Lecture 5

Phi Sigma Biological Honor Society

  • Chapter Beta Lambda; graduate and undergraduate students invited to apply.

  • Eligibility:

    • Graduate students: Minimum GPA of 3.0 & at least 1 semester at ISU.

    • Undergraduate students: Minimum GPA of 3.0 & Junior or Senior standing.

  • Application fee: $50.

  • Perks & Highlights:

    • Research grants available.

    • Phi Sigma Research Symposium (Spring).

    • Fall Picnic.

    • Winter Potluck.

    • Spring Banquet.

    • Line on your precious resume.

  • Applications due: SEPTEMBER 19TH, 2025.

Feedback systems

  • Overview: Feedback systems involve a disturbance, actuators (effectors), a regulated variable, a sensor, a setpoint, and a feedback loop.

  • Page 2 components:

    • Disturbance: external change.

    • Effector.

    • Variable.

    • Sensor.

    • Feedback loop.

  • Page 3 details:

    • (a) Disturbance (example: 17).

    • (b) Effectors, e.g., sweat glands, thermogenesis, behavior.

    • Variable (example: 7b).

    • Setpoint.

    • Comparator.

    • Error.

  • Page 4 flow:

    • Substrate (c).

    • Enzyme A.

    • Error signal.

    • Enzyme B.

    • Enzyme C.

    • Product A.

    • Product B.

    • End-product.

Scaling

  • Page 5: Table 3.1 – Ranges of organism and animal sizes (Mass in grams; Units to scale).

    • Mycoplasma: $10^{-13}$ g; < 0.1 pg.

    • Typical bacterium: $10^{-10}$ g; 0.1 ng.

    • Tetrahymena: $10^{-7}$ g; 0.1 μg.

    • Amoeba: $10^{-4}$ g; 0.1 mg.

    • Rotifer: $10^{-4}$ g; 0.1 mg.

    • Aphid: $10^{-3}$ g; 1 mg.

    • Bee: $10^{-1}$ g; 100 mg.

    • Pygmy shrew: $10^{2}$ g; 1 g (note: table shows a size jump toward small mammals).

    • Hamster: $10^{2}$ g; 100 g.

    • Human: $10^{5}$ g; 100 kg.

    • Elephant: $5 imes 10^{6}$ g; 5000 kg (5 tonnes).

    • Blue whale: $10^{8}$ g; 100,000 kg (100 tonnes).

  • Page 6: Scaling summary

    • Many physiological processes vary with organism size.

    • Not always in a straightforward fashion (e.g., metabolic rate vs locomotion rate do not scale in lock-step with size).

    • A hamster is roughly 100x more massive than a pygmy shrew, but its metabolic rate is not 100x that of the shrew.

    • Statement: Metabolic rate tends to be lower as mass increases when correcting for body mass, i.e., mass-specific metabolic rate decreases with size.

  • Page 7: Other size-related traits

    • Some traits increase with size and are tightly linked to body size (e.g., bone thickness).

    • Purpose of scaling: remove body size as a confounding factor to reveal underlying variation (SCALING).

    • Scaling reveals structural and functional consequences of size changes among otherwise similar organisms.

  • Page 8–9: Scaling can reveal constraints

    • Example: Elephants cannot fly because of environmental and physiological constraints.

    • Concept: Something roughly 20x larger than an elephant could exist in water, where water provides support and aids heat loss.

    • On land, those constraints create limits on biological possibilities and adaptation.

  • Page 10: Isometric scaling & Allometry; Log plots

    • Isometric scaling: a trait varies in direct proportion with body size.

    • Example: Surface area scales with volume by the exponent ~0.67 (i.e., 2/3).

    • In general: Y∝MbY \propto M^{b} where bb is the mass exponent.

    • Log form: log⁡Y=log⁡a+b log⁡Mb\log Y = \log a + b \, \log M_b where

    • aa = intercept (proportionality constant),

    • bb = slope (mass exponent).

    • Why use log plots? They linearize power-law relationships and help compare scaling across sizes.

  • Page 11: Real-world scaling patterns

    • In reality, few properties vary isometrically; most show allometric variation between body size and the trait of interest.

    • The plotted curve often does not pass through the origin.

  • Page 12: Scaling and confidence intervals

    • Confidence intervals are often shown on log plots.

    • Log plots reduce large differences on linear scales, so small slope differences can be biologically important.

    • Many previously interpreted adaptive differences may reflect scaling differences.

    • Organisms deviating from the line (well above or below) are often targets of focused study for insights into constraints and biological possibilities.

  • Page 13: Metabolic rate and body size (Figure 3.5)

    • Metabolic rate (MR): rate of calories expended.

    • Body size is a strong predictor of MR; MR typically follows an allometric relationship (no line through the origin).

    • About 90% of variation in MR observed within groups is attributable to variation in body mass; taxonomic affiliation also contributes to differences.

  • Page 14: Mice, small birds, and marmots (Figure 3.5)

    • Mice and small birds: birds of similar body size have higher MR than mammals of similar size; small birds must feed more frequently or consume energy-dense foods to support high MR.

    • Marmots: low MR for their size, often at high elevations; spend many months hibernating; store fat to support long periods of inactivity.

  • Page 15: Sex differences in MR

    • On average, women have lower MR than men.

    • When sexes are combined, the data align with the overall MR line, indicating a sex-specific difference in MR.

  • Page 16: Implications of size on heat and water loss

    • Larger animals have a lower surface area:volume ratio.

    • This affects heat loss/retention and evaporative water loss.

  • Page 17: Oxygen consumption (Figure 3.6)

    • Oxygen consumption (as a proxy for MR) shows a slope similar to MR vs body mass.

    • When MR is scaled for body mass, oxygen consumption per unit mass decreases with increasing body mass (specific consumption) as long as the slope is less than 1.

    • Other traits show similar scaling relationships.

  • Page 18: Specific cost of locomotion (Figure 3.10)

    • The cost of locomotion scales with body mass in a way that is broadly consistent across taxa.

    • Within and among taxonomic groups, there are similar scaling patterns for locomotion costs.

  • Page 19: Locomotion mode and endothermy/ectothermy differences

    • The mode of locomotion affects efficiency; some modes are more efficient than others.

    • Endotherms and ectotherms show differences in scaling of locomotion costs.

    • Figure 3.14 indicates that while moving a larger body costs more energy, more ground may be covered per unit of movement depending on mode and physiology.

Connections and implications

  • Practical implications:

    • Scaling informs comparative physiology, ecology, and evolutionary biology by isolating size effects from other traits.

    • Understanding MR scaling helps explain energy budgets, feeding strategies, and activity patterns across species.

  • Conceptual implications:

    • Distinguishing isometric vs allometric relationships clarifies why simple ruler-based comparisons can be misleading.

    • Allometry highlights constraints that shape the evolution of form and function.

  • Ethical/philosophical notes:

    • When applying scaling concepts to real-world biology, consider limitations of cross-species generalizations and the importance of taxonomic context.

    • Recognize that deviations from allometric predictions can reveal novel biology requiring deeper investigation.

Key equations and definitions (summary)

  • Allometric relation (general form):
    Y=a MbY = a \, M^{b}
    where YY is the trait, MM is body mass, aa is a constant, and bb is the mass exponent.

  • Log-transformed linear form:
    log⁡Y=log⁡a+blog⁡M\log Y = \log a + b \log M
    This yields a straight line with intercept log⁡a\log a and slope bb on a log-log plot.

  • Isometric scaling example (surface area vs volume):
    extSurfacearea∝Volume2/3≈Mass2/3ext{Surface area} \propto \text{Volume}^{2/3} \approx \text{Mass}^{2/3}

  • Mass-specific metabolic rate concept:

    • Mass-specific MR typically decreases with increasing body mass (i.e., MR per unit mass decreases as MM increases).

  • Oxygen consumption scaling (concept):

    • If MR scales as MR=kMbMR = k M^{b} with b<1b<1, then specific (per-mass) MR decreases with increasing MM; similarly for oxygen consumption with a slope similar to MR.

  • Conceptual terms to remember:

    • Isometry: trait changes in direct proportion to body size (b≈1b \approx 1).

    • Allometry: trait changes with body size at a rate different from direct proportion (b≠1b \neq 1).

    • Mass-specific metabolic rate: MR per unit body mass; tends to decrease with larger body mass.