Body size and shape: LECTURE 1

How do body sizes in organisms differ

7 orders of magnitude

How to body masses differ

More than factors of 10²1

Due to differing size differences in organisms

• e.g bacteri and whale live in different phyrical worlds

  • like a bcateria swimming in molasses

• Body shape and physiology differ accordingly

  • e.g ‘mouse can be dropped at a height, humans broken, horse splashes’

Body size has a number of physical implications that…

Leads to constraints to which organisms have to adapt:

• e.g small fly→ need to grip on smooth surface

• vs e.g cat→ needed to grip on rough surface (claws)

Scaling analysis

1. Isometry (geometric similarity)

2. Allometry (when isometry not met)

1. Isometry: what is it

• When two objects have identical relative dimension

  • i.e the same shape (although different sizes)

1. Isometry: scaling up, how worked out if length x2

1. Different shapes have different pre-factors (in blue)

   • e.g sphere, cube etc

2. Scale what happens to SA and Volume (depending on shape formula)

3. See what happens to SA and Volume is length x 2

In general:

𝐴 ∝ 𝐿 ²

V∝ 𝐿 ³

(makes sense cos A is 2D and V is 3D)

As mass ∝ Volume ∝ Length³

→ L ∝ m^1/3

→ A∝ L² ∝ m^2/3

1. Isometry: Rules for isometric organisms

1. Area prop to L²

2. Volume/Mass prop to L³

3. Length prop to Volume^1/3/Mass^1/3

4. Area prop to Volume^2/3/Mass^2/3

1. Isometry: Plotting SA against Body mass

Curve of the form: y=ax^b

a→ depends on object

b→ depends on whether relationship is length, areas or volumes

• Here it is 2/3 (scaling coefficient)

1. Make it easier→ Logarithmic Transformation

Now in form:

logy = loga +blogx

b→ scaling coefficient→ gradient

Makes a straight line

1. Isometry used as a null hypothesis

• These are used as expected lines

• Then compared to actual bio data

• see if isometry or allometry

2. Allometry: What is it

• Deviations from isometry

or

• study of the relationship between body size and some measurable biological parameter of an organism (paramter could be if crawl on ceiling or not??)

Positive vs Negative allometry

• Positive: real slope> expected slope (characteristic bigger than predicted by isometry)

• Negative: real< expected slope (characteristic smaller than predicted by isometry)

2. Example 1: Is it allometry? Body length vs body mass

• Expected slope→ 0.33

• Real slope→ 0.34

→ Probably Isometry

2. Example 2: SA vs Mass

• Expected→ 0.66

• Real slope→ 0.63

→ Negative allometry

e.g Whale has a smaller surface area than would be expected for its size predicted with isometry, compared to mouse

The most important factor that changes with size of an organism

Surface area to volume ratio

• Volume→ reserves (food, water or heat) and need for fuel

• SA→ extent to which exposed to environment

  • exchange of heat, gases or nutrients

Relationship: The volume of the body is supplied via surfaces

• nutrient uptake, respiration, photosynthesis

How SA:V ratio changes with mass

SA decreases with mass^-1/3

• Small animals→ a lot of surface area

• Large ones→ alot of volume

Size can have an effect on

1. Heat loss

2. Transport of substances (diffusion)

3. Standing on stems/legs (if terrestrial)

4. Relative mass of skeleton

5. Muscle force

6. Surface tension vs gravity

7. Animal flight

8. Surface enlargement

9. Exchange surfaces

1. Heat loss→ Bergmann’s rule

• Within a taxonomic clade

• Populations/ species of larger size are found in colder environments

• species of smaller size found in warmer

e.g penguins

2. Transport of substances

• Diffusive flux prop SA

• Diffusion time = (average diffusion distance)²/2D

Consequences:

→ large organism have to transport substances via bulk flow (convection)

e.g bacteria vs larger stuff

3. Standing on stems/legs

• Max force a long vertical column can support:

  → prop to Cross Sectional Area: square of linear dimensions

but

• Weight prop to cube of dimensions

3. Standing on stems/ legs: Example

E.g Stem with spore on top:

• Mass is prop to L³

• Force stem can support is only prop to L²

  → If increased isometrically→ Stem would not hold the weight of the spore

Solution: Positive Allometry

• Disproportionally thicker stems

4. Bone mass vs body mass

• If isometric:

  • Bone mass prop m^1.0

• With constant bone stress:

  • Bone mass prop bone CSA x bone length

    → prop to bone mass x bone length

    → L³ x L prop L⁴ prop m^4/3

4. Bone mass to Body mass→ measurements

• shows it is positively allometric

Prediction:

→ slope=1.3

Real:

→ slope=1.09

An 8-gram shrew is about 4% skeleton. Assuming that skeletal mass scales with body mass to the power of 4/3, how many percent of the body mass should the skeleton be for an 8- tonne elephant? What is the biological implication of this result?

• RBM= skeletal mass/body mass= km^1.09/m=km^0.09=0.04 for mous

• RBM of elephant/ RSM of mouse= (m_e/m_s)^0.09= 3.5

• Move about= RBM for elephant= 14%

What about aquatic?

• Show allometric (scaling coefficients closer to 1)

  → Only really needed again gravity

5. Muscle force

For isometric animals, muscle force prop muscle Cross-sectional area

→ prop to mass^2/3

This means:

Relative to their body weight→ small animals are stronger

5. Muscle force→ data weight lifters

• log lifted weight vs log body weight

slope= 0.67 (slope to predicted 2/3)

6. Surface tension→ walking on water

Force on the water prop to perimeter of contact zone with feet

• i.e with length, not area

THEREFORE:
surface tension prop body mass^-2/3

• Surface tension decreases massively with size

Only very small animals can walk on water

7. Flight

Lift prop wing area prop speed²

7. Flight: What this means

Under the assumption of isometry:

• Larger bird need to produce more force per unit wing area

  → flying faster

7. Flight: Issues with needing more speed

1. Gaining lift off speed if difficult

2. Landing can be damage

Some solutions to gaining lift off speed

• albertosses plunge from cliffs

Instead of increasing speed?

→ Larger wings

• BUT:

  • difficult to flap

Overall flight of larger body sizes

• difficult to do!

Largest birds are flightless→ ostriches

8. Surface enlargement: Meaning?

• Larger oragnisms

• Have smaller SA:V ratio

Solution

→ increase surfaces over which they take up essential substances from environment i.e internal surface areas

e.g:

• respiratory surfaces gill/lungs

• convoluted gut epithelia

• circulatory system capillaries fine

• root and leaf surface of plants

9. Exchange surfaces: Allometry of mammalian lung surface

• Lung SA scales isometrically with body mass

Why are scaling analyses useful?

Most physiological factors are strongly affected by body size:

1. medically relevant parameters:

   • cardiac output, renal clearance

   → need to be corrected for body surface area (or metabolic rate)

   • allow comparisons between different-sized patients

2. Drug dosage

3. Any analysis comparing different individuals or species needs to be corrected for body size

   • by looking at residuals of regression against body mass of the trait being measured

Can also using scaling analysis for

Testing general hypotheses about functions of an organism

• what determines met rate

• How do animals ceiling walk

• why do big animals have straight legs

• How large can fling animals be

• How thick do tree stems have to be

• How far can animals jump

→ Assessed by deriving theoretical predictions and testing them using scaling analysis

How?

→ Looking at scaling exponent

How animals walk on ceiling

Hypothesis of adehive forces allometry experiment

• To measure adhesion forces in ants

Hypothesis of ant adhesion allometry

Do we have more brain than other animals?

Yes

Exams questions

1. Why does size matter for organisms?

2. How does consideration of size influence our understanding of physiological processes?