.

Question 33

starfish example

Answer 33

Due to escape from predation, there is a significant amount of allee effects occurring in starfish populations.

Question 34

define compensatory Dynamics

Answer 34

The idea that the density of all individuals within a functional group should be a conserved quantity has been termed “compensatory dynamics” or sometimes also called “community-level density dependence” or even “zero-sum dynamics” Taking a look at densities at the community level, predicts that as one species abundance decreases other species that have a high degree of niche overlap should increase.

Question 35

How does the abundance of one species within a function group (i.e. trophic level) affect the abundance of other species within that same group? This question looks at

Answer 35

compensatory Dynamics ( the impact of each species on each other in terms of abundance)

Question 35

James Brown

Answer 35

Focuses on comparing natural dynamics of the rodent communities in the control plots with those in the kangaroo rat removal plots. Found that: 1. there was a shift from grassland to shrubland species 2. Species richness remained quite consistent, despite significant species turnover 3. Decrease in rodent body size, but an increase in rodent abudance concluded that compensatory dynamics were occurring in their plots.

Question 36

Are common or rare species more likely to experience density dependence?

Answer 36

-common species showed little variation in abundance and significant density dependence. -Rare species were short-lived in the ecosystem and showed low density dependence

Question 36

observational graph from book

Answer 36

the steeper the line the higher the density dependence

Question 37

The Lotka-Volterra Model

Answer 37

assumes that the prey consumption rate by a predator is directly proportional to the prey abundance. This means that predator feeding is limited only by the amount of prey in the environment.

Question 38

simple assumption of Lotka-V

Answer 38

One assumption of this simple model is that prey populations grow exponentially. ( J curve mdoel)

Question 39

equation for exponential growth

Answer 39

dN/dt = rN Where N = number of individuals in the prey population and r = prey’s per capita population growth rate

Question 40

If predation is the only source of mortality for a prey population and the predator has a

Answer 40

linear (type I) functional response (which means the number of prey killed is directly proportional to prey density), then we can alter the equation to be this: dN/dt = rN – aNP Here a = predator’s per capita attack rate and P is the number of predators

Question 41

IN THE ABSENCE OF PREY A predator population would be expected to

Answer 41

decline exponentially at the rate of: dP/dt = -qP Here, q is the predator’s mortality rate (which is density-independent) and is measured as the number of deaths per predator per unit time.

Question 41

growth rate of predator population

Answer 41

which depends on the number of prey consumed per unit time, is equal to: aNP.

Question 42

f =

Answer 42

eating prey will turn into new predators at a constant rate of f.

Question 42

eating prey will turn into new predators at a constant rate of f. So, birth of the predator population is equal to:

Answer 42

faNP

Question 43

r =

Answer 43

b prime - d prime prime = per capita

Question 44

dynamics of the predator population is described by:

Answer 44

dP/dt = faNP-qP

Question 45

Net change in predator populations

Answer 45

dP/dt = faNP-qP

Question 45

Net change in prey populations

Answer 45

dN/dt = rN – aNP

Question 46

two equations that make up Lotka-Volterra Predator-Prey Model

Answer 46

dN/dt = rN – aNP Net change in prey populations And dP/dt = faNP-qP Net change in predator populations

Question 47

ZERO growth isocline aka

Answer 47

equilibirum

Question 48

ZERO growth isocline

Answer 48

when a population is neither growing nor declining. dN/dt = 0

Question 49

Prey Population Dynamics

Answer 49

Reach zero growth isocline when dN/dt = 0 and the prey population will be at equilibrium when the density of predators P = r/a (remember that r = prey per capita growth rate and a = attack rate). ( horizontal lines0

Question 50

prey population will be at equilibrium when density of predators is equal to

Answer 50

P = r/a (remember that r = prey per capita growth rate and a = attack rate).

Question 51

Predator Population Dynamics

Answer 51

Reach zero growth isocline when dP/dt = 0 and the predator population will be at equilibrium when the density of prey N = q/fa (remember that q = number of predator deaths, f = rate of conversion of consumed energy into new predators). ( vertical lines)

Question 52

PUTTING PREDATOR AND PREY ISOCLINES TOGETHER…

Answer 52

It is the number of predators present that determines whether the prey population is at equilibrium AND it is the number of prey present that determines whether the predator population is at equilibrium. Placing the two graphs on top of one another yields four regions of predator-prey state space, the narrow arrows show the response of the predator and prey populations in each region. Heavy diagonal arrows show the combined trajectories of the predator/prey populations in each region. Over time, the predator and prey populations will cycle continuously (seen in the ellipse).

Question 53

prey-predator dynamics looking only at density

Answer 53

cyclical action - see slide image We can use some of the information gleaned in the mathematical models to determine how much one can harvest a population without making it go extinct.

Question 54

when to harvest

Answer 54

1/2K ?? ask ( see graph) harvest above equilib. will generally cause pop to go extinct and instability

Question 55

tragedy of the commons.

Answer 55

This idea describes a situation where each entity harvesting an open resource receives the direct benefit of harvesting that resource, whereas all consumers of the resource share the cost.