Section 5 Professor Donald McFarlane Biology 44 Section 5 Professor Donald McFarlane Lecture 18 Ecology: Population Growth

Population – group of interbreeding individuals occupying the same habitat at the same time Water lilies in a particular lake Humans in New York City Population ecology – study of what factors affect population size and how these factors change over space and time

How populations grow Life tables can provide accurate information about how populations grow from generation to generation Simpler models can give insight to shorter time periods Exponential growth – resources not limiting, prodigious growth Logistic growth – resources limiting, limits to growth

Per capita growth rate Change in population size over any time period Often births and deaths expressed per individual 100 births to 1000 deer = 0.10 50 deaths in 1000 deer = 0.05 Net Reproductive Rate, R0, is approximately birth rate – death rate R0 ~ (b – d) ~ (0.1 – 0.05) = 0.05

dt r = “intrinsic rate of increase” = -ln R0 Tgen The differential growth equation: dN = rN dt

R0 for deer was 0.05 Tgen is 4 years Therefore r = - ln(0.05)/4 = 0.748 dN = rN dt Starting with 10 deer (N0 = 10) N0 = 10 N1 = 17 N2 = 31 ` N3 = 53 N4 = 94 N5 = 163

Exponential growth When r>0, population increase is rapid Characteristic J-shaped curve Occurs when population growth is UNREGULATED by the environment e.g., growth of introduced exotic species, yeast in brewing medium, and global human population

(b) Black-footed ferrets Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 600 400 Predicted abundance Actual abundance 500 400 200 Number of animals Population size 300 200 100 100 2000 2001 2003 2004 2005 2006 1970 1980 1990 2000 Year Survey year (a) Tule elk (b) Black-footed ferrets

Logistic growth Eventually, resources become limiting as populations grow Carrying capacity (K) or upper boundary for population Logistic equation dN = rN ( K – N ) dt K

Not all individuals in a population are the same with respect to births and deaths….. We can account for differences with a LIFE TABLE

Age-specific fertility rate, mx Proportion of female offspring born to females of reproductive age 100 females produce 75 female offspring mx=0.75 Age-specific survivorship rate, lx Use survivorship data to find proportion of individuals alive at the start of any given age class lxmx = contribution of each age class to overall population growth

Density-dependent factors Mortality factor whose influence varies with the density of the population Parasitism, predation, and competition Predators kill few prey when the prey population is low, they kill more prey when the population is higher Detected by plotting mortality against population density and finding positive slope Density-independent factor Mortality factor whose influence is not affected by changes in population size or density Generally physical factors – weather, drought, flood, fire

Life history strategies Continuum r-selected species – high rate of per capita population growth, r, high mortality rates K-selected species – more or less stable populations adapted to exist at or near carrying capacity, K Lower reproductive rate but lower mortality rates

Survivorship curve – plots numbers of surviving individuals at each age Use log scale to make it easier to examine wide range of population sizes Beavers have a fairly uniform rate of death over the life span

3 patterns of survivorship curves Type I – rate of loss of juveniles low and most individuals lost later in life Type II – fairly uniform death rate Beaver example Type III – rate of loss for juveniles high and then loss low for survivors

Population (billions) Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 8 7 6 2000 5 Population (billions) 4 1975 3 1950 2 1900 1 1800 1 C.E 1000 C.E 2000 C.E 7000 B.C.E 6000 B.C.E 5000 B.C.E 4000 B.C.E 3000 B.C.E 2000 B.C.E 1000 B.C.E