CBSE · Class 12 · Biology · Chapter 12

Ecosystem — Formula Sheet

Board Formulas

15 formulas

1.Primary Production and Productivity
$Production: g m^{- 2} or kcal m^{- 2}; Productivity: g m^{- 2} yr^{- 1} or kcal m^{- 2} yr^{- 1}$
Primary production is the biomass made per unit area by plants during photosynthesis. The rate of biomass production is productivity, so it carries a per-time unit.
2.Net Primary Productivity★
$NPP = GPP - R$
$GPP$ : Gross primary productivity (g m⁻² yr⁻¹ or kcal m⁻² yr⁻¹) · $R$ : Respiration losses of the producers (same units) · $NPP$ : Net primary productivity (same units)
GPP is the rate of production of organic matter in photosynthesis. Plants use part of it in respiration (R). NPP is the biomass available to heterotrophs (herbivores and decomposers).
3.Secondary Productivity
$Secondary productivity = rate of formation of new organic matter by consumers$
Primary productivity depends on the plant species, environmental factors, nutrient availability and the photosynthetic capacity of plants.
4.Global Net Primary Productivity
$NPP_{biosphere} \approx 170 \times 1 0^{9} tons yr^{- 1}; NPP_{oceans} \approx 55 \times 1 0^{9} tons yr^{- 1}$
Dry weight of organic matter per year. Oceans cover about 70% of the surface but give only about 55 of the 170 billion tons.
5.Steps of Decomposition★
$Fragmentation \to Leaching \to Catabolism \to Humification \to Mineralisation$
Detritivores (earthworm) fragment detritus; water-soluble nutrients leach into the soil and precipitate as unavailable salts; bacterial and fungal enzymes catabolise detritus; humus forms; humus is mineralised to release inorganic nutrients. The steps operate simultaneously.
6.Humus
$Humus: dark, amorphous, colloidal, very slow to decompose, reservoir of nutrients$
Humification and mineralisation happen in the soil. Humus resists microbial action, which is why it decomposes at an extremely slow rate.
7.Rate of Decomposition
$Faster: nitrogen-rich, water-soluble sugars, warm and moist; Slower: lignin, chitin, low temperature, anaerobiosis$
Decomposition is an oxygen-requiring process. Chemical composition of detritus and climatic factors (temperature, soil moisture) control the rate.
8.Food Chains
$GFC: Grass \to Goat \to Man; DFC: begins with dead organic matter (detritus)$
Decomposers (mainly fungi and bacteria) are saprotrophs. In aquatic ecosystems the GFC is the major conduit for energy; on land a much larger fraction of energy flows through the DFC.
9.Trophic Levels
$T_{1} : producers \to T_{2} : primary consumers \to T_{3} : secondary consumers \to T_{4} : tertiary consumers$
Herbivores are primary consumers; carnivores feeding on them are secondary consumers. Food chains interconnect to form a food web.
10.Photosynthetically Active Radiation
$PAR < 50% of incident solar radiation; plants capture 2 to 10% of PAR$
Except for deep-sea hydrothermal ecosystems, the sun is the only source of energy. This small captured fraction sustains the entire living world.
11.Unidirectional Energy Flow
$Sun \to producers \to consumers; energy lost as heat at each step$
Ecosystems obey the second law of thermodynamics: they need a constant input of energy to counteract the tendency towards disorder.
12.Ten Per Cent Law★
$E_{n + 1} = 0.1 \times E_{n}$
$E_{n}$ : Energy at trophic level n (J or kcal) · $E_{n + 1}$ : Energy transferred to the next trophic level
Only about 10% of the energy at one trophic level is transferred to the next; the rest is lost, mostly as heat. This limits the number of trophic levels.
13.Energy at the nth Trophic Level
$E_{n} = E_{1} \times (0.1)^{n - 1}$
$E_{1}$ : Energy fixed by producers (J or kcal) · $n$ : Trophic level number (producers are n = 1)
Repeated application of the 10% law. Going down the chain, divide by 0.1 for each step: E₁ = Eₙ/(0.1)ⁿ⁻¹.
14.Standing Crop
$Standing crop = mass of living material at a trophic level at a given time$
Measured as biomass or as number per unit area. Biomass in dry weight is more accurate than fresh weight.
15.Ecological Pyramids★
$Number, biomass: usually upright, can be inverted; Energy: always upright$
Pyramid of biomass in the sea is generally inverted because the biomass of fishes far exceeds that of phytoplankton. Energy is always lost as heat at each step, so the energy pyramid can never be inverted.