Analyze the biosphere: population dynamics, species interactions, ecosystem stability and biodiversity

Learning goal: Describe the biosphere as the living sphere of the Earth system; explain how populations grow, are limited and adapt through natural selection; describe species interactions and what makes an ecosystem stable or unstable; and measure biodiversity with a diversity index so that two habitats can be compared with numbers rather than impressions.

What the biosphere is. The biosphere is every living thing on Earth together with the parts of the atmosphere, hydrosphere and lithosphere that living things occupy. It is thin: a few kilometers of ocean depth, the soil, and the lower atmosphere. Environmental science treats the biosphere as one of four interacting spheres, and this lesson looks inside it. The organizing units are the population (all the individuals of one species in one area at one time), the community (all the populations that live together) and the ecosystem (the community plus the abiotic factors, such as sunlight, temperature, water, soil and nutrients, that it exchanges matter and energy with).

Population dynamics. A population changes size through births, deaths, immigration and emigration. If resources are unlimited, each individual contributes the same average number of offspring regardless of crowding, and the population grows exponentially: the increase each year is a fixed fraction of the current size, so the curve gets steeper and steeper. Real populations cannot do this for long. Food, space, water and nesting sites become scarcer per individual as numbers rise, while disease spreads more easily and predators may concentrate on the abundant prey. These are limiting factors, and the ones whose effect gets stronger as the population gets denser (competition for food, spread of disease, predation) are called density-dependent. Factors that hit a population regardless of its density (a hard frost, a flood, a fire) are density-independent. As density-dependent factors bite, growth slows, and the population levels off near the carrying capacity, the largest population the environment can sustain over time. This produces the S-shaped logistic curve. A population can overshoot carrying capacity, especially when food is abundant for a season, and then crash; the historical stories of deer on the Kaibab Plateau and moose on Isle Royale are often used to illustrate overshoot, but the exact counts in those cases are debated, so this lesson uses a clearly hypothetical data set instead.

A worked model in the prose. Suppose a hypothetical island is colonized by 20 herbivores and the count is repeated every two years: year 0, 20; year 2, 45; year 4, 95; year 6, 180; year 8, 290; year 10, 370; year 12, 410; year 14, 425; year 16, 430. Between years 0 and 6 the population roughly doubles every two years: 20 to 45 to 95 to 180. That is the exponential phase. From year 8 the doublings stop: 290, 370, 410, 425, 430. The additions shrink from 110 to 80 to 40 to 15 to 5. The curve is flattening toward about 430 animals, which is the estimate of carrying capacity from these data. Notice what the data do not tell us: they do not say which limiting factor is responsible. That requires a separate investigation, such as measuring available forage or recording causes of death.

Survivorship. Populations also differ in when their members die. A survivorship curve plots the fraction of a cohort still alive against age. Type I species (large mammals, including humans in wealthy countries) have high survival until old age; Type II species have a roughly constant chance of dying at any age (some birds and rodents); Type III species produce enormous numbers of offspring of which most die young (oysters, many fish, many plants). A survivorship curve is a diagnostic tool: a shift toward early deaths in a Type I population suggests a new stress on the young, such as a toxin or a food shortage.

Evolution and adaptation in populations. Individuals do not adapt in the evolutionary sense; populations do, over generations. The conditions are simple: individuals vary, some of that variation is heritable, and individuals with some variants leave more surviving offspring than others in the current environment. Over generations the favored variants become more common. This is natural selection, and the result is adaptation: a population better matched to its environment. Three warnings. First, adaptation is to the present environment; if the environment changes faster than the population can respond, the population declines or vanishes. Second, an adaptation that is useful against one pressure may be costly against another. Third, a population that has lost genetic variation (after a crash, for example) has less raw material for future selection, which is one reason small populations are vulnerable.

Species interactions. Populations in a community interact in a handful of ways. Competition (both species harmed) occurs when two species use the same limited resource. Predation and herbivory (one benefits, one is harmed) transfer energy up the food web and regulate prey numbers. Parasitism is predation in slow motion: the parasite benefits, the host is harmed but usually not killed at once. Mutualism benefits both partners: pollinators and flowering plants, or nitrogen-fixing bacteria and legume roots. Commensalism benefits one and leaves the other unaffected. Some species have effects out of proportion to their numbers; a keystone species is one whose removal reorganizes the whole community, such as a top predator whose absence lets one herbivore overrun the vegetation.

Equilibrium and stability. An ecosystem is in equilibrium when its populations fluctuate around fairly steady values and its flows of energy and nutrients are balanced over time. Stability has two components: resistance (how little the system changes when disturbed) and resilience (how quickly it returns afterwards). Diversity generally contributes to stability because a community with many species has more alternative pathways for energy and more chance that some species tolerate a given disturbance. Feedback matters too: a predator population that grows when prey are abundant and shrinks when prey are scarce is a negative feedback that damps swings. Ecosystems are not guaranteed to return to the same state; a severe disturbance can push a system past a threshold into a different equilibrium, as when a clear lake becomes a turbid, algae-dominated one.

Biodiversity, measured. Biodiversity has three levels: genetic diversity within a species, species diversity within a community, and ecosystem diversity across a region. Species diversity is more than a species count. Richness is the number of species; evenness is how equally individuals are spread among them. A field with 30 plants of three species split 10-10-10 is more diverse in practice than one split 26-2-2, even though both have richness 3. Simpson's index captures both: D = 1 − Σ n(n − 1) / N(N − 1), where n is the count of each species and N is the total. D is the probability that two individuals drawn at random belong to different species, so higher D means more diverse. For the 10-10-10 field, Σ n(n − 1) = 3 × 90 = 270 and N(N − 1) = 30 × 29 = 870, so D = 1 − 270/870 ≈ 0.69. For the 26-2-2 field, Σ n(n − 1) = 650 + 2 + 2 = 654, so D = 1 − 654/870 ≈ 0.25. The numbers make the difference visible.

Bioaccumulation and biomagnification. Some substances (mercury, certain pesticides, PCBs) are stored in tissue rather than excreted. Bioaccumulation is the build-up within one organism over its lifetime; biomagnification is the increase in concentration from one trophic level to the next, because each predator eats many prey and keeps their stored load. Top predators and long-lived fish therefore carry the highest concentrations, which is why fish-consumption advisories target particular species and sizes. The remedy is upstream: reduce the input of the substance, because once it is in the food web it stays for years.

Worked growth calculation: A hypothetical deer population of 100 grows by 20% per year with no limits. Year 1: 100 × 1.2 = 120. Year 2: 120 × 1.2 = 144. Year 3: 144 × 1.2 = 172.8, about 173. Year 4: about 207. The yearly increase (20, 24, 29, 35) grows because it is a fixed fraction of a growing base. If the same population were near a carrying capacity of 500, the logistic model gives growth = 0.2 × N × (1 − N/500). At N = 100 that is 0.2 × 100 × 0.8 = 16 per year; at N = 250 it is 0.2 × 250 × 0.5 = 25; at N = 450 it is 0.2 × 450 × 0.1 = 9. Growth is fastest at half of carrying capacity and shrinks toward zero as N approaches 500.

Worked diversity comparison: Two hypothetical woodlots are sampled for trees. Woodlot A: oak 12, maple 9, hickory 6, beech 3 (N = 30). Woodlot B: maple 27, oak 2, ash 1 (N = 30). For A: Σ n(n − 1) = 12 × 11 + 9 × 8 + 6 × 5 + 3 × 2 = 132 + 72 + 30 + 6 = 240; N(N − 1) = 870; D = 1 − 240/870 ≈ 0.72. For B: 27 × 26 + 2 × 1 + 0 = 702 + 2 = 704; D = 1 − 704/870 ≈ 0.19. Woodlot A has both higher richness (4 versus 3) and far higher evenness, and its D is nearly four times B's. Conclusion, with its condition: on the basis of this one sample of trees, A is the more diverse habitat; the sample says nothing about birds, insects or soil organisms.

Worked interaction analysis: A pond has algae, small fish that graze algae, and a heron that eats the small fish. A student proposes removing the heron to "help the fish." Reasoning: with the predator gone, the density-dependent control on the fish weakens, fish numbers rise, grazing pressure on algae rises, algae decline, and then the fish face food scarcity and a possible crash. The heron was part of a negative feedback loop. Removing a top predator does not simply add its prey to the system; it changes the interactions that stabilized the system.

Worked survivorship reading: A hypothetical cohort of 1,000 turtles hatches. Alive at age 1: 80; at age 5: 40; at age 20: 30; at age 40: 15. The steep drop in the first year (92% dead) followed by slow decline is a Type III pattern. Management implication: protecting nests and hatchlings addresses the stage where most deaths occur, but because so few reach adulthood, each breeding adult is disproportionately valuable, so protecting adults may also have a large effect on population growth; which protection matters most needs data on reproduction and age at maturity.

Representation task: Using the island herbivore data in the lesson (years 0 to 16), draw the curve on graph paper, mark the exponential phase and the leveling phase, draw a dashed horizontal line at your estimate of carrying capacity, and annotate the graph with two density-dependent and one density-independent limiting factor that could plausibly act on an island herbivore. Write one sentence explaining why the additions between counts shrink after year 8.

Safe investigation, quadrat sampling: Choose two nearby habitats, for example a mown lawn and an unmown edge or wooded strip. In each, place a 0.5 m × 0.5 m square frame (string on four stakes works) at five random spots. In each quadrat, count the individual plants of each recognizable type (you may use working names such as "broad-leaf A" if you cannot identify species). Total the counts per type for each habitat and compute Simpson's index. Record weather, date and any disturbance. What the sample supports: a comparison of plant diversity at these spots on this day. What it cannot show: animal diversity, seasonal change, or whether the difference is caused by mowing rather than by soil or shade; a fair test of mowing would need matched plots with only mowing varied.

Independent performance: Write an explanation of at least 250 words titled "Why a bigger species list is not the whole story of biodiversity." Success criteria: it defines richness and evenness and shows with a small numeric example how two habitats with the same richness can differ in Simpson's index; it explains what carrying capacity is and names one density-dependent and one density-independent limiting factor; it explains how natural selection produces adaptation in a population, including why individuals do not adapt in this sense; it explains one way diversity contributes to ecosystem stability; and it states one thing a diversity index calculated from a single sample cannot tell you.