Exam 2 - Lecture Notes Flashcards
Define life table
age-specific mortality schedule of a population
Define cohort life table
an age-specific mortality schedule based on following a cohort throughout life
Define the variables in the life table (x nx lx dx qx)
x = age nx = # alive at age x lx = proportion surviving from start to age x dx = # dying during age interval x to x+1 qx = per capita rate of mortality during age interval x to x+1
Define a Type I survivorship curve
Low mortality for most of life (higher mortality of older organisms)
Example of Type I survivorship pop
Humans
Define a survivorship curve
Per capita rate plotted on a logarithmic scale to make a curve - uses Nx column of life table
Define a Type II survivorship curve
Constant rate of mortality
Example of a Type II survivorship curve
Small mamals
Define Type III survivorship curve
High mortality rates early in life, followed by a lower/constant mortality rate
Examples of Type III survivorship curve
Invertebrates, Song sparrow of BC
Define static life table
calculated from cross section of a population at a specific time, like a snapshot. Easy for humans (census) harder for plants and animals
Example of a static life table
Human females in Canada, 2006 - data taken from a census
Find the age intervals, fill in data, calculate qx
What are the three types of data used for non-human life tables (list)
Survivorship directly observed
Age at death observed
Age structure directly observed
What is surviroship directly observed
Following a single cohort until death to create a cohort life table
Example of surviroship directly observed
Connell’s classic competition experiment following two species of barnacles Chthalamus and Semibalanus
What are the assumptions of age at death observed and what is it
1 - that the pop size is constant through t
2 - birth and death rates for each group are constant
This is a method for creating a non-human life table
Examples of age at death observed (3)
1 - Baboons in Kenya National Park - 274 females ID and aged at death
2 - Murie examined Dall Sheep in National Park Alaska - direct observations and collecting skulls (608) analyzed to create static life table
3 - Human demography data collected from cemetery
Define age structure directly observed and state an assumption
Forming static life tables by determining how many individuals exist at each age. Assume constant age distribution (rare)
Examples of age structure directly observed
1 - fish through otolith and body scales
2 - tree rings through core samples
Define Malthusian parameter
The intrinsic capacity for increase (r) determined by combined effects of both the environment and certain innate qualities of the organism
What are the variables of the malthusian parameter and what do they mean
lx - capacity for increase (proportion surviving to age x)
bx - births (# of female offspring produced per female aged x to x+1, often only females counted)
R0 - net reproductive rate - rate per generation obtained by lx * bx and summing across all groups
Define net reproductive rate (R0)
The rate per generation obtained by multiplying lx and bx and then summing across all groups, which weighs natality against number of survivors per interval
Define R0 values vs 1
R0 = 1, pop replaces itself exactly = stable
R0 < 1, pop decreasing
R0 >1, pop increasing
What did Lotka show that would eventually create a stable age distribution? What is the equation?
That when a pop has constant natality and mortality rates, it would approach a stable age distribution
dN/dt = rN
What is the mean length of generation in terms of r?
r = ( ln R0) / G where G = 1 , r = ln R0
For mean length of generation in terms of r, define significance of r in relation to 0
r = 0, pop stable
r > 0, pop up
r < 0, pop down
Define finite rate of increase (lambda)
net reproductive rate over a certain t interval - long t interval
What is lambda equal to and what does it mean in comparison to 1
lambda = R 0
lambda = 1, stable
lambda > 1, up
lambda <1, down
Define population dispersion
pattern of spacing among individuals within a certain area (NOT DISPERSAL)
List the three main types of dispersion
Clumped Distribution
Random Distribution
Uniform Distribution
Define clumped distribution
A model of dispersion where individuals have a higher probability of being found in some area than in others = pattern
Animal example of clumped distribution
school of fish
Plant example of clumped distribution
Plants, but water in a desert
What is the process of clumped distribution
Attraction b/t individuals or attraction of individuals to a common resource - perhaps more common in areas with spotty resources
Define Uniform Distribution
A model of dispersion where the individuals are regularly spaced = pattern
Example of uniform distribution
Birds on a wire (distance to peck)
What is the process of uniform distribution
Result of antagonistic interactions b/t individuals or local depletion of resources - where individuals repel each other
Define Random distribution
A model of dispersion where the individuals have an equal chance of living anywhere within the area, cannot predict one with knowledge of another
What is the process of random distribution
A result of neutral interactions between individuals and even between them and the environment
What are the types of population growth
Exponential Pop. growth
Logistic Pop. growth
Define exponential pop growth & state what kind of pop appropriate for
Continuous pop growth in an unlimited environment appropriate for a pop w/ overlapping generations - the rate of growth keeps increasing over time
What is the equation for exponential pop growth and define the variables and state if constant
dN/ dt = r(m)N
r(m) = max per capita rate of increase - constant
N = pop size - increases
Example of exponential pop growth
Scots Pine colonizing after a glacial recession - used pollen from lake sediments and grew at exponential rates for 500 yr about 9500 years ago
Define logistic pop growth & state curve shape
As pop size increase, growth rate eventually slows and then ceases as pop size levels off, resulting in a s-shaped curve
Define carrying capacity (K)
The number of individuals of a particular pop that the environment can support
When growth stops, b=d, growth = 0
Equation for logistic pop growth and explain variables
dN/dt = r(m) *N *(1 - N/K)
r(m) = max per capita rate of increase (usually larger than r - realized per capita rate of increase)
(1- N/K) gets smaller until N=K where growth is then 0
In the logistic model, what does realized per capita rate of increase depend on
r= r(m) *(1-N/K) is dependent on the population size
In logistic growth, what is the relationship between r, r(m) and N?
When in is very small, r approx equals r(m)
As N increase, r will decrease until N=K and then r=0
It is a straight line with r decreasing as N increases
For the logistic model, compare N and K
N < K, r is positive as pop grows
N = K, r = 0 and growth stops
N > K, r is negative and pop declines
What is an example of logistic pop growth lab
Paramecium (Gause) put 20 in a tube and added constant quantity of bacteria each day as food and every 2nd day he washed away waste.
Growth was slow 5 days, rapid 5 days, then leveled off after 10 days
Example of logistic pop growth in the field
Ibex pop following successful reintroduction to switzerland; slow to increase early, mid-30s increase, level off in the 60s and then oscillations around K
What are the assumptions of the logistic model
1 - the rln b/t density and rate of increase is linear
2 - the pop has a stable age distribution initially
3 - the density has been measured in appropriate units
4 - the depressive influence of density on the rate of increase operates instantaneously without any time lags
What is an example of the density being measured in appropriate units for the logistic model?
Flies - model may be adding larger individuals at the start of growth and smaller individuals near the end - maybe it would be more accurate to measure biomass instead of flies
List the types of models of Logistic growth
Deterministic models
Stochastic models
Define deterministic models
A model of logistic growth that, given certain initial conditions, predicts one exact outcome (red line) with a clean, smooth line
Define stochastic models
A model of logistic growth that recognizes that population trends represent outcomes of many individual probabilities, with some observations higher than normal and others lower.
Use given data to create prob masses that represent a range of possible values the pop could follow
Example of stochastic model factors
1 - # of young born per female or # taken by predators
2 - flip a coin to determine # of offspring, h = 1 t = 3
Define competition
two species seek or use the same limited resource to the detriment of both