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Reminders: Not here last time? Send me an so I can put you on the list Assignment 1 due on Monday Quiz on Monday and Friday – bring calculator; open book First Lab (Lab 2) is on Sept 18th

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bp t l m T Chapter 2 Quantities N e

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Quantity: five-part definition 1.Name 2.Symbol 3.Procedural Statement 4.Set of numbers collected into a vector 5.Units on a defined measurement scale Length l 14.5, 10.1, 15.9, 15.4, 14.1, 13.3, 16.1, 12.8, … cm (ratio) measurement scale (ratio)

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Types of Measurement Scales

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Ordinal 1 st 2 nd 3 rd No information on the magnitude of the difference

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Interval Direction Lat/Long Units known, but zero does not mean nothing Temperature ( o C)

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Mass Ratio LengthVolume Units and zero known Can take ratios

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Ratio vs. Interval o C vs. K Zero in K means no heat Zero in o C is freezing point of water

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Ratio vs. Interval o C/ o F vs. ft/cm 50 o F = 10 o C, 41 o F = 5 o C 50 o F / 41 o F = o C / 5 o C = ft = cm, 2 ft = cm 6 ft / 2 ft = cm / cm = 3 3 = 3

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Methods and scale type Measurement procedure scale type – Example Record presence/absence of copepods in diet sample Nominal Count number of copepods in diet sample Ratio Scale type statistics – Example Nominal logistic regression Ratio (count) Poisson regression

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Recording quantities Detailing methods is at the heart of the scientific method

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Computer assisted data collection Becoming more common Fewer errors, better resolution

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Recording Data DATECANADA GOOSEBLACK DUCK 27-May-101, Jun-102,5 2,3 10 Save data in common formats (e.g..txt,.csv) Avoid matrix-format: … …

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Recording Data Save data in common formats (e.g..xls,.txt,.csv) Use flat-format: … datespeciescount 27/05/2010Canada Goose1 27/05/2010Herring Gull1 27/05/2010Great Black-backed Gull1 27/05/2010American Crow1 27/05/2010Savannah Sparrow1 27/05/2010Herring Gull1 27/05/2010Great Black-backed Gull1 27/05/2010Savannah Sparrow1 27/05/2010Herring Gull1 27/05/2010Great Black-backed Gull1 27/05/2010Herring Gull1 27/05/2010Herring Gull1

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Error checking Review your data Get a second person to review your data Plot and check Transcription error: 167 entered for 16.7

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Displaying data Tables Archival Provide summaries Graphs Display pattern Discover pattern Burrow Temperature bT ( o C) Specific Metabolic Rate E (kcal/kg/day)

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Displaying data Burrow Temperature bT ( o C) Specific Metabolic Rate E (kcal/kg/day) Fully Defined Quantities Names Units Numbers Symbols (optional)

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Now take a second to read Table 5.2 in the lecture materials

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Critique this graph

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Critique this table

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Ratio continued… Utility 3 years ? 30% Can do fancy calculations

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N t = N i e -Dt Extend notation and generate cool plots % remaining see Box 2.1 Initial pop. size Future pop. size N i = 1000 Ratio continued… Utility

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N t = N i e -Dt Predict trend in student registration % remaining see Box 2.1 Initial pop. size Future pop. size Ratio continued… Utility

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This example highlights four utilities 1.Accurate computation 2.Interpret symbolic notation 3.Combine to make new units 4.Permit analysis across multiple scales N t = N i e -Dt Ind. = Ind. year/year …well kinda

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3.Combine to make new units 1 hectare = 10,000 m 2 = 100 m x 100 m 4.Permit analysis across multiple scales Ratio continued… Utility 100 m 50 m 25 m

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Ecologists often use transformations …but think about what youre doing Note on transformations 100 m

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NOTE: Supplementary units defunct since 1995 m s K A mol cd kg SI Base Units Seven standard base units – facilitate comparable results Unit abbreviations

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Derived units Combinations of the base units Which derived units have you used? Unit (eg.) Acceleration (m·s -2 ) Area (m 2 ) Energy (N·m; J) Force(kg·m·s -2 ; N) Frequency (s -1 ; Hz) Light intensity(W·m -2 ) Power(J·s -2 ; W) Pressure(N·m -2 ; Pa) Velocity(m·s -1 ) Volume(cm 3 ; cc) Wavelength(m) Others? (eg.)

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Standard multiples Is it a coincidence the base is 10 and humans have 10 fingers and toes? TextSymbolFactorExample teraT TW gigaG GW megaM MW kilok1000kW hectoh100hW 1W decid0.1dW centic0.01cW millim0.001mW microμ μWμW nanon nW

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Unconventional Units It is sometimes useful to use non-standard units Read this excerpt from the notes: If our interest were in the foraging ranges of owls, we might decide to define the range in biological terms, based on the minimum area (in standard units) required to meet daily energy requirements. If we define this area as one unit, we can then examine the problem of foraging area needed by a pair of owls to successfully produce 1 chick, 2 chicks, and so on, relative to the number of minimum foraging units. To phrase this as a question, if 1 owl requires a certain area to meet its own energy needs, then how many of these units will be needed by 2 owls to raise 1 chick? By defining a new unit, we can address this problem with biologically meaningful units, rather than with arbitrary units.

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Unconventional Units Number (#) of entities commonly used in biology – Base pairs, birds, branches, cells, etc. Consequently, unconventional exponents are also common – Offspring · year -1, fitness, etc.

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Dimensions Dimensions are a way of thinking about quantities based on similarity – Euclidean Dimensions(L, L 2, L 3 ) – Mechanical Dimensions(M, L, T) – Composite dimensions(M·L 2 ·T -2 ) – Additional dimensions($, A) – Entities(#) – Fractal dimensions(L D )

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Euclidean Dimensions(L, L 2, L 3 ) cm m yards cm 2 hectares acres cc m 3 yards 3 Related by an integral change in exponent (L 1, L 2, L 3 )

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Mechanical Dimensions(M, L, T) MASS LENGTHTIME kglbstonesmfathomftspearlengthshyears light-yearsmillennia

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Composite dimensions(L·T -1 ) Distance (cm) Ant traveled 16 cm in 2 seconds 8 cm · sec -1 L·T -1 What are the dimensions of the ants momentum? 3 mg · 8 cm · sec -1 = 24 mg · cm · sec -1 M·L·T -1

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Additional dimensions ($, A) Gameboard Economics Measuring electric eel amps

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Entities (#) Biochemical entities: ions, atoms, molecules (including proteins) Genetic entities: chromosomes, genes, alleles, mutations Cellular entities: nuclei, mitochondria, cells Behavioural entities: attempts, successes, modal action patterns (MAPs) Population entities: interacting species Community level entities: number of taxa (species, order, etc), number of trophic levels.

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Entities (#) Useful units: Pairs Kilocounts Megacounts Less useful units: Mol Dozen Murder School

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Fractal dimensions(L D ) Fractal dimensions are related to one another by fractional exponents L D where 1 D 2 More convoluted than a straight line (D = 1), but not so convoluted as to fill a plane (D = 2). Convolution increases as D 2

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So why are fractals important? Fractals are common in nature

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