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Biology & Life Sciences

Genetics, ecology, physiology and cellular biology formulae

Hardy-Weinberg Equilibrium

Intermediate
p2+2pq+q2=1p^2 + 2pq + q^2 = 1

Genotype frequencies in a non-evolving population.

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Allele Frequency Sum

Basic
p+q=1p + q = 1

The two allele frequencies must total 1.

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Exponential Population Growth

Intermediate
Nt=N0ertN_t = N_0 e^{rt}

Unlimited growth of a population over time.

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Logistic Growth

Advanced
dNdt=rN(1NK)\frac{dN}{dt} = rN\left(1 - \frac{N}{K}\right)

Population growth limited by carrying capacity.

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Per Capita Growth Rate

Basic
r=bdr = b - d

Net growth rate from birth and death rates.

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Population Doubling Time

Intermediate
td=ln2rt_d = \frac{\ln 2}{r}

Time for a population to double.

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Surface Area to Volume

Basic
SA:V=surface areavolumeSA:V = \frac{\text{surface area}}{\text{volume}}

Ratio governing cellular exchange efficiency.

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Microscope Magnification

Basic
M=image sizeactual sizeM = \frac{\text{image size}}{\text{actual size}}

How much larger an image appears than the object.

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GC Content

Intermediate
%GC=G+CA+T+G+C×100\%GC = \frac{G + C}{A + T + G + C} \times 100

Proportion of G and C bases in DNA.

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Shannon Diversity Index

Advanced
H=pilnpiH = -\sum p_i \ln p_i

Measures species diversity in a community.

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Simpson Diversity Index

Advanced
D=1pi2D = 1 - \sum p_i^2

Probability two random individuals differ in species.

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Lincoln-Petersen Estimate

Intermediate
N=M×CRN = \frac{M \times C}{R}

Population size from mark-and-recapture sampling.

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Net Primary Production

Intermediate
NPP=GPPRNPP = GPP - R

Energy stored by producers after respiration.

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Cardiac Output

Intermediate
CO=HR×SVCO = HR \times SV

Blood pumped by the heart per minute.

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Respiratory Quotient

Intermediate
RQ=CO2 producedO2 consumedRQ = \frac{CO_2\ produced}{O_2\ consumed}

Ratio revealing which fuel is being metabolised.

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Michaelis-Menten Kinetics

Advanced
v=Vmax[S]Km+[S]v = \frac{V_{max}[S]}{K_m + [S]}

Rate of an enzyme-catalysed reaction.

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Cell Dilution Factor

Basic
DF=VfinalVsampleDF = \frac{V_{final}}{V_{sample}}

Factor by which a sample is diluted.

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Hemocytometer Cell Count

Advanced
C=nˉ×DF×104C = \bar{n} \times DF \times 10^4

Cells per mL from a counting-chamber average.

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Bacterial Generations

Intermediate
n=logNtlogN0log2n = \frac{\log N_t - \log N_0}{\log 2}

Number of divisions over a growth period.

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Bacterial Growth Count

Basic
Nt=N0×2nN_t = N_0 \times 2^n

Cell count after n binary fissions.

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Kleiber's Law

Advanced
q0=70M0.75q_0 = 70\,M^{0.75}

Metabolic rate scales with body mass to the ¾ power.

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Osmolarity

Intermediate
Osm=n×C\text{Osm} = n \times C

Solute particle concentration in solution.

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Monohybrid Cross Ratio

Basic
3:13 : 1

Phenotype ratio from a heterozygous monohybrid cross.

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Dihybrid Cross Ratio

Intermediate
9:3:3:19 : 3 : 3 : 1

Phenotype ratio from a dihybrid cross.

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Recombination Frequency

Advanced
RF=recombinantstotal offspring×100RF = \frac{\text{recombinants}}{\text{total offspring}} \times 100

Genetic map distance in centimorgans.

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Enzyme Activity Unit

Intermediate
U=μmol productminU = \frac{\mu mol\ product}{min}

One unit converts 1 µmol of substrate per minute.

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Ecological Efficiency

Intermediate
E=energy at level n+1energy at level n×100E = \frac{\text{energy at level } n+1}{\text{energy at level } n} \times 100

Energy transfer between trophic levels (~10%).

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Biochemical Oxygen Demand

Advanced
BOD=D1D2PBOD = \frac{D_1 - D_2}{P}

Oxygen consumed by microbes decomposing organic matter.

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Total Magnification

Basic
M=Mobj×MeyeM = M_{obj}\times M_{eye}

Total magnification of a compound microscope.

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Surface-to-Volume Ratio

Intermediate
SA:V=surface areavolumeSA:V = \frac{\text{surface area}}{\text{volume}}

Ratio governing cell exchange efficiency.

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Net Primary Productivity

Intermediate
NPP=GPPRNPP = GPP - R

Energy available to an ecosystem after respiration.

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Population Growth Rate

Intermediate
r=BDNr = \frac{B - D}{N}

Per-capita growth from births and deaths.

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Allele Frequency

Basic
p+q=1p + q = 1

Frequencies of two alleles sum to one.

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Bacterial Doubling

Intermediate
N=N0×2t/gN = N_0\times 2^{t/g}

Exponential bacterial growth by generations.

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Respiratory Quotient

Advanced
RQ=CO2 producedO2 consumedRQ = \frac{CO_2\text{ produced}}{O_2\text{ consumed}}

Ratio revealing which fuel is being metabolized.

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Enzyme Turnover Number

Advanced
kcat=Vmax[E]k_{cat} = \frac{V_{max}}{[E]}

Reactions catalyzed per enzyme per second.

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