Scaling

of

offspring

number

and

mass

to

plant

and

animal

size

model

and

meta-analysis

The

scaling

of

reproductive

parameters

to

body

size

is

important

for

understanding

ecological

and

evolutionary

patterns

Here

we

derived

allometric

relationships

for

the

number

and

mass

of

seeds

eggs

and

neonates

from

an

existing

model

on

population

production

In

a

separate

meta-analysis

we

collected

empirical

regressions

on

offspring

mass

and

number

covering

different

taxa

and

various

habitats

The

literature

review

served

as

a

validation

of

the

model

whereas

vice

versa

consistency

of

isolated

regressions

with

each

other

and

related

ecological

quantities

was

checked

with

the

model

The

total

offspring

mass

delivered

in

a

reproductive

event

scaled

to

adult

size

with

slopes

in

the

range

of

about

to

Exponents

for

individual

seed

egg

and

neonate

mass

varied

around

for

most

heterotherms

and

between

and

for

most

homeotherms

The

scaling

of

the

progeny

number

released

in

a

sowing

clutch

or

litter

was

opposite

to

that

of

their

size

The

linear

regressions

fitted

into

a

triangular

envelope

where

maximum

offspring

mass

is

limited

by

the

size

of

the

adult

Minimum

seed

and

egg

size

scaled

with

weight

exponents

of

approximately

up

to

These

patterns

can

be

explained

by

the

influence

of

parents

on

the

fate

of

their

offspring

covering

the

continuum

of

r-strategists

-LRB-

pelagic

aquatic

arial

most

invertebrates

heterotherms

-RRB-

and

K-strategists

-LRB-

littoral

terrestrial

some

invertebrates

homeotherms

-RRB-

Introduction

Scaling

of

processes

and

patterns

to

body

size

has

fascinated

biologists

for

centuries

-LRB-

e.g.

Peters

Damuth

-RRB-

Plant

and

animal

characteristics

have

been

correlated

to

organisms

body

mass

-LRB-

m

-RRB-

by

simple

scaling

relationships

of

the

form

a

mb

or

if

log

transformed

log

-LRB-

a

-RRB-

b

log

-LRB-

m

-RRB-

Properties

include

various

reproductive

parameters

such

as

the

mass

and

number

of

the

offspring

important

for

understanding

life

history

strategies

of

species

The

scaling

of

reproduction

reflects

several

important

trade-offs

e.g.

investment

of

energy

in

somatic

versus

gonadic

growth

in

continuous

or

intermittent

release

and

in

many

small

or

a

few

large

offspring

Studies

have

derived

empirical

regressions

for

offspring

mass

and

number

within

one

taxon

-LRB-

see

review

by

Peters

-RRB-

In

addition

several

partly

contradictive

physical

biochemical

and

ecological

constraints

related

to

parental

energy

investment

have

been

hypothesized

to

be

responsible

for

the

observed

patterns

-LRB-

May

Gordon

Reiss

Charnov

and

Downhower

Hendry

et

al.

Charnov

Aarssen

-RRB-

Although

the

trade-offs

in

reproductive

investment

reflect

universal

dilemmas

that

every

species

has

to

face

most

work

so

far

has

covered

either

several

progeny

characteristics

within

a

single

species

group

or

a

single

offspring

parameter

within

at

most

two

taxa

-LRB-

Moles

et

al.

Grubb

et

al.

-RRB-

In

the

present

paper

we

will

focus

on

the

relationship

of

offspring

mass

and

number

to

adult

weight

for

miscellaneous

groups

of

species

The

aim

is

to

obtain

a

set

of

straightforward

equations

that

are

coherent

with

allometric

theory

and

underpinned

by

empirical

regressions

available

in

literature

To

this

end

we

will

first

derive

body-size

functions

for

the

mass

and

number

of

offspring

delivered

in

a

reproductive

event

which

comply

with

allometric

macroecology

-LRB-

e.g.

West

et

al.

Hendriks

-RRB-

Next

we

will

compare

the

acquired

relationships

to

independent

empirical

regressions

collected

in

a

meta-analysis

Separating

model

development

and

testing

allows

for

a

comparison

of

theoretical

and

empirical

evidence

reducing

weaknesses

of

both

In

this

approach

model

predictions

of

e.g.

offspring

mass

are

underpinned

by

independent

measurements

Likewise

isolated

empirical

regressions

for

this

reproductive

parameter

are

checked

for

consistency

with

body-size

dependence

of

related

ecological

factors

such

as

population

production

or

survival

In

our

analysis

we

will

seek

a

balance

between

model

transparency

and

accuracy

needed

for

underpinning

assumed

mechanisms

and

identifying

exceptions

The

equations

are

not

intended

to

cover

detailed

or

speculative

differences

observed

in

empirical

regressions

for

sufficient

taxa

In

our

interpretation

we

will

follow

the

classical

distinction

between

r-strategists

and

K-strategists

-LRB-

MacArthur

and

Wilson

Pianka

-RRB-

as

well

as

more

recent

applications

thereof

-LRB-

Winemiller

and

Rose

McCann

and

Shuter

Cox

and

Moore

-RRB-

However

it

should

be

emphasized

that

the

traditional

classification

of

many

small

offspring

versus

few

large

offspring

as

used

in

the

present

paper

is

no

more

than

a

convenient

way

to

structure

the

discussion

Materials

and

methods

Regression

collection

and

treatment

Allometric

regressions

derived

from

data

before

were

collected

from

an

extensive

review

-LRB-

Peters

-RRB-

Papers

published

afterwards

were

obtained

by

screening

books

and

by

an

electronic

literature

search

in

Web

of

Science

in

All

body-size

correlations

acquired

for

the

meta-analysis

were

checked

in

the

original

papers

Collection

and

treatment

of

data

by

the

authors

was

assumed

to

be

adequate

Where

multiple

types

of

regressions

were

reported

we

took

the

least-squares

equations

to

increase

compatibility

with

the

other

studies

If

regression

characteristics

were

not

given

or

suspected

to

be

wrong

we

derived

them

from

the

original

data

or

digitized

graphs

To

allow

for

comparison

all

values

were

converted

to

fresh

biomass

using

dry

wet

weight

fractions

A

database

containing

dry

matter

fractions

of

species

collected

by

the

present

authors

for

various

purposes

yielded

averages

-LRB-

with

confidence

intervals

-RRB-

of

-LRB-

-RRB-

for

herbs

-LRB-

-RRB-

for

invertebrates

-LRB-

-RRB-

for

cold-blooded

vertebrates

and

-LRB-

-RRB-

for

warm-blooded

vertebrates

In

addition

the

literature

reports

means

of

for

wood

for

fruit

for

seeds

for

insects

for

marine

invertebrates

for

fish

and

for

birds

and

mammals

-LRB-

Peters

Suzuki

-RRB-

Although

the

samples

may

be

somewhat

biased

towards

particular

taxa

average

levels

do

not

deviate

substantially

In

the

present

analysis

we

therefore

used

dry

wet

weight

fractions

of

for

fruits

forbs

herbs

and

invertebrates

of

for

cold-blooded

vertebrates

of

for

warm-blooded

vertebrates

of

for

shrubs

and

trees

-LRB-

wood

and

leaves

together

-RRB-

and

of

for

seeds

Differences

between

species

around

these

values

have

on

average

a

negligible

influence

on

the

intercept

of

the

regressions

Even

more

apparent

conversion

does

not

affect

the

slope

of

the

allometric

relationships

Seeds

mass

was

multiplied

by

to

arrive

at

the

fresh

weight

of

sprouts

with

a

water

content

that

is

comparable

to

that

of

eggs

and

neonates

Since

total

plant

weight

is

not

used

as

the

independent

variable

for

vegetation

regressions

we

took

the

closest

alternatives

being

the

above-ground

or

stem

mass

In

one

study

on

insects

animal

size

was

expressed

on

a

length

basis

instead

of

a

weight

basis

-LRB-

Berrigan

-RRB-

For

these

regressions

length

-LRB-

m

-RRB-

was

converted

to

weight

-LRB-

kg

-RRB-

as

mass

assuming

that

the

total

size

equals

times

the

elythra

length

and

twice

the

abdomen

length

Rate

constants

for

reproduction

of

plants

were

reported

as

annual

standing

reproductive

mass

delivered

by

all

plants

including

both

reproducing

and

non-reproducing

individuals

We

assumed

that

the

seed

and

fruit

mass

are

renewed

each

year

For

animals

total

clutch

mass

reflected

the

total

reproductive

mass

released

in

an

event

or

present

in

ovaries

sometimes

calculated

in

the

original

studies

as

a

product

of

the

total

number

of

eggs

-LRB-

neonates

-RRB-

in

a

clutch

-LRB-

litter

-RRB-

the

number

of

eggs

per

clutch

-LRB-

neonates

per

litter

-RRB-

and

the

egg

-LRB-

neonate

-RRB-

weight

To

allow

for

comparison

between

plants

invertebrates

cold-blooded

vertebrates

and

warm-blooded

vertebrates

we

calculated

the

arithmetic

average

of

all

slopes

-LRB-

b

-RRB-

reported

for

each

taxonomic

group

To

correct

for

differences

in

the

amount

of

information

included

in

the

regressions

we

also

computed

an

average

weighted

by

the

number

of

data

For

instance

the

weighted

average

of

a

regression

with

b

and

n

and

another

with

b

and

n

was

calculated

to

be

As

we

are

interested

in

both

the

absence

and

presence

of

links

to

organism

mass

weak

and

insignificant

correlations

were

included

in

the

analysis

as

well

Where

used

however

they

will

be

explicitly

mentioned

in

the

text

Model

development

The

relationship

of

offspring

mass

and

size

to

adult

weight

can

also

be

derived

theoretically

from

previous

modeling

efforts

-LRB-

Hendriks

-RRB-

The

starting

point

in

this

model

is

production

because

coefficients

and

slopes

of

allometric

regressions

for

this

parameter

differ

only

slightly

for

various

groups

of

species

The

rate

constant

for

population

turnover

-LRB-

production

kp

-RRB-

measured

as

the

production/biomass

ratio

-LRB-

P/B

-RRB-

-LRB-

kg

kg

day

-RRB-

is

related

to

adult

mass

-LRB-

m

-RRB-

as

The

exponent

-LRB-

κ

-RRB-

was

close

to

for

a

wide

range

of

cold-blooded

species

but

tended

to

be

somewhat

higher

for

homeotherms

-LRB-

Peters

Hendriks

-RRB-

The

coefficient

-LRB-

γp

-RRB-

represents

the

intercept

at

the

standard

temperature

of

°C

and

has

a

universal

value

of

kgκ

day

for

all

species

-LRB-

Hendriks

-RRB-

Following

biochemical

reaction

kinetics

the

intercept

increases

by

a

factor

of

qT

as

a

function

of

temperature

-LRB-

Gillooly

et

al.

-RRB-

Production

kp

by

warm-blooded

species

with

a

body

temperature

of

is

qT

times

higher

than

that

of

equally

sized

cold-blooded

species

at

°C

-LRB-

Hendriks

-RRB-

Production

kp

is

allocated

to

somatic

and

gonadic

growth

We

will

consider

the

rate

constant

for

reproduction

-LRB-

reproduction

kpr

-RRB-

to

be

a

fraction

-LRB-

prp

-RRB-

of

total

production

kp

according

to

In

Spermatophyta

of

the

total

dry

weight

production

is

diverted

to

reproduction

via

seeds

-LRB-

Niklas

and

Enquist

-RRB-

After

correction

to

a

dry

wet

weight

fraction

of

as

described

in

the

methods

section

the

reproductive

fraction

-LRB-

prp

-RRB-

equals

-LRB-

Table

-RRB-

In

animals

prp

varies

between

for

juveniles

and

for

adults

without

somatic

growth

Filling

in

the

slope

and

the

intercepts

yields

the

reproduction

rate

constant

as

a

function

of

m

-LRB-

Fig.

-RRB-

Table

factors

used

in

the

equationsSymbolDescriptionUnitValuea

sourceγpScaling

coefficients

for

productionkgκ

day

-LRB-

Hendriks

-RRB-

kp

kprRate

constants

for

production

and

reproductionday

exponent

p

c

-LRB-

Hendriks

-RRB-

mAdult

masskgVariablemrTotal

reproductive

mass

in

a

batchkgEquation

egg

or

neonate

masskgmin

-LRB-

me

-RRB-

p

inter-reproductive

period

of

average

life

time

prpFraction

of

production

directed

to

reproduction

-LRB-

Niklas

and

Enquist

-RRB-

i

number

of

offspring

released

in

a

reproductive

eventno

individual

quotient

p

-LRB-

Hendriks

-RRB-

τrInter-reproductive

perioddayEquation

p

plants

c

cold-blooded

w

warm-blooded

i

invertebrates

v

vertebrates

a

aquatic

t

terrestrialFig

rate

constants

-LRB-

kpr

-RRB-

-LRB-

kg

kg

day

-RRB-

decrease

with

adult

mass

-LRB-

m

-RRB-

-LRB-

kg

-RRB-

to

the

power

of

about

Model

estimations

-LRB-

thick

lines

with

letter

-RRB-

as

well

as

empirical

regressions

-LRB-

thin

lines

-RRB-

for

vascular

plants

-LRB-

A

green

dotted

-RRB-

invertebrates

-LRB-

B

yellow

dashed-dotted

-RRB-

cold-blooded

vertebrates

-LRB-

C

blue

dashed

-RRB-

and

warm-blooded

vertebrates

-LRB-

D

red

solid

-RRB-

as

listed

in

Table

d

Day

Usually

seeds

eggs

and

neonates

are

not

delivered

continuously

but

released

in

discrete

batches

i.e.

sowings

clutches

and

litters

The

total

offspring

mass

-LRB-

mr

-RRB-

accumulated

in

a

period

between

two

successive

reproductive

events

-LRB-

τr

-RRB-

equals

The

inter-reproductive

interval

-LRB-

τr

-RRB-

might

be

related

to

the

organisms

metabolism

and

to

environmental

conditions

Initially

we

did

not

find

empirical

regressions

that

link

τr

to

organism

size

However

many

other

biological

time

parameters

including

gestation

and

weaning

time

of

homeotherms

scale

to

m

with

an

exponent

of

κ

-LRB-

Peters

Hendriks

-RRB-

For

an

average

mammal

the

age

at

birth

weaning

off

and

average

death

is

at

about

of

the

total

period

from

conception

to

death

respectively

-LRB-

Peters

-RRB-

τr

covering

at

least

gestation

and

weaning

-LRB-

-RRB-

thus

equals

at

least

-LRB-

-RRB-

of

the

average

lifetime

τl

i.e.

τr

prl

τl

τl

To

allow

for

additional

time

to

recover

and

mate

we

set

the

inter-reproductive

period

at

a

fraction

-LRB-

prl

-RRB-

of

the

average

lifetime

τl

This

lemma

is

indirectly

demonstrated

by

one

long-term

study

on

metabolism

reproductivity

and

average

lifetime

-LRB-

τl

-RRB-

of

earthworms

-LRB-

Mulder

et

al.

-RRB-

In

fact

although

no

evidence

of

a

correlation

between

τr

and

the

offspring

was

found

τl

and

m

were

strongly

correlated

Following

a

more

general

theory

τl

can

indeed

be

defined

here

as

the

mean

residence

period

in

the

population

and

can

thus

be

replaced

by

-LRB-

Odum

-RRB-

In

this

way

τr

can

now

be

assumed

to

equal

Filling

in

the

parameter

values

for

mammals

yields

τl

-LRB-

m

-RRB-

This

is

a

factor

of

larger

than

the

value

of

-LRB-

n

-RRB-

derived

from

a

compilation

of

data

on

South

American

mammals

that

was

published

after

our

estimation

-LRB-

Pereira

and

Daily

-RRB-

Obviously

this

relationships

needs

to

be

confirmed

for

other

species

groups

Substituting

Eq

into

Eq

yields

the

reproductive

mass

-LRB-

mr

-RRB-

accumulated

between

batches

as

a

linear

function

of

adult

size

-LRB-

m

-RRB-

as

-LRB-

Fig.

-RRB-

Fig.

or

litter

-LRB-

reproductive

-RRB-

mass

-LRB-

mr

-RRB-

-LRB-

kg

-RRB-

increases

with

m

-LRB-

kg

-RRB-

to

the

power

of

about

to

Legend

as

in

Fig.

Regressions

listed

in

Table

The

total

reproductive

mass

derived

from

Eq

can

be

divided

into

many

small

or

a

few

large

young

At

one

end

of

the

interval

species

called

r

strategists

here

maximize

the

number

of

young

per

female

-LRB-

-RRB-

up

to

a

limit

set

by

the

absolute

minimum

size

-LSB-

min

-LRB-

me

-RRB-

-RSB-

of

a

seed

egg

or

neonate

The

existence

of

such

a

threshold

has

been

attributed

to

various

restrictions

but

to

our

knowledge

supporting

quantitative

evidence

is

still

lacking

Since

each

individual

starts

off

as

a

single

cell

the

average

size

of

parental

cells

may

serve

as

a

first

indication

for

the

minimum

egg

or

seed

mass

-LRB-

me

-RRB-

The

weight

of

a

cell

is

reported

to

be

in

the

range

of

kg

for

plants

and

animals

-LRB-

Raven

West

et

al.

Mulder

et

al.

-RRB-

Lower

taxa

with

multi-cellular

organization

such

as

mycorrhizal

conidia

and

fruit

bodies

of

basidiomycetes

actually

release

offspring

as

single

cells

-LRB-

Mulder

et

al.

-RRB-

Higher

species

reproduce

by

multi-cellular

sexual

spores

seeds

eggs

and

neonates

with

sizes

at

or

above

that

range

With

this

variability

in

mind

min

-LRB-

me

-RRB-

was

tentatively

set

at

the

minimum

observed

for

the

taxon

covered

-LRB-

Table

-RRB-

At

the

other

side

of

the

range

K

type

organisms

invest

all

reproductive

mass

into

a

few

young

In

this

strategy

seed

egg

and

neonate

mass

are

maximized

by

dividing

the

total

reproductive

mass

over

a

few

offspring

Low

values

are

noted

for

e.g.

birds

with

an

average

of

eggs

per

clutch

and

for

mammals

with

means

of

neonates

per

litter

-LRB-

Blueweiss

et

al.

Ernest

-RRB-

Apparently

the

risk

of

premature

death

is

typically

spread

over

on

average

at

least

three

young

so

that

the

maximum

mass

of

individual

offspring

-LSB-

max

-LRB-

me

-RRB-

-RSB-

is

calculated

as

max

-LRB-

me

-RRB-

prp

prl

With

seed

egg

and

neonate

mass

ranging

between

min

-LRB-

me

-RRB-

and

max

-LRB-

me

-RRB-

we

can

now

derive

as

The

number

of

seeds

eggs

and

neonates

-LRB-

-RRB-

is

thus

expected

to

scale

to

m

with

exponents

in

the

range

of

for

K-strategists

and

r-strategists

respectively

The

corresponding

intercepts

are

prp

prl/min

-LRB-

me

-RRB-

and

respectively

Intermediate

values

indicate

that

both

types

of

species

are

present

in

the

sampled

taxon

If

strategies

are

uniformly

distributed

among

species

one

expects

a

mean

slope

of

with

the

geometric

average

of

prp

prl/min

-LRB-

me

-RRB-

and

as

a

coefficient

Vice

versa

the

mass

of

a

seed

egg

or

neonate

-LRB-

i.e.

me

-RRB-

varies

between

min

-LRB-

me

-RRB-

and

max

-LRB-

me

-RRB-

also

with

an

average

at

-LRB-

Figs.

-RRB-

Fig.

or

neonate

mass

-LRB-

me

-RRB-

-LRB-

kg

-RRB-

increases

with

m

-LRB-

kg

-RRB-

to

a

power

varying

around

for

cold-blooded

animals

and

in

the

range

of

for

warm-blooded

animals

Legend

as

in

Fig.

in

addition

model

estimations

for

organisms

in

general

-LRB-

E

dashed-dotted

me

me

m

-RRB-

Regressions

listed

in

Table

egg

or

neonate

number

in

ovaries

clutch

or

litter

-LRB-

-RRB-

-LRB-

young/individual

-RRB-

increases

with

m

-LRB-

kg

-RRB-

to

a

power

varying

around

for

cold-blooded

animals

and

close

to

for

warm-blooded

animals

Legend

as

in

Fig.

in

addition

model

estimations

for

organisms

in

general

-LRB-

E

dashed-dotted

-RRB-

Regressions

as

listed

in

Table

Equations

apply

to

cases

where

τr

is

related

to

the

metabolism

of

the

organisms

Alternatively

τr

may

depend

on

cyclic

processes

in

the

environment

Since

optimal

conditions

for

offspring

usually

occur

in

specific

seasons

synchronization

of

reproduction

to

annual

cycles

of

temperature

light

or

food

availability

by

e.g.

hibernation

or

fetal

growth

retardation

is

most

likely

With

τr

days

Eq

becomes

indicating

that

the

mass

released

in

a

yearly

sowing

clutch

or

litter

-LRB-

mr

-RRB-

scales

to

m

with

an

exponent

of

κ

Organisms

with

an

intrinsic

τr

close

to

year

can

exploit

such

synchronization

most

readily

Smaller

species

may

somewhat

postpone

their

reproduction

increasing

the

gonadic

mass

released

Larger

species

may

do

the

opposite

decreasing

the

slope

of

the

regression

towards

Fitting

Eq

into

and

writing

m

explicitly

gives

Using

the

typical

values

for

the

parameters

-LRB-

Table

-RRB-

cold-blooded

and

warm-blooded

organisms

with

a

τr

of

days

are

expected

to

have

an

m

of

about

and

kg

respectively

Organisms

that

are

much

smaller

mature

sufficiently

fast

to

allow

multiple

generations

within

a

year

or

growing

season

Species

which

are

substantially

larger

need

more

than

year

to

produce

one

egg

or

neonate

Results

Reproduction

rate

constant

We

will

now

compare

the

derived

equations

to

the

empirical

regressions

obtained

in

the

meta-analysis

The

few

correlations

available

for

gonadic

growth

show

that

reproduction

kpr

indeed

decrease

significantly

with

increasing

adult

mass

-LRB-

P

Table

-RRB-

Average

slopes

for

plants

and

animals

are

in

the

range

of

to

-LRB-

Table

-RRB-

Slopes

for

warm-blooded

species

tend

to

be

steeper

than

those

for

cold-blooded

species

The

empirical

regressions

for

seed

plants

were

derived

from

one

study

with

annual

reproductive

mass

expressed

as

a

function

of

foliage

and

stem

mass

because

total

weight

correlations

were

not

provided

-LRB-

Fig.

Niklas

and

Enquist

-RRB-

The

invertebrate

regressions

apply

to

short-term

studies

on

different

types

of

copepods

The

outlier

noted

in

field

experiments

with

sac

spawners

was

not

confirmed

by

other

correlations

including

those

for

high

food

levels

-LRB-

Hirst

and

Bunker

p

-RRB-

Low

intercepts

for

fish

and

mammals

apply

to

long-term

observations

including

intervals

without

gonadic

growth

-LRB-

Charnov

Charnov

et

al.

-RRB-

High

values

were

noted

for

reproductive

growth

in

gestation

periods

-LRB-

Payne

and

Wheeler

Blueweiss

et

al.

-RRB-

Reproduction

within

primates

is

slower

as

earlier

noted

for

production

-LRB-

Table

no.

Western

and

Ssemakula

Hendriks

-RRB-

Table

-LRB-

kg

female

kg

day

-RRB-

as

a

function

of

m

-LRB-

kg

-RRB-

according

to

empirical

regressions

-LRB-

y

amb

-RRB-

collected

in

the

meta-analysis

For

abbreviations

see

Table

Niklas

and

Enquist

-LRB-

-RRB-

Niklas

and

Enquist

-LRB-

-RRB-

Hirst

and

Bunker

-LRB-

-RRB-

Hirst

and

Bunker

-LRB-

-RRB-

Kiørboe

and

Sabatini

-LRB-

-RRB-

Kiørboe

and

Sabatini

-LRB-

-RRB-

Charnov

et

al.

-LRB-

-RRB-

Charnov

-LRB-

-RRB-

Blueweiss

et

al.

-LRB-

-RRB-

Payne

and

Wheeler

-LRB-

-RRB-

Payne

and

Wheeler

-LRB-

-RRB-

The

differences

between

regressions

for

the

reproduction

kpr

-LRB-

kg

kg

day

-RRB-

follow

the

trends

expected

from

the

model

based

on

average

turnover

kp

-LRB-

Eq

-RRB-

That

is

to

say

slopes

κ

for

both

reproduction

and

production

tend

to

be

close

to

for

heterotherms

and

at

or

below

for

homeotherms

-LRB-

Table

White

and

Seymour

Hendriks

-RRB-

Intercepts

for

seed

growth

in

plant

populations

including

all

life

stages

follow

Eq

independently

confirming

the

value

of

for

the

prp

The

reproduction

rate

regressions

for

animals

are

expressed

on

a

female

basis

With

the

exception

of

deviations

noted

for

some

regressions

on

copepods

and

primates

levels

for

true

gonadic

growth

in

heterotherms

are

within

a

factor

of

of

the

model

based

on

a

γp

of

kg

kg

day

previously

derived

for

production

-LRB-

Fig.

-RRB-

In

general

the

variability

of

the

intercepts

for

reproduction

reflects

differences

in

methods

conditions

and

species

and

is

similar

to

the

variability

observed

for

e.g.

individual

growth

or

consumption

-LRB-

Hendriks

-RRB-

Keeping

this

variability

in

mind

we

might

approximate

reproduction

by

kp

in

plants

and

kp

in

adult

animals

as

predicted

by

Eq

of

the

model

Total

offspring

mass

in

a

reproductive

batch

With

average

production

kp

as

a

predictor

of

reproduction

we

can

now

compare

measurements

and

estimations

for

the

reproductive

masses

and

numbers

-LRB-

Fig.

-RRB-

Regressions

indicate

that

total

seed

egg

and

neonate

weight

increase

with

parent

size

-LRB-

P

in

Table

Fig.

-RRB-

Most

confidence

intervals

for

the

average

of

the

slopes

encompass

or

but

the

whole

animal

size

range

can

only

be

covered

by

an

exponent

of

-LRB-

Table

-RRB-

The

outcome

for

plants

is

dominated

by

a

regression

with

a

slope

of

observed

for

fruit

versus

stem

mass

-LRB-

in

Table

-RRB-

Expressed

on

leaf

mass

annual

standing

reproductive

weight

in

plants

scaled

to

-LRB-

Niklas

and

Enquist

-RRB-

Comparing

weighted

averages

the

mean

slope

for

invertebrates

is

significantly

higher

than

the

confidence

interval

calculated

for

plants

and

cold-blooded

vertebrates

-LRB-

Table

-RRB-

The

confidence

intervals

noted

for

exponents

of

birds

and

mammals

cover

but

not

All

intercepts

for

cold-blooded

and

warm-blooded

species

are

close

to

each

other

with

the

exception

of

one

low

value

noted

for

fish

-LRB-

Fig.

Table

Stolz

-RRB-

This

outlier

however

reflects

year-round

observations

while

other

regressions

apply

to

peak

gonad

mass

Similar

intercept

differences

were

noted

for

the

reproduction

kpr

Table

mass

-LSB-

sowing

clutch

litter

-LRB-

mr

-RRB-

seed

egg

neonate

-LRB-

me

-RRB-

-RSB-

-LRB-

kg

-RRB-

as

well

as

the

number

of

offspring

-LRB-

seed

egg

neonate

-RRB-

as

a

function

of

m

-LRB-

kg

-RRB-

according

to

empirical

regressions

-LRB-

y

amb

-RRB-

collected

in

the

meta-analysis

Values

in

italics

approximated

by

us

because

not/wrongly

reported

in

the

original

study

Offspring

mass

or

number

measured

in

event

-LRB-

clutch

litter

-RRB-

or

organ

-LRB-

ovary

fruits

-RRB-

n.a.

Not

available

n.s.

not

significant

for

other

abbreviations

see

Tables

and

Taxone

omr

-LRB-

kg

-RRB-

me

-LRB-

kg

-RRB-

-LRB-

no

female

-RRB-

Niklas

and

Enquist

-LRB-

-RRB-

Aarssen

and

Jordan

-LRB-

-RRB-

Greene

and

Johnson

-LRB-

-RRB-

Shipley

and

Dion

-LRB-

-RRB-

Moles

et

al.

-LRB-

-RRB-

Grubb

et

al.

-LRB-

-RRB-

Walz

et

al.

-LRB-

-RRB-

Kiørboe

and

Sabatini

-LRB-

-RRB-

Kiørboe

and

Sabatini

-LRB-

-RRB-

Blueweiss

et

al.

-LRB-

-RRB-

Berrigan

-LRB-

-RRB-

n.s.Berrigan

-LRB-

-RRB-

n.s.Berrigan

-LRB-

-RRB-

Marshall

and

Gittleman

-LRB-

-RRB-

Llewellyn

and

Brown

-LRB-

-RRB-

Wood

and

O'dor

-LRB-

-RRB-

Stolz

-LRB-

-RRB-

Blueweiss

et

al.

-LRB-

-RRB-

McCann

and

Shuter

-LRB-

-RRB-

McCann

and

Shuter

-LRB-

-RRB-

Winemiller

and

Rose

-LRB-

-RRB-

Winemiller

and

Rose

-LRB-

-RRB-

Kaplan

and

Salthe

-LRB-

-RRB-

Kaplan

and

Salthe

-LRB-

-RRB-

Kaplan

and

Salthe

-LRB-

-RRB-

n.a.

Blueweiss

et

al.

-LRB-

-RRB-

Cabana

et

al.

-LRB-

-RRB-

a.Blueweiss

et

al.

-LRB-

-RRB-

n.a.

n.a.Western

and

Ssemakula

-LRB-

-RRB-

Cabana

et

al.

-LRB-

-RRB-

a.Blueweiss

et

al.

-LRB-

-RRB-

n.a.

Western

and

Ssemakula

-LRB-

-RRB-

Sacher

and

Staffeldt

-LRB-

-RRB-

n.s.Millar

-LRB-

-RRB-

Millar

and

Zammuto

-LRB-

-RRB-

Purvis

and

Harvey

-LRB-

-RRB-

Ross

-LRB-

-RRB-

Table

scaling

of

reproductive

parameters

as

listed

in

Tables

and

plotted

in

Figs.

Measured

arithmetic

mean

and

data-weighted

mean

-LRB-

in

italics

-RRB-

for

the

regression

exponent

b

with

confidence

interval

and

model

values

For

abbreviations

see

Tables

and

rateBatch

massOffspring

massOffspring

numberSymbolpap

of

individualsEmpirical

averagePlants

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

to

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

Invertebrates

-LRB-

to

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

to

-RRB-

-LRB-

to

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

vertebrates

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

to

-RRB-

Mammals

-LRB-

to

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

to

-RRB-

Model

valueCold-blooded

to

-LRB-

-RRB-

-LRB-

-RRB-

For

the

overall

range

empirical

slopes

for

heterotherms

approach

the

value

of

expected

from

Eq

of

the

model

In

addition

the

intercepts

for

plants

and

animals

are

at

the

level

expected

from

the

coefficients

prl

prp

of

Eq

Exponents

collected

for

homeotherms

and

some

large-sized

heterotherms

tend

towards

suggesting

synchronization

to

annual

cycles

as

explained

by

Eq

The

steep

lines

observed

for

invertebrates

in

comparison

to

the

flatter

slopes

of

cold-blooded

vertebrates

confirm

the

prediction

that

heterotherms

of

ca.

kg

are

likely

to

experience

some

kind

of

synchronization

In

addition

exponents

for

mammals

including

large

species

weighting

up

to

kg

are

close

to

Exponents

for

birds

are

smaller

and

obviously

their

weight

range

does

not

include

this

value

Seed

egg

and

neonate

mass

Regressions

show

that

seed

and

egg

masses

are

significantly

related

to

adult

size

for

most

heterothermic

species

groups

-LRB-

P

Table

-RRB-

Exceptions

are

noted

for

some

correlations

that

cover

a

small

size

range

or

a

few

data

-LRB-

P

Table

nos.

and

and

-RRB-

The

slope

varies

within

a

small

interval

around

the

mid-point

value

of

-LRB-

Fig.

-RRB-

Averages

for

invertebrates

are

higher

than

those

for

plants

and

cold-blooded

vertebrates

mainly

because

regressions

on

egg-carrying

copepods

and

wasps

have

slopes

closer

to

-LRB-

Table

and

Berrigan

Kiørboe

and

Sabatini

-RRB-

The

egg

and

seed

masses

-LRB-

me

-RRB-

for

plants

invertebrates

and

-LRB-

semi

-RRB-

aquatic

vertebrates

of

the

same

size

are

within

order

of

magnitude

of

each

other

-LRB-

Fig.

-RRB-

Eggs

of

aquatic

crustaceans

tend

to

be

smaller

than

those

of

terrestrial

spiders

and

insects

with

equal

body

size

-LRB-

Table

nos.

-RRB-

Likewise

intercepts

for

cold-blooded

vertebrates

increase

in

the

sequence

of

fish

water-bound

salamanders

land-dwelling

salamanders

and

reptiles

-LRB-

Table

Blueweiss

et

al.

Kaplan

and

Salthe

-RRB-

Warm-blooded

animals

distribute

their

reproductive

effort

over

a

small

and

size-invariant

leading

to

exponents

for

egg

and

neonate

mass

-LRB-

me

-RRB-

between

and

-LRB-

Fig.

-RRB-

The

partitioning

of

the

reproductive

mass

over

seeds

eggs

and

neonate

thus

follows

a

combination

of

both

strategies

distinguished

in

the

model

The

empirical

regressions

collected

are

within

the

minimum

and

maximum

boundaries

set

by

Eq

of

the

model

-LRB-

Fig.

-RRB-

The

slopes

for

plants

most

invertebrates

and

all

cold-blooded

vertebrates

vary

around

indicating

some

intermediate

value

between

min

-LRB-

me

-RRB-

and

max

-LRB-

me

-RRB-

Egg-carrying

copepods

wasps

birds

and

mammals

largely

consists

of

K-strategists

with

egg

and

neonate

mass

-LRB-

me

-RRB-

exponents

near

those

noted

for

clutch

and

litter

mass

-LRB-

mr

-RRB-

Almost

all

regressions

are

above

the

intermediate

intercept

calculated

by

the

model

for

an

overall

minimum

offspring

size

min

-LRB-

me

-RRB-

of

kg

-LRB-

Table

-RRB-

Using

typical

minimum

values

min

-LRB-

me

-RRB-

of

kg

for

plants

fish

and

amphibians

and

of

kg

for

reptiles

rather

than

the

overall

kg

gives

a

better

fit

of

the

model

Seed

egg

and

neonate

number

The

number

of

seeds

and

eggs

released

by

heterotherms

scales

to

size

with

exponents

largely

between

and

-LRB-

Table

Fig.

-RRB-

The

difference

between

intercepts

reflects

the

fraction

of

the

lifetime

covered

being

near

for

herbs

and

a

few

percent

of

less

for

trees

reflecting

lifetime

and

batch

fecundity

-LRB-

-RRB-

respectively

-LRB-

Table

vs.

Shipley

and

Dion

Greene

and

Johnson

Aarssen

and

Jordan

-RRB-

The

amount

of

eggs

delivered

by

crustaceans

flies

spiders

and

aphids

is

significantly

correlated

to

adult

size

but

those

for

wasps

and

beetles

are

size-independent

-LRB-

Table

nos.

vs.

Llewellyn

and

Brown

Blueweiss

et

al.

Berrigan

Marshall

and

Gittleman

-RRB-

The

low

intercept

for

vertebrate

heterotherms

applies

to

reptiles

-LRB-

Table

Blueweiss

et

al.

-RRB-

The

clutch

and

litter

size

of

warm-blooded

species

does

not

increase

with

adult

size

In

fact

four

out

of

seven

regressions

have

slightly

negative

slopes

As

expected

average

slopes

of

regressions

for

are

in

the

same

range

as

those

calculated

for

the

ratio

of

total

and

individual

offspring

mass

-LRB-

mr/me

-RRB-

-LRB-

Table

-RRB-

The

largest

deviation

between

arithmetic

means

is

noted

for

plants

and

equals

However

this

difference

is

due

to

one

study

in

which

sowing

weight

and

number

but

not

seed

weight

scale

significantly

to

m

-LRB-

b

P

vs.

b

P

-RRB-

With

parameters

set

at

typical

values

the

model

follows

these

trends

-LRB-

Table

-RRB-

Discussion

Data

variability

The

meta-analysis

yielded

regressions

for

various

species

groups

However

important

phylogenetically

lower

taxa

such

as

bacteria

algae

fungi

mosses

ferns

Protozoa

and

annelids

have

not

been

included

in

allometric

relationship

on

reproductive

parameters

Budding

or

binary

fission

in

unicellular

organisms

yields

new

cells

that

become

independent

at

about

of

the

parent

cell

volume

respectively

-LRB-

Woldringh

et

al.

-RRB-

Unicellular

taxa

thus

maximize

the

mass

rather

than

the

number

of

their

offspring

Fungi

mosses

and

ferns

release

spores

that

are

at

the

lower

end

of

the

palynological

range

noted

for

seed

plants

-LRB-

e.g.

Nilsson

Haig

and

Westoby

Moore

et

al.

Mulder

and

Janssen

-RRB-

Their

strategy

is

thus

comparable

to

that

of

some

seed

plants

such

as

orchids

Additional

study

of

the

size-related

reproduction

of

these

cryptogams

is

required

Plant

offspring

is

characterized

by

seed

and

fruit

mass

with

or

without

ancillary

tissues

while

adult

mass

refers

to

leaves

and/or

stems

Animal

studies

either

cover

the

whole

annual

cycle

or

reproductive

periods

only

In

addition

deviations

from

average

values

of

other

factors

such

those

for

length

weight

conversion

or

life-stage

may

increase

variability

Slopes

on

the

trade-off

between

reproduction

and

production

Despite

uncertainties

clear

patterns

on

the

average

trends

emerge

-LRB-

Fig.

-RRB-

Reproduction

kpr

-LRB-

kg

kg

day

-RRB-

decrease

with

size

as

expected

from

the

model

According

to

Eq

reproduction

is

considered

to

be

a

fraction

-LRB-

prp

-RRB-

of

the

production

kp

representing

the

P/B

of

a

population

Reproduction

kpr

by

homeotherms

has

steeper

slopes

and

larger

intercepts

in

comparison

with

heterotherms

as

earlier

noted

for

production

kp

-LRB-

Fig.

Table

-RRB-

It

indicates

that

the

trade-off

between

somatic

and

gonadic

growth

is

rather

invariant

to

size

and

metabolism

The

fraction

of

the

production

directed

to

reproduction

-LRB-

prp

-RRB-

was

found

to

be

for

plants

after

conversion

to

seedling

wet

weight

indeed

independent

of

the

species

weight

-LRB-

Niklas

and

Enquist

-RRB-

The

similarity

between

slopes

for

reproduction

and

overall

population

production

indicates

that

such

a

relationship

also

exists

for

animals

However

the

derivation

of

such

a

fraction

is

yet

impeded

by

large

variability

among

intercepts

by

a

lack

of

information

on

many

heterothermic

species

and

by

the

focus

on

adult

animals

instead

of

whole

populations

Fig.

-LRB-

lines

-RRB-

and

empirical

-LRB-

dotted

area

-RRB-

trends

of

seed

egg

or

neonate

mass

-LRB-

mr

me

-RRB-

-LRB-

kg

-RRB-

and

number

-LRB-

-RRB-

versus

m

-LRB-

kg

-RRB-

for

several

species

groups

Slopes

on

the

trade-off

between

offspring

number

and

mass

The

meta-analysis

in

the

present

paper

shows

that

the

mass

released

in

a

single

reproductive

event

-LRB-

mr

-RRB-

-LRB-

kg

-RRB-

is

a

constant

fraction

of

the

parents

weight

for

a

remarkable

variety

of

plant

and

animal

species

-LRB-

Table

Fig.

-RRB-

Over

the

whole

range

of

species

studied

the

slope

is

close

to

but

exponents

for

specific

groups

such

as

homeotherms

and

possibly

plants

are

smaller

Ignoring

differences

in

slopes

and

intercepts

about

of

the

adult

mass

is

released

in

a

sowing

clutch

or

litter

-LRB-

Eq

-RRB-

This

supports

though

not

necessarily

implies

the

existence

of

a

size-independent

prp

In

addition

to

the

trade-off

between

somatic

and

gonadic

growth

organisms

may

divert

their

reproductive

mass

over

many

small

or

a

few

large

offspring

-LRB-

Fig.

-RRB-

In

other

words

the

is

inverse

proportional

to

seed

egg

or

neonate

mass

-LRB-

me

-RRB-

As

elaborated

in

the

Model

development

section

one

may

distinguish

between

species

with

r-tactics

that

maximize

the

number

of

offspring

with

increasing

adult

mass

-LRB-

me

-RRB-

and

K-strategists

that

amplify

seed

egg

or

neonate

weight

-LRB-

me

-RRB-

Slopes

of

regressions

on

and

me

of

the

offspring

generally

vary

around

the

intermediate

value

of

expected

if

species

with

an

r

and

K-strategy

are

equally

distributed

-LRB-

Table

-RRB-

However

regressions

on

egg-carrying

copepods

wasps

birds

and

mammals

have

exponents

close

to

for

egg

and

neonate

size

-LRB-

me

-RRB-

and

near

for

-LRB-

Table

-RRB-

These

species

groups

thus

largely

consist

of

K-strategists

Graphically

seed

egg

and

neonate

mass

are

confined

to

a

triangular

envelope

that

contains

small

species

with

small

offspring

and

large

species

with

small

or

large

offspring

-LRB-

Figs.

-RRB-

Such

a

pattern

has

been

previously

recognized

in

original

data

on

plants

and

fish

The

triangle

was

found

to

be

right-angled

for

fish

with

a

minimum

egg

size

-LSB-

min

-LRB-

me

-RRB-

-RSB-

of

kg

independent

of

the

m

-LRB-

e.g.

Duarte

and

Alearaz

-RRB-

In

plants

the

envelope

was

reported

to

be

obtuse-angled

where

the

tile

and

the

tile

of

seed

size

scaled

to

total

plant

mass

with

exponents

in

the

range

of

and

respectively

-LRB-

Grubb

et

al.

Moles

et

al.

-RRB-

The

slopes

for

the

lower

boundary

encompass

the

value

of

known

for

scaling

of

biological

time

variables

-LRB-

Peters

Hendriks

-RRB-

Although

the

period

to

adulthood

has

been

suggested

to

limit

egg

and

seed

size

such

a

relationship

may

be

more

complex

than

a

power

scaling

to

size

-LRB-

see

e.g.

Kiflawi

-RRB-

In

addition

some

proof

for

the

underlying

mechanisms

including

an

explanation

for

its

absence

and

presence

in

different

species

as

well

as

taxon-specific

slope

values

is

yet

lacking

Similar

considerations

apply

to

the

upper

boundary

The

egg

and

neonate

mass

-LRB-

me

-RRB-

in

warm-blooded

species

is

proportional

to

the

weight

of

their

parents

Each

of

the

slopes

is

steeper

than

observed

for

clutch

or

litter

mass

-LRB-

mr

-RRB-

However

confidence

intervals

for

the

averages

indicate

that

may

be

the

appropriate

exponent

in

addition

to

at

least

within

small

size

ranges

such

as

noted

for

birds

Slopes

of

can

be

understood

from

inter-reproductive

periods

that

synchronize

to

annual

cycles

rather

than

to

adult

mass

-LRB-

Eq

-RRB-

Yet

the

difference

between

cold-blooded

-LRB-

-RRB-

and

warm-blooded

-LSB-

-LRB-

-RRB-

-RSB-

species

indicate

that

metabolism-related

mechanisms

may

be

important

too

Just

as

size

of

warm-blooded

adults

appears

to

be

constrained

by

heat

exchange

neonate

mass

may

be

also

be

determined

by

thermodynamic

principles

However

the

exploration

and

underpinning

of

other

values

for

the

slopes

is

beyond

the

scope

of

the

present

paper

For

now

we

assume

that

the

lower

and

upper

end

of

the

range

scale

to

between

and

Most

species

groups

contain

both

an

r

and

K-strategists

yielding

an

average

of

slope

of

about

whereas

some

animal

taxa

were

shown

to

scale

to

Future

refinement

by

thermodynamic

principles

may

lead

to

a

smaller

range

between

e.g.

and

still

yielding

average

slopes

around

Intercepts

on

the

trade-off

between

aquatic

and

terrestrial

habitats

Having

described

the

possible

values

of

the

slopes

we

will

now

take

a

look

at

the

intercepts

The

variability

of

the

exponents

excludes

detection

of

subtle

differences

between

coefficients

Yet

there

is

an

evident

increase

in

egg

size

from

aquatic

to

terrestrial

habitats

both

among

invertebrates

and

vertebrates

The

difference

has

historically

been

attributed

to

oxygen

limitations

as

its

diffusion

in

air

is

times

faster

than

in

water

-LRB-

Hendry

et

al.

-RRB-

However

experiments

within

the

same

species

do

not

confirm

this

explanation

-LRB-

Einum

et

al.

-RRB-

We

therefore

suggest

that

an

alternative

more

universal

mechanism

may

be

more

important

A

parent

is

more

willing

to

invest

in

the

size

of

a

seed

or

egg

when

it

can

influence

its

fate

Organisms

have

little

control

of

transport

and

development

in

large

homogeneous

compartments

such

as

water

and

air

Consequently

clutches

of

aquatic

animals

consist

of

many

small

eggs

-LRB-

Fig.

Blueweiss

et

al.

Kaplan

and

Salthe

Berrigan

Winemiller

and

Rose

McCann

and

Shuter

Wood

and

O'dor

-RRB-

Even

within

fish

pelagic

species

reproduce

by

smaller

and

more

eggs

than

demersal

counterparts

of

equal

size

-LRB-

Duarte

and

Alearaz

-RRB-

The

intercepts

for

the

amphibians

increase

in

the

sequence

of

pond

breeders

that

attach

eggs

to

plants

followed

by

stream

and

land

breeders

with

nests

-LRB-

Table

Kaplan

and

Salthe

-RRB-

Within

the

heterogeneous

terrestrial

environment

land

animals

can

direct

their

offspring

to

sites

that

provide

shelter

or

food

to

avoid

wasting

reproductive

mass

in

unfavorable

patches

-LRB-

Blueweiss

et

al.

Berrigan

Marshall

and

Gittleman

-RRB-

The

small

seed

size

of

terrestrial

plants

in

comparison

to

egg

masses

in

reptiles

can

be

understood

from

the

extra

dispersal

function

of

propagules

in

the

former

case

Obviously

other

factors

that

covary

with

the

water

land

gradient

may

be

responsible

for

the

observed

patterns

For

instance

the

dry

wet

weight

fraction

of

adults

increases

from

aquatic

to

terrestrial

habitats

and

a

similar

trend

might

exist

in

their

offspring

too

However

this

explanation

and

the

related

interpretation

is

unlikely

to

cover

the

orders

of

magnitude

of

the

noted

differences

Integration

of

theoretical

and

empirical

evidence

Integrating

these

trends

we

can

now

derive

common

patterns

within

the

triangular

envelope

of

offspring

and

adult

mass

-LRB-

Fig.

-RRB-

In

general

r-strategists

are

found

amongst

small

adults

-LRB-

Fig.

left-hand

side

-RRB-

with

many

small

offspring

in

aquatic

environments

-LRB-

Fig.

lower

end

-RRB-

Large

adults

-LRB-

Fig.

right-hand

side

-RRB-

with

a

few

large

young

live

in

terrestrial

habitats

-LRB-

Fig.

upper

end

-RRB-

Obviously

these

patterns

can

not

cover

all

reproductive

and

non-reproductive

characteristics

associated

with

r

K

gradients

For

instance

ruderal

plants

typically

reproduce

as

r-strategists

but

more

K-type

species

especially

in

close

canopies

may

also

regenerate

via

wind

dispersal

of

small

seeds

-LRB-

Grime

et

al.

Grime

Aarssen

-RRB-

In

addition

seed

mass

is

known

to

be

negatively

correlated

with

the

leaf

size

or

the

life

span

of

plant

species

-LRB-

Díaz

et

al.

-RRB-

Such

results

for

plants

strongly

imply

the

existence

of

correlated

traits

in

other

taxa

and

demand

further

investigation

O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

macroecology
reproduction
body size
fecundity