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Chapter 4

+. Chapter 4. Equations (Formal Models). Expressing Biological Concepts. Most common. “ Bacterial growth rate is exponential ”. Verbal. Data. Graphical. Formal. Less common, but necessary. To make calculations, we need an equation. Also common.

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Chapter 4

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  1. + Chapter 4 Equations (Formal Models)

  2. Expressing Biological Concepts Most common “Bacterial growth rate is exponential” Verbal Data Graphical Formal Less common, but necessary To make calculations, we need an equation Also common

  3. Equations– What’s the good of um? • They’re the basis for most of quantitative biology • Have several uses: • Demonstrate how a quantity was calculated • Make theoretical conclusions • Test hypotheses • Scale up experimental scope

  4. How to “read” equations? • Dissect into components, then reconstructmeaning • Begin by dissecting equations into terms • Net energy balance, , is the sum of ingestion,, metabolic losses,, and energy devoted to growth, . , , ,

  5. How to “read” equations? • Two types of terms: • Variable quantities [124.22, 135.59, …] Kg • Many possible values • Parametric quantities [23.35] Kcal·Kg-1 • Fixed – applied “across measurements” • e.g. Metabolic rate depends on body size: Variable Variable Parametric Parametric

  6. How to “read” equations? • The identification of quantities identify the meaning of each term , ,

  7. How to “read” equations? • The identification of quantities identify the meaning of each term , ,

  8. How to “read” equations? • The identification of quantities identify the meaning of each term , ,

  9. How to “read” equations? • The identification of quantities identify the meaning of each term , ,

  10. How to “read” equations? • The identification of quantities identify the meaning of each term , ,

  11. Translation aids comprehension • Translate to units • Helps visualize meaning • Translate to dimensions • Helps visualize relation of quantities • Translate into computations • Translate to graphics

  12. Graphical: Units: Dimensions: Computations:

  13. “Exponential growth and decay of populations”

  14. Formal  Verbal • Use words to connect the formal model to experience • e.g. Efficiency of carbonate utilization by marine gastropods:

  15. 1 Parametric: Shell density 2.71 g/cc 3 Variable: Shell area mm2 Shell thickness mm Shell internal volume mm3 = =

  16. Homogeneity of Units • Equations in biology have units • Terms (sep. =,+,-) have to have the same units • Both sides of an equation must have the same units • Check:

  17. Homogeneity of Units • Check: • Solve for α:

  18. Homogeneity of Units • Solve for α: • Re-check:

  19. Homogeneity of Dimensions • In addition to checking units, it is useful to apply the concept of similarity • Recognizing dimensional homogeneity is a valuable skill – key for the “reading” of equations

  20. Homogeneity of Dimensions • Equation for memory retention: where • m is the memory trace's strength (measured by recognition) • L is initial strength at the end of learning • t is the retention interval • D is the time decay rate • I is the measure of degree of interference • Is the equation legit?

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