Ecology (BIO C322) Population Ecology (cont’d)

Concepts of Rate Population a changing entity  Population dynamics. N = Number of organisms; t = time Average growth rate = ΔN / Δt Specific growth rate (SGR) = ΔN / NΔt Percentage growth rate = SGR x 100

Instantaneous Rates Rate of change when Δt  0 Instantaneous growth rate = dN/dt Instantaneous SGR = dN/Ndt Growth curve vs growth rate curve. Slope at any point on growth curve  growth rate. Point of Inflection: The point where growth rate is maximum.

In non-limiting environment (w.r.t. food, space, others): dN/dt = rN; r = r max = Instantaneous coefficient of population growth or intrinsic rate of natural increase or biotic potential or reproductive potential. ‘r’ depends on environmental condns.

N t = N 0 e rt  r = (ln N t - ln N 0 ) / t; b & d = inst. specific birth & death rates i & e = inst. immigration, emigration rates r = b – d + (i – e); If i = e, then r = b – d; r>0 (b>d)  Population increases exponentially; r<0 (b<d)  Exponential decline; r=0 (b=d)  No change in population size.

Read this… Populations in nature often grow exponentially for short periods when there is ample food & no crowding effects, etc. e.g. plankton blooms, pest eruptions, bacterial growth in new culture media. But exp increase can’t continue very long. Interactions within population & external environmental resistances soon slow down the rate of growth.

Population Growth Forms J-shaped  Exponential increase followed by sudden decline; dN/dt = rN; Sudden decline due to shortage of food resource, sudden temperature change, end of reproductive season. Boom-and-bust pattern.

S-shaped growth form Sigmoid or logistic  4 phases: –Establishment or lag phase; –Logarithmic phase; –Negative acceleration (environ resistance); –Equilibrium. dN/dt = rN [(K - N) / K] = rN [1 – N/K] K = (Max) carrying capacity = Max no. of individuals of a population that can survive in a given habitat = 2 x Inflection point.

Practice Concept The equation for logistic growth patterns is the same as the exponential one, with the exception of the expression [1 – N/K]. This term indicates the environmental resistance created by the growing population itself, which brings about an increasing reduction in the potential reproduction rate, as population size approaches carrying capacity.

Human population is constantly increasing…

But it is predicted that we would reach ‘K’ value in 21 st century!!

Exponential: Highest growth form; Logistic: Lowest growth form (-ve feedback); Intermediate pattern for most populations.

Fluctuations around ‘K’ value The S-shaped (logistic) growth curve suggests a levelled-off stage in which population and environment are at equilibrium (at the carrying capacity). However, in biological systems, equilibrium is a dynamic state of fluctuation rather than an unwavering constant.

Irruptive Populations Insects, some plants, pests. Explode in numbers unexpectedly in a boom-and-bust pattern. e.g. At certain time of year, mosquitoes ↑. Fluctuations in population size: –Due to extrinsic factors (temp, rainfall); –Due to intrinsic factors (disease, predation). Cyclic species: Show regular variation in population size (irrespective of environ).

9- to 10-year Oscillations (Canada) Prey: Snowshoe hare (Lepus americanus). Predator: lynx (Felix lynx).

Lynx population peak  9-10 years. Peaks of abundance followed by crashes. Similar cycle for hare. Hare cycle precedes lynx cycle by 1-2 years. Hare cycle either predator-driven {top-down} or resource (food)-driven {bottom-up}  Both.

Pests always harmful? Time to rethink… Coniferous forests: Older trees suppressing growth of young trees (shade). But older trees vulnerable to defoliation by caterpillars of budworm. Older trees killed  Nutrient return to soil. Younger trees released from shade- suppression, grow rapidly.

Coniferous Forest rejuvenated!!

Mechanisms of Population Regulation Density-independent factor (Extrinsic): If its effect is independent of the population size. –Climate  Determinant of J-shaped growth form. Density-dependent factor (Intrinsic): Its effect on population is a function of population density. –Biotic factors (self-crowding, competition, parasites, pathogens)  Determinants of S- shaped growth form.

Density-dependent Regulation in Plants Log of average plant weight (y-axis; grams) plotted against log of population density (x-axis; plants per m 2 )  Line with a slope of -3/2; Self-thinning or -3/2 power law.