Single-Species Populations I: Population Growth and Intraspecific Competition

Question 1

Ecology is a discipline that is concerned with

Answer 1

distribution and abundance of organisms

Question 2

Describe ecology

Answer 2

• quantitative subject
• heavy reliance on both analytical and statistical models with simple and tractable mathematics

Question 3

Models based upon

Answer 3

empirical evidence

Question 4

Give some examples of population dynamics

Answer 4

• stability
• increase from a low density
• increase cessation upon environmental limitation
• random population fluctuations

Question 5

Describe negative density-dependence

Answer 5

results in population regulation about the environmental carrying capacity

Question 6

Describe the linear model

Answer 6

• time on the x
• abundance (n) on the y
• gradient shows the instantaneous growth rate of the population
• absolute growth rate does not depend on n
• differentiating the equation gives gradient 0: variables are independent
• simple but not biologically accurate

Question 7

Describe the exponential model

Answer 7

• assumes that growth rate is proportional to N
• Dn/dt = rN
• goes through the origin
• the gradient is r; growth is when r > 0
• D/dt is the per capita population growth rate
• r = birth – deaths, and N > 0
• N(t) = N(0)e^rt
• abundance only depends on the parameter r
• absolute growth rate is dependent on population size
• D/dt against N is constant and has a gradient of 0, because it is r
• no equilibrium
• better but still unrealistic

Question 8

Describe the theory behind the logistic model

Answer 8

• useful tool for density-dependent mathematical representations
• introduces regulation to a population
• reflects the limitations of the environment by reflecting the dynamics of the per capita growth rate

Question 9

Describe the logistic growth model

Answer 9

• DN/dt = rN [k-N/k]
• k shows the limits of the environment, as the maximum number of individuals that that environment can support
• if n is small then exponential growth is possible
• as population gets to large, the population growth rate zeroes out
• DN/dt = 0 and is found at equilibrium
• occurs when N = K
• DN/dt on the y against r [K-N/N]; R equals theoretical maximum per capita growth rate (with maximum resources). - linear decline with equilibrium reached at K.
• Nt on x against t creates sigmoid curve - a continuous time formation where it is impossible to exceed K and there is a smooth approach
• DN/dt against N on y is a n shaped curve
• multiplying out this equation, dN/dt = rnK – rn^2 / k

Question 10

Describe the effects of immigration on the logistic model

Answer 10

• N grows above K
• pulling back to equilibrium through per capita growth rate
• negative density dependence: the per capita growth rate declines with population size.