1. What is a population?
Within a given area where the scale of the area is study-dependent
Localised group of individuals of the same species
e.g. population of aphids on a leaf
e.g. population of baboons on the Cape Peninsula
e.g. population of orchids in a 10km2 area of the Peninsula

2. Population Biology Describe Explain (Influencing factors)50
100
150
200
250
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
Year 8
Year 9
Year 10
Year 11
Year 12
Population size
Time (t)
Describe
Explain (Influencing factors)
Intrinsic
Birth
Mortality
Death
Emigration
Extrinsic
Environment
Weather

3. Quantifying population growth
Dependent on organisms life cycle
Overlapping and non-overlapping
Birth
Death
Immigration
Emigration
Population growth + - =
Original population
Nt+1 = Nt + B + I – D - E
N = population size
t = time period (eg. Days, months, years…depends on study organism)
Populations grow IF (B + I) > (D + E)
Populations shrink IF (D + E) > (B + I)

4. Non-overlapping (discrete) generations
Life cycles
Non-overlapping (discrete) generations
Population growth potential
Overlapping generations

5. Life cycles – discrete generations
Often seasonally determined
Pods
Adults1
Generation 1
Eggs
Instar I
Replace
Instar II
Instar III
Adults2
Generation 2
Instar IV

6. Differential reproduction Differential survival
Life cycles – overlapping generations R1
Time 1
Differential reproduction
Differential survival R2 R1
Time 2
Individuals of different ages reproducing at the same time R3 R1
Time 3 R2

7. Overlapping generations
Life cycles
Overlapping generations
Non-overlapping generations
Population growth potential
Frequency of reproduction
Semelparous
Iteroparous

8. Population Life Tables

9. Semelparous vs Iteroparous Life Cycles
Reproductive phase
Growth phase
Post-Reproductive phase
Single Reproductive Event
One individual
E.g. most invertebrates
SEMELPAROUS: only one reproductive event in their lifetime
Year 1
Reproductive phase
Growth phase
Post-Reproductive phase
Multiple Reproductive Events
One individual
E.g. most birds & mammals
ITEROPAROUS: multiple reproductive events over extended portions of their lives
Year 1
Year 2
Year 3
Year 4

10. Differential reproduction Differential survival
Quantifying population growth
Dependent on organisms life cycle:
Generation overlap & Semel/Iteroparous
Age and stage specific
Birth
Death
Immigration
Emigration
Population growth + - =
Original population
Differential reproduction
Differential survival

11. Adults
M F
Pods
Eggs
Instar I
Instar II
Instar III
Instar IV
P=0
7.3 11
0.079
0.72
0.78
0.76
0.69
Adults Nt
Nt+1
Seeds
Nt.f
Seedlings
Nt.f.g
Fecundity (f)
Different ages and stage classes have different probabilities of survival and different probabilities of successful reproduction
BIRTH
Germinate (g)
Survival (p)
SURVIVAL
Survival to maturity (s)
Nt+1 = (Nt.p) + (Nt.f.g.s)

12. Tool for quantifying population growth
Dependent on organisms life cycle:
Generation overlap & Semel/Iteroparous
Birth
Death
Immigration
Emigration
Population growth + - =
Original population
Tool for quantifying population growth
Age and stage specific
Differential reproduction
Differential survival

13. Quantifying population growth
LIFE TABLES
a simple method for keeping track of births, deaths, and reproductive output in a population of interest
Birth
Death
Immigration
Emigration
Population growth + - =
Original population
Number of young produced in each reproductive event
Length of each generation
Frequency of reproductive events

14. 2 ways of constructing Life tables
COHORT LIFE TABLE
STATIC LIFE TABLE
compares population size from different cohorts, across the entire range of ages, at a single point in time
Snapshot in time
Time 1
N of Age 1
N of Age 2
N of Age 3
Used to estimate population growth

15. Static tables make two important assumptions:
Static Life Tables
Static tables make two important assumptions:
the population has a stable age structure (i.e. the proportion of individuals in each age class does not change from generation to generation)
the population size is stationary , or nearly stationary lx
Cohort 1 lx
Cohort 2
Population size (n) lx
Cohort 4 lx
Cohort 3

16. 2 ways of constructing Life tables
COHORT LIFE TABLE
follows a group of same-aged individuals from birth (or fertilized eggs) throughout their lives
STATIC LIFE TABLE
compares population size from different cohorts, across the entire range of ages, at a single point in time
Less accurate than cohort tables
Age 1birth
Age 1death
Time (t)
Considers differential probabilities at each life stage
Note: For organisms that have separate sexes, life tables frequently follow only female individuals.

17. Cohort Life Tables Simplest form: annual life cycle
Semelparous (only one breeding season in its life time)
no overlap of generations
Animal with
To make a life table for this simple life history, we need only count (or estimate) the population size at each life history stage and the number of eggs produced by the adults.

18. From this raw data we can calculate several LIFE HISTORY FEATURES
Cohort Life Tables
Age classification
From this raw data we can calculate several LIFE HISTORY FEATURES
One generation
COUNT DATA

19. Cohort Life Tables Calculated life history features Calculate by:
Age classification
Proportion of original cohort surviving to each stage lx
Calculated life history features
Calculate by:
divide the number of individuals living at the beginning of each age (ax) by the initial number of eggs (a0)
This data is STANDARDIZED therefore comparable between populations
...Raw data is NOT
COUNT DATA

20. Proportion of original cohort surviving to each stage
Cohort Life Tables
Age classification
Calculated life history features
Proportion of original cohort surviving to each stage lx
DISADVANTAGE: > ax = > lx and dx values ; Therefore dx does not indicate the stage where mortality is most INTENSE
Calculate by:
lx - lx+1
ADVANTAGE:
Proportions can be added together to get a measure of mortality for different stage groups
COUNT DATA

21. Proportion of original cohort surviving to each stage
Cohort Life Tables
Age classification
Calculated life history features
Proportion of original cohort surviving to each stage lx
qx is the fraction of the population dying at each stage
ADVANTAGE: qx does indicate the stage where mortality is most INTENSE
Calculate by:
dx/lx
Stage specific ∑
CANNOT
DISADVANTAGE:
COUNT DATA

22. Cohort Life Tables
Combining advantages of dx (can be summed) and qx (indicates mortality intensity) is K (killing power) K
p age specific survivorship, calculated as 1 - qx (or ax+1 / ax): cannot be summed
log

23. Proportion of original cohort surviving to each stage
Cohort Life Tables
Assessing the populations reproductive output
Age classification
Proportion of original cohort surviving to each stage lx
Calculated life history features
Age specific
COUNT DATA
COUNT DATA

24. Proportion of original cohort surviving to each stage
Cohort Life Tables
Assessing the populations reproductive output
Age classification
Proportion of original cohort surviving to each stage lx
Calculated life history features
Age specific
mx is the eggs produced per surviving individual at each age or individual fecundity
Calculate by:
Fx/ax
COUNT DATA
COUNT DATA

25. Proportion of original cohort surviving to each stage
Cohort Life Tables
Assessing the populations reproductive output
Age classification
Proportion of original cohort surviving to each stage lx
Calculated life history features
Age specific
The number eggs produced per original individual at each age (lxmx)
Calculate by:
lx*mx
COUNT DATA
COUNT DATA

26. Proportion of original cohort surviving to each stage
Cohort Life Tables
Assessing the populations reproductive output
Age classification
Proportion of original cohort surviving to each stage lx
Calculated life history features
R0 is the population’s replacement rate:
If R0 = 1.0…no population growth
If R0 < 1.0…the population is declining
If R0 > 1.0…the population is increasing
Age specific
lxmx is an important value to consider in population studies
basic reproductive rate
∑ lxmx = R0
individuals produced for every individual in every generation
If only females in the life table then: individuals produced for every female in every generation
COUNT DATA
COUNT DATA

27. Calculating population features from life tables
Raw count data
Reproductive output
Life history features
R0 – the basic reproductive rate
Tc = cohort generation time
ex = life expectancy
r = intrinsic growth rate
Can use life tables to determine characteristics about the population:
∑ lxmx

28. Cohort generation time (Tc)
Cohort generation time (Tc) can be defined as the average length of time between when an individual is born and the birth of its offspring.
Tc is quite easy to obtain from our first example…
But Tc is less obvious for more complex life cycles – must be calculated
Calculate Tc:
Calculate the length of time to offspring production for each age class
Add all the lengths of time to offspring production for the entire cohort
Calculate the total offspring produced by the survivors
Divide by lengths of time to offspring production/the total offspring produced by the survivors
BIRTH
DEATH
OFFSPRING
Generation time
semelparous annual life cycle (Tc =1 year)
610.32
Tc = 3.1
TOTAL

29. Calculating population features from life tables
Raw count data
Reproductive output
Life history features
R0 – the basic reproductive rate
Tc = cohort generation time
ex = life expectancy
r = intrinsic growth rate
Can use life tables to determine characteristics about the population:

30. Time still to live (probability) Time still to live (probability)
Life expectancy (ex)
Life expectancy = the probability of living ‘x’ amount of time beyond a given age.
Most commonly quoted as the life expectancy at birth, e.g.,
life expectancy for South Africans females = 50 yrs, and for South African males = 55 years (
Note: time unit depends on organims being studied)
We can also calculate the mean length of life beyond any given age for the population.
Age 1
Age 2
Age 3
Time still to live (probability)
Time still to live
Death
Any Age
Time still to live (probability)
Death

31. NB. Units of e must be the same as those of x
Life expectancy (ex)
Calculating ex:
Calculate Lx - number of surviving individuals in consecutive stage/age classes
Calculate Tx - the total number of living individuals at age ‘x’
Calculate ex
NB. Units of e must be the same as those of x
Thus if x is measured in intervals of 3 months, then ex must be multiplied by 3 to give life expectancy in terms of months

32. Calculating population features from life tables
Non-overlapping generations
R0 – the basic reproductive rate
Tc = cohort generation time
ex = life expectancy
r = intrinsic growth rate
Can use life tables to determine characteristics about the population:
HOW??
Overlapping generations

33. Intrinsic growth rate (r)
Non-Overlapping generations
= ∑ lxmx
R0 considers birth of new individuals
Basic reproductive rate (R0) N0 NT
1 generation
R0 converts the initial population size (N0) to the new size one generation later (NT)
NT=N0.R0
If R0 remains constant from generation to generation, then we can also use it to predict population size several generations into the future. N0 N1
1 generation N2 N3 Nn
2 generations
3 generations
n generations
Constant R0

34. Intrinsic growth rate (r)
Overlapping generations
Rearrange
Fundamental Reproductive Rate (R)
Consider birth of new individuals + survival of existing individuals
If R= 1.0…no population growth
If R < 1.0…the population is declining
If R > 1.0…the population is increasing
As for R0
R=20/10
Nt = 10
Nt+1 = 20
R=2
Population size at t+1 = N0.R
N1 = N0.R1
Nt = N0.Rt
Population size at t+2 = N0.R.R
N2 = N0.R2
Population size at t+3 = N0.R.R.R
N3 = N0.R3

35. Intrinsic growth rate (r)
Non-Overlapping generations
Overlapping generations
NT=N0.R0
Combine
Nt = N0.Rt
NT = N0.RT
IF t = T, then
Can now link R0 and R
R0 = RT
lnR0 = T.lnR
lnR0/T = lnR
But lnR = r
Used to project population growth in population models
r = average rate of increase/individual
takes generation time into account

36. 2 ways of constructing Life tables
COHORT LIFE TABLE
follows a group of same-aged individuals from birth (or fertilized eggs) throughout their lives
STATIC LIFE TABLES
is made from mortality data collected from a specified time period
Problems:
Most organisms have complex life histories (overlapping generations)
Not always possible or feasible to follow a single cohort from birth to death

37. They have limited value in comparisons unless same units used
Finite and instantaneous rates
The values of p, q hitherto collected are FINITE rates…their units of time = units of time for x (months, days, three-months etc)
They have limited value in comparisons unless same units used
To convert FINITE rates at one scale to (adjusted) finite rates at another:
Finite SURVIVAL rates
[Adjusted FINITE] = [Observed FINITE] ts/to
ts = Standardised time interval (e.g. 30 days, 1 day, 365 days, 12 months etc)
to = Observed time interval
e.g. convert annual survival (p) = 0.5, to monthly survival:
Adjusted = Observed ts/to
= 0.5 1/12 =
= 0.944
e.g. convert daily survival (p) = 0.99, to annual survival
Adjusted = Observed ts/to
= /1 = =

38. Finite and instantaneous rates
INSTANTANEOUS MORTALITY rates = Loge (FINITE SURVIVAL rates)
ALWAYS negative
Finite Mortality Rate = 1 – Finite Survival rate
Finite Mortality Rate = 1.0 – e Instantaneous Mortality Rate
MUST SPECIFY TIME UNITS