organisms at different life stages can have vastly different reproduction and mortality rates:...

Organisms at different life stages can have vastly different reproduction and mortality rates:

Juveniles: often high mortality risk and no reproduction

Mature adults: often low mortality until old age, with reproduction

Some juveniles have low mortality.

Age of first reproduction:

Mouse: 5 weeks

Rabbit: 5 months

Elephant: 5 years

Arabidopsis: 5 weeks

Scarlet Oak: 20 years

Bamboo: 100 years

Maximal life span:

Shrews: 1.5 years

Human: 122 years

Giant Tortoise: 177 years

Redwood tree: 2200 years

Litter/brood size:

Albatross: 1 eggsongbirds: 2-5 eggsPheasants: 8-18 eggs

Human: 1gophers: 1 Lion: 3-4Wolf 4-6 Pig: 10

Sea slug: up to 500,000 eggsSaguaro 10,000s of seeds Coconut: 100 seeds

Life cycle of a fir

Life cycles can be quite complex:

Sexual adult

larvae,1st instar

egg

pupae

larvae,3rd instar

larvae,2nd instar

oviposition

1st molt

2nd molt

hatching

diapause, pupation

emergence

Organize all relevant information about birth and death rates as a function of age;

Provide the data for answering questions, like:

• What is the average number of offspring that an organism produces in its life time?

• What is the average generation time of a population?

• What is the growth rate of the entire population?

Life Tables:

What is Life Table Analysis used for?

Population management:

1. If the goal is to destroy a population, which life history stage should we target to get the most bang for the buck?

2. If the goal is to conserve a population at risk, which life history stage should get the most protection?

3. If the goal is sustainable harvest: which life history stages should be exempted from being killed?

Life Tables represent “life histories”

Life history: the timing of life cycle events, particularly as relating to growth, fertility and death.

Life tables contain two sorts of data:

Fecundity schedules:

Survivorship schedules:

The average reproductive output of individuals as a function of the age of an individual.

The probabilities of surviving from birth to all ages.

Two types of fecundity schedules:Semelparous (in animals) or monocarpic (in plants) reproduction:

when organisms reproduce only once in their lifetime.

Iteroparous (in animals) or polycarpic (in plants) reproduction:when organisms reproduce more than once in their lifetime.

Marine salmon Century plant

Elephant Cherry tree

Three types of survivorship schedules:

In plants we distinguish: annuals, biennials, perennials.

An annual: sunflower

A biennial: spinach

A perennial: sequoia

Age

ln S

urvi

vors

hip

Type I: mammals with much parental care in a low risk environment.

Three types of survivorship curves:

Type II: (rare) Individuals of all ages have the same probability of dying.

Type III: Species with many, small and vulnerable young.

This is equivalent to exponential decay:

constant mortality risk throughout a lifetime

How does one collect age-specific survivorship and fecundity information

that is representative of an entire population?

HORIZONTAL METHOD:• follow the fate of a group of individuals all born at the same time (= a cohort)• record all births and deaths until the last individual died • equivalent to “longitudinal studies” in medical research• preferred method but difficult to conduct

VERTICAL METHOD:• examine the age and birth rate of a representative, random sample of the population at one point in time• reconstruct age-specific mortalities from age distributions• equivalent to “cross-sectional studies” in medical research• preferred method but difficult to conduct

Example of horizontal study:

At t0 : 1000 eggs

1 week later: 400 small tadpoles 6 months later:

50 mature frogs

4 weeks later: 100 immature frogs

2 weeks later: 200 large tadpoles

1 year later:10 mature frogs

Book keeping: (assuming post-breeding census)

Life historyinterval

Age (x) x = 1 x = 4x = 3x = 2 x = 5x=0

BIRTH DEATH OF OLDEST INDIVIDUAL

S(0) S(1) S(2) S(3) S(4) S(5) = 0

S(x): the number of survivors at the beginning of age x

Book keeping: (assuming post-breeding census)

Life historyinterval

Age (x) x = 1 x = 4x = 3x = 2 x = 5x=0

S(0) S(1) S(2) S(3) S(4) S(5) = 0

newborns

b(0) b(1) b(2) b(3) b(4)

b(x): offspring produced per female during the interval from x to x+1 and still alive at the end of the interval.

Life Table:

x S(x) b(x)

0 1000 0

1 800 2

2 400 3

3 100 1

4 0 0

No of survi

vors

to start

of interva

l

Avera

ge capita

fecu

ndity of

survi

vors

during th

e interva

l

Age at start

of interva

l

Life Table:

x S(x) b(x) l(x)

0 1000 0

1 800 2

2 400 3

3 100 1

4 0 0

1

0.8

0.1

0

0.4

Step 1: Calculate survivorship at the beginning of each age:

)0(

)()(S

xSxl

Life Table:

x S(x) b(x) l(x) g(x)

0 1000 0 1

1 800 2 0.8

2 400 3 0.4

3 100 1 0.1

4 0 0 0

0.8

0.5

0

0.25

Step 2: Calculate survivorship from one age class to the next:

)(

)1()(

xS

xSxg

Life Table:

x S(x) b(x) l(x) g(x) l(x)b(x)

0 1000 0 1 0.8

1 800 2 0.8 0.5

2 400 3 0.4 0.25

3 100 1 0.1 0

4 0 0 0

0

1.6

0.1

1.2

= 2.9

R0 = 2.9

Step 3: Calculate the net reproductive rate of an individual over its lifetime:

)()(0 xbxlR

The average contribution of an individual to the future generation.

Partitioning overall population growth rates into contributions made by members of specific age classes is very useful for purposes of population genetics and

population management.

Definition of Reproductive Value:

Life Table:

x S(x) b(x) l(x) g(x) l(x)b(x)

0 1000 0 1 0.8

1 800 2 0.8 0.5

2 400 3 0.4 0.25

3 100 1 0.1 0

4 0 0 0

0

1.6

0.1

1.2

= 2.9

R0 = 2.9

Step 3: Calculate the net reproductive rate of an individual over its lifetime:

)()(0 xbxlR

Life Table:

x S(x) b(x) l(x) g(x) l(x)b(x) l(x)b(x)x

0 1000 0 1 0.8 0

1 800 2 0.8 0.5 1.6

2 400 3 0.4 0.25 1.2

3 100 1 0.1 0 0.1

4 0 0 0 = 2.9

0

1.6

0.3

2.4

= 4.3

R0 = 2.9G = 1.48 yrs

Step 4: Calculate the generation time:

)()(

)()(

xbxl

xxbxlG

The average age of breeding females (e.g. of new-born’s mothers)

It is the average length of time between successive generations.

Definition of Generation Time:

Life Table:

x S(x) b(x) l(x) g(x) l(x)b(x) l(x)b(x)x

0 1000 0 1 0.8 0 0

1 800 2 0.8 0.5 1.6 1.6

2 400 3 0.4 0.25 1.2 2.4

3 100 1 0.1 0 0.1 0.3

4 0 0 0 = 2.9 = 4.3

R0 = 2.9G = 1.48 yrsr = 0.72 yrs-1

Step 5: Estimate the population growth rate:

G

Rr

)ln( 0

Plug & Play

Excel Worksheets:

• A life table

Life Table Analysis makes many assumptions:

1. Mortality and fecundity depend only on the age of the organism.

2. Age-specific mortality and fecundity are constant through time.

3. To determine the population growth rate a very specific age structure must be assumed: the stable age distribution.

The age structure of a population refers to the way a population is divided among different age classes.

The age structure is often represented in an age structure pyramid. is is often It is the average length of time between

successive generations.

Definition of Age Structure:

It is a relative age distribution of a population that will not change over time.

The growth rate of a population can be estimated by life table analysis only if the population has a stable age structure.

Definition of Stable Age Structure:

age Individuals        

(years) left in cohort b(x) l(x) l(x)b(x) l(x)b(x)x

0 1000 0      

1 200 3      

2 150 6      

3 120 6      

4 70 4      

5 50 2      

6 0 0      

Life Table for feral cats in San Marcos

1. Determine the population’s r-value

2. Assume that a spay/neuter program prevents 50% of cat pregnancies. What would the r be?

3. What is the likely long-term consequence of the spay/neuter program?

Summary:

1. Life tables organize information about fecundity and mortality schedules for populations. They usually only track females.

2. There are mathematical fomulae that one can use to calculate, based on life tables,

stable age distributions of populations population growth rates the average generation times the reproductive values of females of a certain age.

3. This analysis has application in virtually any task of population control, including the protection of endangered species or the control of invasive species, and is basic to understand the evolution of life history strategies.