Important Formulas to Memorize for AP Environmental Science

Lincoln Index

• The Lincoln Index is a statistical measure used to estimate population sizes. The Lincoln Index is often used in conjunction with the catch and release survey method for calculating populating sizes. The formula is given as (E1)(E2)/S where E1 and E2 represent the number of observed individuals captured and tallied in two different occurrences and S represents the number of overlaps. This is why the Lincoln Index works well with catch and release, after organisms are captured, they are tagged prior to release so that if the organism is captured again, observers know that they represent an overlap. 

• (Number of individuals collected first time)(Number of individuals collected second time)/(number of individuals common to both samples)

• The Lincoln Index assumes three things:

  • ​Tagged organisms are not more likely to be captured again (they are not maimed or hindered)

  • Ample time is allowed for captured/tagged organisms to reintegrate into population again randomly

  • Organisms are mobile (not plants, sponges, etc.)

Population Growth Rate

• A population's growth rate refers to how quickly a population is expanding or contracting. This is calculated by subtracting the number of deaths from the number of births in a year and dividing by the population size. 

• PGR = (Number of Births - Number of Deaths)/(Total Population Size) ​

Energy

• 1000 Joules = 1 kJ

• 1000 calories = 1 kcal

• 1 calorie = 4.184 joules 

• 1 BTU = 1.05 kJ

• 1 therm = 100,000 BTU

Power

• Power = Energy/Time

• 1 watt = 1 j/s

• 1 kwh​

Population Growth Rate

• Formula: (Births - Deaths) / Total Population x 100 

• What it calculates: The percentage change in a population over a specific time period. 

Percent Change

• Formula: (New Value - Old Value) / Old Value x 100 

• What it calculates: The percentage difference between two values. 

Rule of 70

• Formula: 70 / Growth Rate 

• What it calculates: The approximate time it takes for a population to double at a given growth rate. 

Population Density

• Formula: Total Population / Land Area 

• What it calculates: The number of individuals living in a given area. 

Efficiency

• Formula: Energy Output / Energy Input x 100 

• What it calculates: The percentage of energy that is converted from one form to another. 

Rate of Change

• Final - Initial / Final time - Initial time

Gross Primary Productivity (GPP)

• GPP = Total solar energy captured by plants − Energy lost due to respiration by plants

• Aka the rate of photosynthesis by plants

Net Primary Productivity (NPP)

• Gross primary productivity (GPP) - Respiration

The 10% Rule

• The 10% rule states that roughly only 10% of energy transfers between trophic levels in a food chain, with the rest being lost as heat.

Dimensional Analysis

• Quantity 1 x (Conversion factor / Quantity 2 ) = Result

Half-Life

• t½ = ln (2) / λ

• t1/2 represents the half-life and λ is the decay constant

Respiration

• C6H12O6 + 6O2 → 6CO2 + 6H2O

Combustion

• Hydrocarbons (CxHy) + O2 → CO2 + H2O

Photosynthesis

• 6CO2 + 6H2O + sunlight → C6H12O6 + 6O2

Ocean Acidification

• CO2 + H2O ↔ H2CO3 ↔ H+ + HCO3-

Photochemical Smog Formation

• NOx + VOCs + heat + sunlight → smog

Stratospheric Ozone Depletion

• O3 + Cl → O2 + ClO