Lecture 2 - Demography Flashcards
Population size is determined by four events, what are they?
Births, deaths, immigration and emigration.
What is the equation for population size at the next time point?
Nt+1 = Nt + B - D + I - E
Number at next time point = Number Now + Births - Deaths + Immigration - Emigration
What is the finite rate of increase?
The finite rate of increase is the rate of increase per individual per unit time.
λ is the symbol for the finite rate of increase and:
λ = (Nt+1) / (Nt)
Populations generally increase when…
when λ > 1, typically when b > d
or when Immigration is great
What are the two types of life cycle (life history)?
Age-specific and stage specific
Age-specific stages occur at certain time points
Stage specific stages occur based upon environmental conditions or the individuals state.
What are the two mode types of growth?
Modular and Unitary
What is modular growth?
Modular growth is adding extra units to the individual, bolting on certain structures.
What is unitary growth?
Unitary growth individuals have one body plan which grows either determinately or indeterminately.
What is a life table?
A life table allows for examination of population abundance. There are two types of life table, static (time specific) and cohort (dynamic)
What are the two types of life tables?
Static (or time-specific) life table: count all individuals alive at a given timeand record the age of each
This method is less preferred but is simpler to use for long lived organisms, that would be difficult to follow over their entire life time.
Cohort (dynamic) life tables follow all offspring born at a given time (the cohort) from birth until the death of the last individual. This is the preferred method of life table but is best used on organisms that have a short life span.
What information can you get from a life table?
Population age structure, population growth rate and population survivorship patterns.
What variables can be present in a life table?
x = the age or stage class Nx = number of individuals at each stage Lx = the % of the original cohort that survives to age/stage x, the Age-Specific survival rate Dx = the probability of dying during age/stage x Qx = the % dying between age/stage x and x+1 (Dx / Lx), the age specific mortality rate Bx = the number of offspring produced per individual in age/stage x
What is Ro?
Ro is the ‘net reproductive rate’, which is a measure of the change in population size.
Ro = {E} (lx bx)
the sum of lx and bx
If Ro > 1, the population is increasing in size exponentially
If Ro < 1, the population is decreasing in size exponentially
If Ro = 1, the population size is constant (replacement rate)
What is ‘r’?
‘r’ is the instantaneous rate of increase (‘intrinsic’) or the Malthusian parameter.
It is calculated :
r = (ln Ro) / T
r has the following properties:
If r> 0, the population is increasing in size
If r< 0, the population is decreasing in size
If r= 0, the population size is constant
What is ‘T’?
T is the generation time, the time between the birth of one cohort and the birth of their offspring.
What properties can Ro have?
If R0> 1, the population is increasing in size
If R0< 1, the population is decreasing in size
If R0= 1, the population size is constant
What properties does r have?
If r > 0, the population is increasing in size
If r < 0, the population is decreasing in size
If r = 0, the population size is constant
What is the SAD?
SAD is the Stable Age Distribution
It is reached when each age group individually always increases by the exact same value each time period
What does a Lx life table curve look like? (Survivorship curve)
Survival on the Y axis
Age (yrs) on the X axis
Linear negative graph (right angle triangle with axes, y= -x+C)
What does a Bx life table curve look like?
Fecundity on the Y axis
Age (yrs) on the X axis
Mountain like, grows exponentially, then slows, reaches peak and then falls at similar rate to growth.
What is a Type I survivorship curve?
Type I curves are typical of many long lived animals such as humans and elephants, with lots of parental care of the young.
What is a Type III curve?
Type III curves are typical of short lived organisms such as insects and plants where offspring mortality is high.
What is a Type II curve?
Type II curves are uncommon and represent large mammals and birds and seed banks.
What do Type I, II and III curves look like on a graph?
Type II is a linear line joining Y and X axis (y = - x + c). Survivorship is relatively constant throughout life.
Type I connects the ends of the Type II line with a curve above the line (more survival of young due to increased parental care).
Type III connects the ends of the Type II line with a curve below the line (high infant mortality rate due to low parental care
Together the three lines look like a set of diagonal lips.
Dispersal is often done by…
Juveniles and young adults.
Usually only one sex
Why do juveniles and young adults disperse?
There is often competition amongst young, dispersing reduces the risk of inbreeding.
Exponential growth in discrete time is represented by what equation?
Nt+1 = Nt(1 + b – d + i – e) Nt+1 = λNt
where λ = Finite rate of increase
And the generations do not overlap
λ = (Nt+1)/(Nt)
When λ is between 0 and 1 what is the result?
0 < λ <1
This results in the population decreasing
When λ is 1 what is the result?
If λ = 1
then the population is stable
When λ is greater than 1 what is the result?
If λ > 1
then the population increases
What is a stochastic model?
Random fluctuations in the model and data, the future is probabilistic.
What is a deterministic model?
There is no randomness in the model or the data, the future is completely predictable.
How is the instantaneous rate of increase represented in equation form?
r = ln[λ] = ln[Nt+1/Nt] = instantaneous rate of increase
λ = e^r
When r is greater than 0 what is the result?
When
r > 0 the population increases
When r is less than 0 what is the result?
When r < 0 the population decreases
When r equals 0 what is the result?
When r = 0 the population is stable
How is exponential growth in continuous time represented in equation form?
dN/dt = r N
where
r = ln(λ) and λ = er
What is the Euler equation?
The Euler equation allows for ‘r’ to be found from life tables.
In discrete time (a life table with ages/stages)
1 = {E} (e^rx) (lx) (bx)
In continuous time
1 = $ (e^rx) (lx) (bx) dx
When is growth exponential?
Growth is exponential when there is no competition or any other density dependence.
What is a Leslie matrix?
The Leslie matrix is a discrete, age structured model of population growth. It models the changes in a population of organisms over a period of time.
The population is divided into groups based on age classes.
To build the matrix some information must be known: nx = the count of individuals in each age class sx = the fraction of individuals that survive from class x to class x + 1 fx = fecundity, the average number of female offspring reaching No, born from mother of the age class x.
s is related to lx
F is related to bx
What are the advantages of a Leslie matrix?
Stable-age distribution is not required for valid population projections.
Sensitivity analysis can be conducted to see how changing certain age-specific vital rates affects population size and age structure
Density-dependence can be incorporated, this dampens the values to account for factors that limit population growth.
Useful mathematical properties can be derived from the matrix formulas, including stable-age distribution and finite rate of population change.
Can derive useful mathematical properties from the matrix formulas, including stable-age distribution and finite rate of population change (i.e., lambda).
What is the equation in a Leslie matrix?
Nt+1 = ANt
Where…
A= [F1 F2 F3 F4 F5] |s1 0 0 0 0| |0 s2 0 0 0| |0 0 s3 0 0| [0 0 0 s4 0]
Nt= [N1] |N2| |N3| |N4| [N5] t
Explain the Northern Right Whale study.
The Northern Right Whale is the most endangered of all large whales, there are only 300 individuals alive.
ignore males
There are four life stage: Calf Immature Mature (reproductively able) Mature and Calf Dead
Most stages there is a low chance of death, however mature with calves have 17% chance of dying due to risks arising from shipping.
This has a major impact on the entire population and extinction would occur soon, however only small changes are needed to increase survival.
What are the disadvantages of a Leslie matrix?
A large amount of data is required (age-specific data on survival, fecundity and population structure)
What is stochasticity?
Stochasticity is ‘randomness’, noise that affects the data.
Things that affect r/λ include environmental factors such as resource fluctuations and weather.
However there are other ‘demographic’ factors that can also affect N stochastically:
Who dies first
How many offspring
Male or female
Birth, growth and death rates vary genetically
Are genotypes with more or less variation favoured by natural selection?
Genotypes with low variation (λ) are favoured by natural selection
What is density dependence?
The density of a population is simply how many organisms are living in a given area. Density-dependent factors are factors where the effects on the size or growth of a population vary with the density of the population itself.
They influence the rates of births and deaths, and the effect increases as population size increases. When the density of a population is low (few individuals in a given area), resources are not limiting. There are plenty of resources for everyone. More individuals can give birth, and fewer individuals will die. Overall, the population will grow in size and become denser.
When the density of a population is high (many individuals in a given area), resources are more limited for each individual. Because of this, more individuals will die, fewer individuals will be born, and the population size will decrease and become less dense.
Give a density dependent study.
McKellar 2013
American redstart
Looked at number of offspring per female and also at the number of territories they had
Those with fewer offspring possessed more territories and those with 3 offspring had the fewest territories (25)
Negative correlation
What does high density result in?
High densities typically results in low fecundity as energy is used to gain resources due to increased competition.
What is ‘K’?
K is the carrying capacity, the number of individuals an environment can support indefinitely.
Explain the Cinnabar moth study?
A study describing density dependence
Cinnabar moths, looked at life stages:
Egg, Larve, Cocoon and Adult.
λ found to be 4.6 (population increase 4.6 x per year)
Larval survival is density dependent due to competition. You would expect exponential growth due to high egg production.
However competition for food limits growth in population,
Scramble and contest competition depend on the behaviour of the organism but a compromise is usually found.
What is scramble competition?
Scramble Competition is one of the two types of intraspecific competition, it refers to a situation in which a resource is accessible to all competitors (that is, it is not monopolizable by an individual or group).
However, since the particular resource is usually finite, scramble competition may lead to decreased survival rates for all competitors if the resource is used to its carrying capacity.
What is contest competition?
Contest competition is one of the two types of intraspecific competition. There is a winner and a loser where resources can be obtained completely, or not at all. An individuals physical action plays a key role in securing the resource.
