A2

H1 H2

The food web

Primary producers

Primary consumers

D Detritus and associatedMicroflora (bacteria/fungi)

P

Death and sedimentation

herbivore detritivore

A1

inedible

Secondary Productivity:Primary production supportsa web of consumers—a simple example

Productivity

Biomass

ratedeath specific theis and rategrowth or production specific theis

,population theofty productivi thecalled is birth term The

formed. is biomass newat which rate theisty Productivi

lost. and formed isit at which rate the

between difference theis biomass of rategrowth net theisthat

balance mass a as written becan biomassfor equation rateA

mb

mBbBdt

dB

Defining some productivity terms

Birth (production) term

Death (loss) termB

bB/t

mB/t

The productivity is a combination of the birth of new organisms and the growth of the organisms already present

Similarly, the death process is a combination of death of organisms and weight loss by existing organisms.

If the productivity (birth term) exceeds the death term the biomass is increasing, and if the death term is larger, the biomass is decreasing

Time (t)

Biomass of a consumer

0dt

dB

B

t

0dt

dB

0dt

dB

Time (t)

RotiferBiomass

0dt

dR

R

t

0dt

dR

0dt

dR

So if we measure and B at any point in time and we can estimate the specific birth rate, we can then obtain the specific death rate by subtraction.

dt

dB

dt

dB

Bbm

1

mbdt

dB

B

BmbmBbBdt

dB

1

or

losses minus production

•For a tiny consumer like a rotifer the birth rate is easy to estimate since the adult females carry their eggs around until they hatch

•When they hatch they come out as full sized rotifers. •If we know the fraction of adults carrying egs and the average time it takes for eggs to hatch, we can calculate the birth rate. •Since the rotifers are born more or less full size, so there is no need to model or measure the growth of individuals.

A tiny organism like a rotifer is born at full size, so productivity amounts to measuring the rate at which new animals are born

Rotifers carrying eggs

1-d

rate hatching1

(d) hatchingfor required timeavg

,adults#

eggs#

T

Eb

T

T

E

dt

dB

BT

Em

1

Time (t)

RotiferBiomass

0dt

dR

R

t

0dt

dR

0dt

dR

For a large organism like a fish, biomass production occurs mostly from individual growth. New born fish are so tiny that birth of individuals makes a negligible contribution to biomass production

1W2W

3W

4W

t

tt

W

WSGR

1ln

Year classes

The Wt represent the Weights of each year class

•We can calculate the growth rate of biomass individual fish by weighing fish and determining their age and then seeing how much weight they gain each year.

•The productivity of each age class is the Specific growth rate (SGR) of that age class times the total biomass of that age class in the population.

t

t

B

Bt

t

avg

it

tt

i t

SGRSGR

BSGRP

*

*

be would tablelife wholeover the species afor SGR Average

category trophicin the species allover summed and classes, age ofeach for

present] biomass timesrategrowth [specific of sum Production

This approach assumes that the size vs age relationship is relatively constant.

1W2W

3W

4W

t

tt

W

WSGR

1ln

The Wtrepresent the Weights of each year class

By this method the average SGR for the whole population can be calculated as the weighted average over all age classes

However there is a problem with this approach…???

1

t

T

t

t SGRwSGR

class ageth ' in the Biomass offraction the, where tB

Bw

tt

t

tt

W

WSGR

1ln

However there is a problem with this approach.

By considering only the gain in weight across age classes, this method ignores weight gained and lost within the same year, eg Gonad tissue Adult fish usually convert a considerable portion of their body mass to gonads and release it during spawning every year.Thus it does not add to next year’s weight and would not be recorded as growth

We can quite easily correct for this by factoring in gonad production (add GSI)

weighttotal

weightgonad matureindex) atic(Gonadosom where

GSI

GSISGRt

We would of course only make this GSI correction on adult age classes.

Scales of a chum salmon

2+

3+

4+

Measuredistances fromscale center to eachannulus along a chosenaxis

T

A

L

L

length scale total

annulus todistance

How can we tell how old a fish is?

LA

Age yr

Convert the growth curve based on length to weights usinga length-weight plot for the species

This allows us to construct a growth curve based on length and age.

Many types of bony structures are commonly used to determine age of fish

Scale Otolith Opercular bone

These three structures are all from the same 3+ year old 30 cm cutthroat trout

The specific death rates can also be estimated from the population structure. This time we assume that the age structure of the population is constant, and that the numbers of individuals of each age within a sample reflects the proportion of that age group in the population.Assume we have a sample of 215 pike from a population.

215

1101

t

tN

N

552 N

303 N

204 N

The Nt / Nt represent the proportion of the population in each year class

69.0110

55ln1 m

61.055

30ln2 m

41.030

20ln3 m

t

tt

N

Nm

1ln

Age1 3 50

*

*

*

*

110

30

55

20

#

0

50

100

The survivorship curve assuming stable age structure for the population looks like this

t

tt

N

Nm

1ln

m1 =0.69

150

m3 =0.41

m2 =0.61

equal. are terms two thepopulation stable aFor

biomassin decreasing is population theotherwise

biomassin growing is population thelosses, exceedsty productivi If

processes loss andgrowth itsbetween difference the

as modelledusually is species afor biomass of change of rate The

mSGRBGSImBGSISGRBdt

dB

Productivity term loss term

Summary