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Lecture 5
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From last lecture we reviewed how one develops a demographic profile of a population to study its
behavior.
Defined terminology to describe different breeding patterns and constructed a life table to predict rates of
change in the population from one time to the next.
Defined generation time and noted how it could be linked with net reproductive rate to determine the rate of
increase (or decrease) of a population.
Basically the bookkeeping necessary to study the effects of environment on a population.
Today’s lecture will further investigate how one goes about deriving life table information:
Demography (continued)
Patterns of survivorship in populations
I - low juvenile mortality - associated with high degree of parental care, high mortality (senescence) at oldest
ages. Example: mammals.
II – Constant mortality, independent of age.
Examples: birds, lizards.
III. High juvenile mortality (associated with organisms which have little or no parental care).
Examples: low parental care – little parental investment.
How does one estimate demographic parameters, i.e. l(x) and m(x)?
Methods for estimating life-table statistics from field populations:
Vertical, or cohort method – follow group of individuals born at same time through all ages until death. In
practice this is very difficult to do if organisms are long-lived.
Assumptions:
1) No emigration or immigration.
2) Sample being followed is representative of entire population.
Two procedures:
1) Follow survival, problem is it combines both deaths and emigration.
2) Unlocated individuals counted as deaths
Static or horizontal method – sample pop at 1 time & infer l(x), m(x) pattern from present age structure & pop
size.
Examples in fish population age structure
Comparison of cohort vs. static method in human data. Krebs page 173.
Cohort and static will be identical if the environment (i.e. factors influencing birth and death rates) remain the
same.
Also if the intrinsic rate of increase is greater than, or less than 0, l(x) estimates may be either underestimated or
overestimated in either a static or cohort approach..
So, if r>0, in an expanding population there will be more individuals in younger age classes over time. This will
tend to underestimate l(x).
If r<0, fewer individuals in younger age classes, would overestimate l(x).
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Bottom line: often difficult to get accurate data to estimate population parameters, cohort approach is the best,
but may have limited use.
Utility in estimating r in laboratory setting – can provide insight into how environment may influence r.
Examples from Krebs page 182-183.
Should also note that the relationship between population size and r is loose. Rare species may have high r and
common species may have low r.
A species could be abundant with a low r if survival rates are high (e.g. elephants).
Conversely, a species could have a potentially high r yet only maintain a low population if the potential to
increase is not realized – e.g. parasites produce huge numbers of offspring but high survivorship only occurs
infrequently.
Populations can be characterized by their patterns of age distribution
Age distributions:
When birth and death rates are constant the pattern of growth rate can be characterized as having a stable age
distribution.
Defined as Cx = proportion of individuals in the age category x to x+1 in a population increasing geometrically.
Such that Cx =lambda-xlx/sum lambda -ilI,
Where,
 = er = finite rate of increase
lx = survivorship function from life table
x, i= subscripts indicating time
see Krebs page187 for population =er =e0.881=2.413
Age (x)
0
1
2
3
4
lx
1.0
1.0
1.0
1.0
0.0
lambda-x
1.0
0.4144
0.1717
0.1717
0.0295
lambda -xlx
1.0
0.4144
0.1717
0.01717
0.0
Sum= 1.6572
So, to calculate proportion in age (o) class:
C0 = lambda-0l0/sum-ilI = (1.0)(1.0) / 1.6572 = 0.6035
C1= (0.4144) (1.0)/1.6572
C2= 0.104
C3 = 0.043
C0 + C1+C2+C3 = 1.00
So if the lx,mx parameters remains constant, the proportion of individuals in each age class will remain constant.
Example, handout
Here we see that when the lx, mx parameters are constant the proportion of the population in each age group
rapidly leads to some stable proportion.
Here, @t No=900, n1=300, n2=100
we can calculate the population of No at t+1 using the age-specific fecundity values.
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Where m(0) =0.5
m(1)=1.0
m(2)=0.75
so, population of No @ t+1:
we sum all the births of each age class from time t
No x 0.5 + N1 x 1 + N2 x 0.75
= 900 x 0.5 + 300 x 1 + 100 x 0.75 = 825
to calculate population size in other age classes at t+1, we use the survivorship estimates:
l(1)= 0.666,
l(2) =0.333
so, N1 @t+1
we take,
No x l(1)= 900 x 0.666 = 600 individuals in N1 @t+1
N(1) x l(2) = 300 x 0.333 = 100 individuals in N1 @t+1
Over time this leads to a stable age distribution if the parameters l(x) and m(x) remain constant.
Stable age distribution is different from stationary age distribution – here not only does the proportion of each
age class remain constant but the absolute number of individuals in each age category remains constant as well.
For this to happen the number of births must equal the number of deaths in each generation.
Examples from Krebs (page 189) showing stationary population in Denmark.
Historically demographic life tables track population change using age-related schedules for births and deaths.
This approach works well for cohorts of many plants and animals which develop synchronously through various
life stages – seeds, larvae, juvenile and adult.
For many other organisms growth rates can vary enormously among individuals in the population. This can
result in a poor correlation between age and probability of mortality and fecundity. These differences between
individuals can result from either genetic and/or environmental variation.
Often the fate of individuals can be better predicted by size than by age because:
 Large individuals can be more fecund (e.g.
Invertebrates/fish/plants)
 Small individuals can have higher rates of mortality, independent of age.
Demographic models based on size rather than age are particularly useful in describing the population dynamics
of clonal organisms (i.e. organisms that reproduce asexually, although they may also reproduce sexually).
For unitary organisms (genetically unique individuals) - growth is usually determinate and
survivorship/fecundity is related to size.
For modular organisms (subunits are genetically identical) - growth is indeterminate and
survivorship/fecundity is size-dependent (tend to be immortal). Examples include many species of stony corals,
plants, insects such as aphids (parthenogenic reproduction).
For evolutionary considerations : Genet – aggregation or composition of genetically identical subunits. A
ramet is a subunit.
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Think of modular organisms as clones. The individual is the entire clone which is comprised of clonal units.
These organisms, while they reproduce asexually, can also reproduce sexually.
It is possible to construct a demographic model to predict population structure of subunits but in practice it is
often difficult because one needs to be able to distinguish nonclonemates from clonemates. With growing
refinement in molecular analyses it is becoming routine to conduct rapid, reliable screening of individuals.
However, still expensive.
Evolutionary interpretation of lx, mx difficult as yet for clonal organisms. Particularly when clonal organism
reproduces sexually as well as asexually and fecundity is related to clonal size.
Examples of age-based, size/age-based and size based models.
Data for corals: Hughes study in Jamaica. Assessed size class structure based on observed transition
probabilities from one size to another. Changes based on effects of storms.
Calm – fewer clonal fragmentation events
Stormy – many fragmentation events
Size distribution of fragments were observed on different reefs subject