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A decomposer breaks down dead organic material and absorbs products of that breakdown; many bacteria and fungi perform this role. Decomposers connect detritus from different trophic levels to material recycling, so placing all decomposers at one final step of every food chain is misleading. See Clark, Douglas and Choi, Biology 2e, 46.1: grazing and detrital food webs.

Detritus is nonliving organic material, including dead remains and organic wastes. It is a resource for decomposers, not itself an organism or a predator. In the illustrative food web, the dashed arrow from algae to detritus denotes a material transfer; the solid arrow from detritus to decomposers denotes resource use.

The goal of ecology is to explain where organisms live, how many there are, and how their interactions with one another and their surroundings change those patterns. Living partners include prey, predators and parasites; nonliving conditions include light, temperature and water. An ecosystem brings these interacting parts into one study system. See Clark, Douglas and Choi, Biology 2e, 44.1: the scope of ecology.

Start with an invented aquatic food web: photosynthetic algae feed zooplankton, which feed small fish, which feed large fish. That food chain has four feeding positions and three feeding arrows. Dead material also reaches decomposers through detritus, so the food web branches rather than forming a single ladder.

The appeal of ecology is that an organism's surroundings include other organisms that change those surroundings. Photosynthesis links light to living material; predation transfers that material between organisms; decomposers return its constituent chemical elements to forms that can be used again. These connections help explain why changing one part of an ecosystem can affect distant parts of its food web, although an arrow alone does not predict the size or even the direction of an indirect change. Population dynamics supplies quantitative tools when the question concerns changing counts.

In 1866, Ernst Haeckel's Generelle Morphologie der Organismen included a section titled Oecologie und Chorologie in volume 2, beginning on page 286. This places the terminology of ecology in an early systematic treatment of organisms and their relationships. See Haeckel, Generelle Morphologie der Organismen, volume 2 (1866), contents and p. 286. A later quantitative landmark is Raymond L. Lindeman's 1942 treatment of ecosystems through feeding relationships and energy flow. See Lindeman, The Trophic-Dynamic Aspect of Ecology, Ecology 23 (1942), 399–417.

Energy flow tracks energy entering an ecosystem, passing through organisms and leaving its boundary. To see its quantitative effect, assume net production at one trophic level is $P_1=1000\mathrm{kJ}{\mathrm{m}}^{-2}\mathrm{da}{\mathrm{y}}^{-1}$ and assume a transfer efficiency $\epsilon =0.10$ at each of two successive steps. Here $P_i$ measures the energy incorporated into new living material per unit area per day, after that level's own cellular respiration; it is not a count of organisms or a standing stock. The joule supplies the energy unit, with $1\mathrm{kJ}=1000\mathrm{J}$.

Only $10/1000=0.01$, or one percent, of the initial production reaches level 3 in this toy food chain. The first step leaves $1000-100=900$ and the second $100-10=90$ outside the next level's new production. These differences can include uneaten material, wastes, and energy released as heat during cellular respiration; their separate amounts have not been assigned. Detritus can still carry energy to decomposers. The 10 percent efficiency is an assumption, not a universal law: transfer efficiencies vary with the organisms, food and conditions. The production ratio $P_{i+1}/P_i$ also differs from the fraction of an individual meal converted into growth. See Clark, Douglas and Choi, Biology 2e, 46.2: production and transfer efficiency.

The shrinking budget explains why supporting another trophic level requires enough production below it. It does not prove an exact maximum length for every food chain, particularly when a food web imports resources or has branching diets. Lindeman's 1942 paper grouped feeding relationships into trophic levels, compared transfers and cellular respiration, and emphasized the ecosystem as a unit connecting living and nonliving components. That viewpoint made different organisms comparable through a common energy budget. See Lindeman, The Trophic-Dynamic Aspect of Ecology (1942).

Material recycling and energy flow describe different bookkeeping. Carbon, nitrogen and phosphorus can be reused through chemical reactions and transfers between organisms and their surroundings. Energy transferred as heat is conserved, but is no longer the same store of chemical energy available to a consumer; photosynthetic primary producers need continuing light input. A decomposer helps recycle material and also releases heat through metabolism. Thus loss from one feeding budget means transfer into other forms or routes, never destruction of energy. See Clark, Douglas and Choi, Biology 2e, 46.3: material cycles. Conservation of energy applies to the whole accounting.