Chicxulub impact 2026-10-25
The large impact associated with the Cretaceous–Palaeogene boundary and its mass extinction. Atmospheric dust, aerosols and soot can connect an impact to reduced sunlight, suppressed photosynthesis and disruption of food webs; these environmental mechanisms distinguish the trigger from its biological effects.
Detritus 2026-10-13
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.
Ecology 2026-10-13
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 (ecology) 2026-10-13
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 and assume a transfer efficiency at each of two successive steps. Here 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 .
Only , or one percent, of the initial production reaches level 3 in this toy food chain. The first step leaves and the second 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 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.
Fish 2026-10-13
Food web 2026-10-13
A food web records resource-consumer interactions among species. A linear food chain is a special case. Positive interaction coefficients alone do not imply persistence: the per-capita growth balances must admit feasible positive long-term mean abundances.
The controversy around Silent Spring by Rachel Carson was partly a disagreement about evidence and partly a disagreement about who should decide how chemical benefits and harms were compared. Rachel Carson addressed a public accustomed to hearing successful pest control described as an uncomplicated application of scientific progress. Her ecological argument enlarged the system being assessed: a chemical could affect non-target organisms, move through water and food webs, and remain relevant long after its immediate application.
That made establishing causation a real scientific challenge. A dead bird or a declining population does not by itself identify the cause. Relevant evidence includes exposure, toxicity, timing, persistence, effects on reproduction and comparisons with alternative causes. Conversely, absence of immediate visible mortality is not proof of absence of a delayed population effect. Her account drew attention to the difference between a short laboratory endpoint and a continuing ecological process. The Clear Lake example in the book, involving DDD rather than DDT, also makes the food-web dimension of the argument concrete.[ref]
Silent Spring by Rachel Carson. chapter 4: the Clear Lake DDD case and transfer through the aquatic food web
Critics could therefore raise legitimate questions about generalizing from particular incidents, distinguishing exposure from demonstrated harm and weighing chemical control against its agricultural or disease-control benefits. Those questions required comparative evidence. They did not justify treating every ecological warning as an argument that no pesticide could ever be used. Carson's 1963 congressional testimony acknowledged a continuing role for pesticides while calling for stronger control and research; that position must be distinguished from an indiscriminate prohibition.[ref]
Statement before Congress by Rachel Carson (1963). 1963 congressional testimony, contemporary published summary: continued need for pesticides, tighter controls and stronger research
The public conflict also concerned credibility. Chemical expertise, field biology and observations reported by affected people did not always command equal authority. An argument framed solely in terms of immediate effectiveness could omit costs borne outside the treated site. An argument framed solely in terms of alarming anecdotes could omit dose, exposure and alternatives. The appropriate response was not to declare one camp inherently scientific, but to make the competing claims and standards of inference explicit.
Publication and communication intensified these difficulties. A book for a broad audience had to convey mechanisms and uncertainty without reproducing an entire technical literature. Memorable prose could make neglected evidence visible, while also allowing critics to contest the balance of examples. The historical significance of the dispute is not that every statement in the book became permanently correct. It is that ecological effects and the burden of investigating them became central to the public assessment of chemical interventions.
Carson's challenge was consequently both evidential and institutional: show why effects outside the target organism counted, support causal claims with more than coincidence, and argue that benefits did not remove the need to investigate wider consequences. A sound answer recognizes genuine scientific uncertainties while distinguishing them from objections that simply excluded ecological questions from the assessment.
Past exam of the mathematics course of the University of Cambridge 2002 iii Paper 57 2 c Solution Created 2026-10-03 Updated 2026-10-14
Not in general. A food web with Lotka-Volterra equations has per-capita balances . If all species remain bounded above and away from zero, averaging requires with positive means. Many webs have no feasible positive solution. Even a feasible solution does not ensure stability or persistence when the weighted skew-symmetric matrix structure and its coercive first integral are absent.
A simple resource shared by two consumers already illustrates competitive exclusion principle. Suppose their per-capita equations are and . ThenIf , the ratio has exponential drift, incompatible with bounded persistence of both consumers. The lower break-even-resource consumer has the advantage; equal break-even requirements are a special neutral balance, not generic coexistence. More complicated feeding links can provide additional niches, but positive coefficients and a larger web do not by themselves guarantee that every species survives. One must test feasibility, invasion into the relevant boundary states and stability, with explicit assumptions about resource renewal and self-limitation.
A mass extinction is driven by changes that overwhelm organisms' physiological tolerances or destroy their food and habitat systems. Distinguish the initiating forcing from the linked environmental mechanisms: one event can generate several contributors.
- Large extraterrestrial impact. At the Cretaceous–Palaeogene boundary, the Chicxulub impact injected dust, aerosols and soot that reduced incoming sunlight and photosynthesis, disrupting food webs; rapid heating, fires and subsequent cooling added stresses. The impact is the trigger, while darkness and loss of primary production are proximate mechanisms.
- Large-scale volcanism. Eruption and intrusion of large igneous provinces, notably the Siberian Traps around the end-Permian crisis, release or mobilize gases and can produce rapid climate change. Carbon dioxide favors warming; sulfur-bearing emissions can cause shorter cooling and acid deposition. The outcome depends on rate, duration and interacting reservoirs, rather than eruption volume alone.
- Ocean anoxia and euxinia. Warming lowers oxygen solubility and can strengthen stratification; altered nutrient supply increases oxygen demand. Oxygen loss removes habitable marine volume, while sulfide in anoxic waters can be toxic. These processes contributed to the end-Permian marine crisis and can reinforce warming-driven mortality.
- Ocean ocean acidification and elevated carbon dioxide. Rapid addition of carbon dioxide changes seawater carbonate chemistry and can impair biomineralization, while high carbon dioxide also challenges physiological acid–base regulation. Susceptibility varies with physiology; this is a linked mechanism rather than proof that every calcifying group responds identically.
- Rapid cooling and eustatic sea level change. Late Ordovician glaciation and regression reduced shallow-marine habitat and changed temperatures and circulation; subsequent warming and oxygen loss introduced a different set of stresses. Habitat loss and climate change can therefore contribute in successive phases of one crisis.
These examples supply more than four drivers or contributors. The historical effects of volcanism, warming, oxygen loss and elevated carbon dioxide can act together rather than compete as mutually exclusive explanations.[ref]
Paleophysiology and end-Permian mass extinction by Andrew H. Knoll and others. Abstract and introduction: linked physiological effects of warming, anoxia, sulfide and hypercapnia
Predation 2026-10-13
Predation is the consumption of prey by a predator, affecting the demographic rates of both populations.
In the usual animal-feeding sense, a predator kills and eats its prey. This distinguishes the interaction from feeding on already-dead material and from the prolonged exploitation of a living host in parasitism. In the illustrative food web, a small fish eating zooplankton is a predator; a large fish eating that small fish makes the same small fish its prey. These roles belong to a particular interaction. See Clark, Douglas and Choi, Biology 2e, 45.6: predation and community interactions.
For a toy count, suppose 50 small fish begin a day and 8 are eaten by large fish. With births, other deaths and movement explicitly omitted, 42 small fish remain, and the fraction removed by predation is . This measures removal of prey, not production of new predators. Food intake can support survival and reproduction, but eight meals do not imply eight new predators; energy flow and life-history details intervene. Lotka-Volterra equations provide one idealized account of such population dynamics, rather than a guarantee that every interacting pair must cycle.
Prey Created 2026-10-13 Updated 2026-10-20
Prey is an organism consumed by a predator in predation. The name describes the receiving end of that interaction: a small fish can be prey for a large fish while being a predator of zooplankton. In a food web drawn with resource-to-consumer arrows, a feeding arrow goes outward from the prey toward its predator. This convention makes the route of food and energy easy to follow.
Primary producer Created 2026-10-13 Updated 2026-10-20
A primary producer builds organic chemical compounds from inorganic sources. Photosynthetic algae, plants and cyanobacteria use light energy for this role through photosynthesis and carbon fixation. The role supplies new living material to a food web; it does not mean that the organism creates energy.
Trophic level 2026-10-13
A trophic level describes feeding position relative to primary producers. Assign primary producers level 1; in the illustrated food chain, zooplankton occupy level 2, small fish level 3, and large fish level 4. Following a single feeding path adds one level at each step. The labels make dependence on the initial resource visible, but a branching food web can give an organism several feeding paths. See Clark, Douglas and Choi, Biology 2e, 46.1: feeding positions and branching food webs.
An omnivore can obtain food from more than one trophic level. As an explicitly assumed diet-weighted example, suppose an omnivore gets half its assimilated food energy from level-1 primary producers and half from level-2 consumers. Define its trophic level as one plus the weighted mean level of its food: . This computed position depends on the specified diet and weighting convention; it is not an immutable property of the species. A different life stage or diet can change it.
Zooplankton Created 2026-10-13 Updated 2026-10-18
Zooplankton are drifting aquatic consumers, including small animals. In the illustrative food web, the chosen zooplankton feed on algae and serve as prey for small fish; this assumed diet is not a claim about every kind of zooplankton.

