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Within a given area where the scale of the area is study-dependent. 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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What is a population

Within a given area where the scale of the area is study-dependent

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


Population biology

250 study-dependent

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 Biology

Describe

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)


Non-overlapping (discrete) generations study-dependent

Overlapping generations

Life cycles

Population growth potential


Life cycles discrete generations

www.kidfish.bc.ca/caddis_cycle.htm study-dependent

Life cycles – discrete generations

Often seasonally determined

Pods

Adults1

Generation 1

Eggs

Instar I

Replace

Instar II

Instar III

Adults2

Generation 2

Instar IV


R study-dependent1

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 study-dependent

Frequency of reproduction

Semelparous

Iteroparous

Life cycles

Non-overlapping generations

Population growth potential


Population Life Tables study-dependent


Semelparous vs iteroparous life cycles

Single Reproductive Event study-dependent

SEMELPAROUS: only one reproductive event in their lifetime

E.g. most invertebrates

One individual

Growth phase

Reproductive phase

Post-Reproductive 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

Post-Reproductive phase

One individual

Semelparous vs Iteroparous Life Cycles

Year 2

Year 1

Year 3

Year 4


Dependent on organisms life cycle: study-dependent

Generation overlap & Semel/Iteroparous

Age and stage specific

Original population

Population growth

=

+

+

Immigration

-

Death

-

Emigration

Birth

Quantifying population growth

Differential reproduction

Differential survival


Pods study-dependent

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 study-dependent

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 study-dependent

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 study-dependent

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 study-dependent

Cohort 2

lx

lx

Population size (n)

Cohort 4

Cohort 3

lx

lx

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


COHORT LIFE TABLE study-dependent

follows a group of same-aged 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.


Cohort life tables

  • annual life cycle study-dependent

  • 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 stageand the number of eggs produced by the adults.

Cohort Life Tables

Simplest form:

www.kidfish.bc.ca/caddis_cycle.htm


Age classification study-dependent

Cohort Life Tables

From this raw data we can calculate several LIFE HISTORY FEATURES

One generation

COUNT DATA


Cohort life tables1

Age classification study-dependent

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 Tables

Calculated life history features

This data is STANDARDIZED therefore comparable between populations

...Raw data is NOT

COUNT DATA


Age classification study-dependent

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 study-dependent

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 study-dependent

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 study-dependent

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 study-dependent

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 study-dependent

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 study-dependent0 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


Calculating population features from life tables

Raw count data study-dependent

Raw count data

Reproductive output

Life history features

∑ lxmx

Calculating population features from life tables

  • 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:


Cohort generation time t c

semelparous annual life cycle (T study-dependentc =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

  • 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 bylengths of time to offspring production/the total offspring produced by the survivors

Tc = 3.1

TOTAL


Calculating population features from life tables1

Raw count data study-dependent

Raw count data

Reproductive output

Life history features

Calculating population features from life tables

  • 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:


Life expectancy e x
Life expectancy (e study-dependentx)

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 study-dependentx)

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


Calculating population features from life tables2

Non-overlapping generations study-dependent

Overlapping generations

Calculating population features from life tables

  • 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??


Intrinsic growth rate r

1 generation study-dependent

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)

Non-Overlapping generations

R0 converts the initial population size (N0) to the new size one generation later (NT)

NT=N0.R0


N study-dependentt = 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 study-dependentT = N0.RT

IF t = T, then

Intrinsic growth rate (r)

Overlapping generations

Non-Overlapping 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 study-dependent

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:

Life tables

2 ways of constructing Life tables

  • Most organisms have complex life histories (overlapping generations)

  • Not always possible or feasible to follow a single cohort from birth to death


Finite SURVIVAL rates study-dependent

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, 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:

[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 study-dependentand 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


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