Lecture 3 - Population Dynamics Flashcards
What is the logistic equation?
dN/dT = rN ( 1 - N/K ) The logistic equation allows incorporation of density dependence on the growth rate by using rN( 1 - N/K ). This models that the population grows exponentially until it nears the carrying capacity ‘K’ where it slows and levels of, producing an S shaped curve.
Births and deaths are density dependent, where the death rate crosses the birth rate is point ‘K’. At K: N/K = 1 and dN/dt = 0 At the point where the curve goes exponential: N/K = 0 and dN/dT = rN
Explain scramble competition.
Scramble competition occurs when there are significant resources available but also high density, the competition results in everyone being successful until carrying capacity is reached at which all individuals don’t get enough to survive so the growth becomes negative.
Explain contest competition.
Contest competition is where an individual is either a winner or a loser, their physical ability is usually the determining factor on whether they are able to gain a resource or not. Those unable to get a resource die and the growth reaches an equilibrium.
Explain the Longhorn Cattle experiment.
Shows scramble competition. Initially at low population size each female averages one calf, this continues until the population size reaches around 66. The young per female then starts to rapidly decline after previously having been stable. At P=110 the calves per female is at 0.8, this indicates that the high population density resulted in there being too few resources and mothers dying.
What is net recruitment?
Net recruitment is the addition of individuals to a population through births or emigration. It is maximum at intermediate densities.
What is the maximum sustainable yield?
The maximum sustainable yield (MSY) is the peak of the recruitment curve. It is the largest harvest that can be removed from the population on a regular and repeated (indeed indefinite) basis.
Give an example of maximum sustainable yield.
The Tragedy of the Commons
There was massive overfishing of anchovies in Peru at levels much higher than the MSY, this was unsustainable harvesting and it resulted in the depletion of the anchovy population. Fewer mating females results in lower population growth and resulted in the near extinction of the population.
Catch size went from 12 million tonnes at the peak of unsustainable yield to post crash where the average catch was less than 1 million tonnes. This resulted in great unemployment and economic hardships for those relying on the industry.
What patterns can appear in dynamics?
Stability around an equilibrium
Cycles
Irregular Cycles
Chaos (may be bounded)
What biotic deterministic forces can cause patterns in dynamics?
Biotic deterministic forces:
- Simple density-dependent demography
- Time delays/lags
- Overcompensation
- Non-linear responses to density
- Other interactions (e.g. between ages/stages)
What abiotic factors can cause patterns in dynamics?
Abiotic fluctuations:
• Climatic forcing (large-scale, often low frequency e.g. El Niño, NAO)
• Stochasticity (small-scale, high frequency) :
Demographic
Environmental
These lead to complex dynamics such as cycles and chaos
More variability of K has what effect on the logistics equation?
More variability leads to a lower N (population)
How can variation arise on the logistics equation?
Variations on the carrying capacity, K, that is stochastic resources
Time lags (T) in density response
Non-linear responses to density
The increase in deaths and/or the decrease in births as density rises is not constant resulting in over/under compensation
There can be interactions between ages/stages
The type of competition can cause variation (contest, scramble)
Humans can affect dynamics
A higher ‘r’ value has what effect on the logistics equation?
A high ‘r’ value (intrinsic rate of increase), suggests the organisms is one that reproduces very quickly, is small and has high mortality rates.
The curve rises up to a carrying capacity, K, and then fluctuates, it is ‘tracking’ depending on factors such as climate, resources.
A low ‘r’ value has what effect on the logistics equation?
A low ‘r’ value, indicates a low intrinsic rate of increase, characteristic for large organisms that take a long time to develop and have low mortality rates.
A low value therefore results in the impact of variation in carrying capacity is smoothed out as it takes time for factors such as resources and climate to affect growth.
What are time lags?
Populations do not necessarily respond intstantaneously to changes in their own density. Instead that the amount of resource available is determined by the density one time interval previously. The reproductive rate itself will be dependent on the density one time interval ago.
Time lags promote population fluctuations, the intrinsic rate of increase, r, determines the response time.
R (Low Tr) < 1.33: direct approach to a stable equilibrium
R (average Tr) > 1.33: damped oscillations towards that equilibrium.
High Tr => cycles (period = 4T)
How does over/under compensation arise?
Increase in deaths and/or decrease in births as density rises is not constant
Accurate compensation of density dependence leads to an increase in death rate and/or decrease in birth rate which exactly offsets any change in population size, so that the population stays at the same size.
Undercompensating leads to tge death rate increasing and/or birth rate decreasing as population size goes up, but the change is not great enough to keep population from continuing to grow.
Overcompensating leads to the death rate increasing and/or birth rate decreasing as population size goes up, so strongly that an initial increase in population size will result in a population decline. Increasing levels of overcompensation can first lead to limit cycles then chaos
Descirbe the flour beetle study.
Benoit (1998)
The flour beetle has four life stages-
Small larvae
Large larvae
Pupae
Adults
If the eggs are allowed to be cannibalised the curve appears chaotic with the density of all four stages overlapping.
However if the eggs are given a refuge their density is distinct from the other three stages which are grouped together out in a linear pattern
This shows there is interaction between stages, this causes variation on the logistic equation.
Describe the graph between growth rate and type of competition.
A population where contest competition is prevalent is more likely to rise to equilibrium as growth rate increases.
Whereas a population where scramble competition is prevalent will rise smoothyl to equilibrium with a low growth rate however as growth rate increases damped oscillations may occur, leading to stable cycles and chaos as ‘r’ increases.
