Within a given area where the scale of the area is studydependent. What is a population?. 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.
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Within a given area where the scale of the area is studydependent
What is a population?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
250 studydependent
200
150
Population size
100
50
0
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
Year 8
Year 9
Year 10
Year 11
Year 12
Time (t)
Death
Emigration
Birth
Mortality
Extrinsic
Environment
Weather
Population BiologyDescribe
Explain (Influencing factors)
Intrinsic
Original population
Population growth
=
+
+
Immigration

Death

Emigration
Birth
Nt+1 = Nt + B + I – D  E
Quantifying population growth
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)
Nonoverlapping (discrete) generations studydependent
Overlapping generations
Life cycles
Population growth potential
www.kidfish.bc.ca/caddis_cycle.htm studydependent
Life cycles – discrete generationsOften seasonally determined
Pods
Adults1
Generation 1
Eggs
Instar I
Replace
Instar II
Instar III
Adults2
Generation 2
Instar IV
R studydependent1
R1
R1
Time 1
R1
R1
R1
Differential survival
Differential reproduction
R2
R2
R2
Time 2
R2
R2
R2
R3
R3
R3
R1
R1
R1
R3
R3
R3
Time 3
Life cycles – overlapping generations
Individuals of different ages reproducing at the same time
Overlapping generations studydependent
Frequency of reproduction
Semelparous
Iteroparous
Life cycles
Nonoverlapping generations
Population growth potential
Population Life Tables studydependent
Single Reproductive Event studydependent
SEMELPAROUS: only one reproductive event in their lifetime
E.g. most invertebrates
One individual
Growth phase
Reproductive phase
PostReproductive phase
Multiple Reproductive Events
Year 1
ITEROPAROUS: multiple reproductive events over extended portions of their lives
E.g. most birds & mammals
Growth phase
Reproductive phase
PostReproductive phase
One individual
Semelparous vs Iteroparous Life CyclesYear 2
Year 1
Year 3
Year 4
Dependent on organisms life cycle: studydependent
Generation overlap & Semel/Iteroparous
Age and stage specific
Original population
Population growth
=
+
+
Immigration

Death

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

Death

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

Death

Emigration
Birth
Length of each generation
Number of young produced in each reproductive event
Quantifying population growth
LIFE TABLES
a simple method for keeping track of births, deaths, and reproductive output in a population of interest
Frequency of reproductive events
COHORT LIFE TABLE studydependent
Snapshot in time
N of Age 1
Used to estimate population growth
N of Age 2
N of Age 3
Life tables
2 ways of constructing Life tables
STATIC LIFE TABLE
compares population size from different cohorts, across the entire range of ages, at a single point in time
Time 1
Cohort 1 studydependent
Cohort 2
lx
lx
Population size (n)
Cohort 4
Cohort 3
lx
lx
Static Life Tables
COHORT LIFE TABLE studydependent
follows a group of sameaged individuals from birth (or fertilized eggs) throughout their lives
Less accurate than cohort tables
Time (t)
Considers differential probabilities at each life stage
Age 1birth
Age 1death
Life tables
2 ways of constructing Life tables
STATIC LIFE TABLE
compares population size from different cohorts, across the entire range of ages, at a single point in time
Note: For organisms that have separate sexes, life tables frequently follow only female individuals.
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 stageand the number of eggs produced by the adults.
Cohort Life TablesSimplest form:
www.kidfish.bc.ca/caddis_cycle.htm
Age classification studydependent
Cohort Life Tables
From this raw data we can calculate several LIFE HISTORY FEATURES
One generation
COUNT DATA
Age classification studydependent
Proportion of original cohort surviving to each stage
lx
Calculate by:
divide the number of individuals living at the beginning of each age (ax) by the initial number of eggs(a0)
Cohort Life TablesCalculated life history features
This data is STANDARDIZED therefore comparable between populations
...Raw data is NOT
COUNT DATA
Age classification studydependent
Calculate by:
lx  lx+1
ADVANTAGE:
Proportions can be added together to get a measure of mortalityfor different stage groups
Cohort Life Tables
Calculated life history features
Proportion of original cohort surviving to each stage
lx
DISADVANTAGE: > ax = > lx and dx values ; Therefore dxdoes not indicate the stage where mortality is most INTENSE
COUNT DATA
Age classification studydependent
CANNOT
∑
Cohort Life Tables
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: qxdoesindicate the stage where mortality is most INTENSE
Calculate by:
dx/lx
Stage specific
DISADVANTAGE:
COUNT DATA
log studydependent
p age specific survivorship, calculated as 1  qx (or ax+1 / ax): cannot be summed
Cohort Life Tables
Combining advantages of dx (can be summed) and qx (indicates mortality intensity) is K (killing power)
K
Age classification studydependent
Proportion of original cohort surviving to each stage
lx
Cohort Life Tables
Assessing the populations reproductive output
Calculated life history features
Age specific
COUNT DATA
COUNT DATA
Age classification studydependent
Proportion of original cohort surviving to each stage
lx
Cohort Life Tables
Assessing the populations reproductive output
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
Age classification studydependent
Proportion of original cohort surviving to each stage
lx
Cohort Life Tables
Assessing the populations reproductive output
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
R studydependent0 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 classification
Proportion of original cohort surviving to each stage
lx
Cohort Life Tables
Assessing the populations reproductive output
Calculated life history features
Age specific
lxmxis an important value to consider in population studies
∑ lxmx = R0
basic reproductive rate
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
Raw count data studydependent
Raw count data
Reproductive output
Life history features
∑ lxmx
Calculating population features from life tablesCan use life tables to determine characteristics about the population:
semelparous annual life cycle (T studydependentc =1 year)
1872.03
610.32
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
Generation time
BIRTH
OFFSPRING
DEATH
Tc = 3.1
TOTAL
Raw count data studydependent
Raw count data
Reproductive output
Life history features
Calculating population features from life tablesCan use life tables to determine characteristics about the population:
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 (http://www.who.int/countries/zaf/en/)
Note: time unit depends on organims being studied)
We can also calculate the mean length of life beyond any given age for the population.
Time still to live (probability)
Age 1
Death
Time still to live
Any Age
Age 2
Time still to live (probability)
Death
Death
Time still to live
Age 3
Death
Life expectancy (e studydependentx)
Calculating 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
Nonoverlapping generations studydependent
Overlapping generations
Calculating population features from life tablesCan use life tables to determine characteristics about the population:
HOW??
1 generation studydependent
N0
NT
= ∑ lxmx
Basic reproductive rate (R0)
If R0 remains constant from generation to generation, then we can also use it to predict population size several generations into the future.
R0 considers birth of new individuals
N0
N1
N2
N3
Nn
Constant R0
1 generation
2 generations
3 generations
n generations
Intrinsic growth rate (r)NonOverlapping generations
R0 converts the initial population size (N0) to the new size one generation later (NT)
NT=N0.R0
N studydependentt = 10
Nt+1 = 20
Rearrange
As for R0
If R= 1.0…no population growth
If R < 1.0…the population is declining
If R > 1.0…the population is increasing
Intrinsic growth rate (r)
Overlapping generations
Fundamental Reproductive Rate (R)
Consider birth of new individuals + survival of existing individuals
R=20/10
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
N studydependentT = N0.RT
IF t = T, then
Intrinsic growth rate (r)
Overlapping generations
NonOverlapping generations
NT=N0.R0
Combine
Nt = N0.Rt
R0 = RT
lnR0 = T.lnR
lnR0/T = lnR
But lnR = r
Can now link R0 and R
Used to project population growth in population models
r = average rate of increase/individual
takes generation time into account
COHORT LIFE TABLE studydependent
follows a group of sameaged individuals from birth (or fertilized eggs) throughout their lives
STATIC LIFE TABLES
is made from mortality data collected from a specified time period
Problems:
Life tables
2 ways of constructing Life tables
Finite SURVIVAL rates studydependent
e.g. convert annual survival (p) = 0.5, to monthly survival:
Adjusted = Observed ts/to
= 0.5 1/12
= 0.5 0.083
= 0.944
e.g. convert daily survival (p) = 0.99, to annual survival
= 0.99 365
= 0.0255
Adjusted = Observed ts/to
= 0.99 365/1
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, threemonths etc)
They have limited value in comparisons unless same units used
To convert FINITE rates at one scale to (adjusted) finite rates at another:
[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
Finite studydependentand 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