Concept 53.5 Notes: Density-Dependent Regulation of Populations

Density-independent factors: birth and/or death rates do not change with population density; variation is driven by external abiotic factors (e.g., temperature, precipitation).
Density-dependent factors: birth and/or death rates change as population density changes; higher density often reduces per-capita birth or increases per-capita death.
Per-capita rates: let $b(N)$ be the per-capita birth rate and $d(N)$ the per-capita death rate. Density dependence means $db/dN$ , $dd/dN$ may be nonzero.
Population growth is governed by the difference between births and deaths. With immigration/emigration considered (often assumed zero or equal), population grows if $b(N) > d(N)$ and declines if $d(N) > b(N)$ .
Equilibrium density $Q$ occurs when $b(Q) = d(Q)$ ; at this point per-capita growth is zero and the population can stay stable if other fluxes (immigration/emigration) balance as well.
Model insight: total births $B = b(N) imes N$ and total deaths $D = d(N) imes N$ ; at equilibrium $B = D$ .
Density-independent shocks can cause large, abrupt changes in abundance (e.g., drought causing high mortality), but cannot consistently push a large population down or a small population up over time.
Regulation vs stability: a population is regulated when density-dependent factors cause declines at high density or increases at low density, providing negative feedback.

When density is low: $b(N) > d(N)$ → population grows.
When density is high: $d(N) > b(N)$ → population declines.
Equations to formalize: per-capita growth rate $r(N) = b(N) - d(N)$ ; population growth if $r(N) > 0$ , decline if $r(N) < 0$ ; equilibrium at $r(N)=0$ .
Simple density-dependent model (birth rate changes with density; death rate constant): at equilibrium density $Q$ , $b(Q) = d$ ; below $Q$ , births exceed deaths; above $Q$ , deaths exceed births.

Competition for resources: higher density reduces reproductive rates (e.g., more crowding means fewer nutrients, water).
- Practical note: farmers use fertilizers to mitigate resource limitation and maintain yields.
Disease: transmission rate often increases with crowding, raising mortality and/or reducing birth.
Predation: predation pressure can rise with prey density, reducing survival.
Territoriality: space becomes limiting, preventing further increases in density.
Intrinsic factors: physiological and hormonal changes at high density can suppress reproduction.
Toxic wastes: accumulation of toxins (e.g., ethanol in yeast) can limit growth and survival at high density.
These mechanisms exemplify negative feedback that slows growth as density rises.

Population sizes fluctuate year to year due to multiple factors (biotic and abiotic).
Stability vs fluctuation: long-term studies show large-mammal populations can be variable (e.g., Isle Royale moose and wolves).
Population cycles vary by taxa:
- Small herbivores (voles, lemmings): ~3–4 year cycles.
- Some birds (ruffed grouse, ptarmigans): ~9–11 year cycles.
- Snowshoe hare–lynx: ~10-year cycles in northern forests.
Cycles often arise from predator–prey dynamics and resource availability, with time-lagged responses.

Hare cycles: two main hypotheses—winter food shortage vs predator–prey interactions.
Experimental test ( Yukon, 20 years ): extra winter food increased density but did not stop cycles; cycles persisted, suggesting food shortage alone does not drive cycles.
Predator exclusion (electric fences): reducing predators nearly eliminated the collapse phase; predation appears essential to hare cycles.

Immigration and emigration affect population dynamics, especially when many local populations are linked in a metapopulation.
Metapopulation: discrete habitat patches vary in size, quality, and isolation; local extinctions can be recolonized by immigrants.
Persistence arises from a balance of local extinctions and recolonizations.

Species: Glanville fritillary butterfly (Melitaea cinxia) across Åland Islands (~500 occupied patches, ~4,000 suitable patches).
Key concept: movement between local populations allows recolonization and persistence of the metapopulation.
Dispersal is influenced by genotype at the Pgi gene (phosphoglucoisomerase), which affects glycolysis and dispersal ability.
Findings: heterozygous individuals disperse farther than homozygotes, especially in cooler conditions in the morning, implying a fitness advantage for heterozygotes in movement and colonization.

Population size is shaped by density-dependent (regulated) and density-independent factors.
Equilibrium density $Q$ occurs when $b(Q) = d(Q)$ ; regulation requires negative feedback that slows growth as density increases.
Mechanisms of density dependence include competition, disease, predation, territoriality, intrinsic physiology, and toxins.
Population dynamics show cycles and fluctuations driven by complex interactions; experimental evidence highlights the role of predators in generating cycles.
Metapopulations emphasize immigration/emigration and patch dynamics; dispersal genetics (e.g., Pgi) can influence connectivity and persistence of the network of populations.