BIO326 : Population : Population Dynamics : Lesson

Glossary terms that are important in this lesson: Density-dependence, density-independence, deterministic, emigration, exponential, fecundity, geometric, habitat fragmentation, immigration, intrinsic rate of increase, metapopulation, mortality, rate, regulation, steady-state, stochastic, territoriality

Populations change in size and density, depending on birth rates and death rates. Environmental conditions affect life table values and population models predict future changes in population density.

I. Population Growth and Regulation

1. Exponential Growth
   • A population increases in proportion to its size: larger the population, the more individuals are added
   • Model of population growth N(t) = N(0)e^rt
     • t = time
     • 0 = beginning time; N(0) = population size at time, 0
     • e = a constant, 2.718281828 (rounded off to 3 significant digits = 2.72)
     • r = exponential growth rate, called the intrinsic rate of increase, and is the increase rate of a population on a per capita basis at each instant of time (an instantaneous growth rate); it equals the difference between birth rate (b) and death rate (d)

2. Geometric Growth
   • Growth over discrete intervals
   • Rate of growth (lambda) is the ratio of population size at the end of one interval to population size at the end of the previous interval
     • N(t+1) = N(t) * (lambda);    N(t)=N(0) * (lambda)^t
     • r = log_e(lambda) and lambda = e^rt; when r = 0, lambda = 1 and population density is stable

3. Intrinsic Rate of Increase
   • Approximated by a formula from a life table
   • Net reproductive rate is the sum of the l_xb_x column in the life table; it is the expected total offspring production in a lifetime

4. Growth Potential
   • Ring-necked pheasants on Protection Island
     • 8 adults increased to 1,325 in 5 years:
       • 166-fold increase = 1325 = N(5) = 8e^r5,   log_e(1325/8) = r5    (log_e(1325/8))/5 = r = 1.022; lambda = e^r = 2.779
       • 8*2.78⁵ = 8*2.78*2.78*2.78*2.78*2.78 = 1328 pheasants in 5 years
     • Doubling time: N(t) = N(0)e^rt    where N(t)/N(0) = 2 = e^rt     log_e(2) = rt
       • t = 0.69147/r,   if r = 1.02, the population will double in 67.8 years
       • if lambda = 2.78, this is a 178% annual rate of increase; the population almost tripled (= 2.78) every year

5. Growth Varies with Environmental Conditions
   • Rhizopertha grows more rapidly than Calandra at warmer temperatures
   • Grain beetles grow poorly at low temperatures and humidities; therefore, store grain in cool, dry conditions (Fig. 15.7)
   • Environmental conditions determine the age-specific birth and death rates in a life table and growth rates are calculated for a life table: rabbits in arid and Mediterranean climates (Table 15.10)

6. Regulation of Population Size
   • Under ideal conditions, population growth rates produce more offspring than the earth can hold = exponential growth
   • As a population increases, it decreases its further opportunity for growth
   • Carrying capacity: there is a population density that the environment can sustain at equilibrium; steady-state condition of a stable population density even though there are births and deaths
   • Model: r = r_o(1-N/K): the actual rate of growth is equal to the maximum (instrinsic) rate times the unutilized opportunity for growth represented by the difference between the population density and the density of the population at carrying capacity (s-shaped, or sigmoid growth, is modeled by the logistic equation)
   • Then dN/dt = rN, dN/dt = r_oN((K-N)/K)
   • Pearl and Reed fit the logistic equation (population growth model) to U.S. census data to predict U.S. population density in the future

7. Density Dependent Factors
   • The logistic model of population growth is constructed on the assumption that density affects mortality and fecundity rates
   • Density-dependence: effects from habitat factors influence mortality and fecundity and vary with population density; more constraining at high densities and less constraining at low densities in a negative feedback way; since the impact of the factors varies with population density, these factors can regulate population density (i.e. the population regulates its own density)
     • Food
     • Places to live and build nests for young
     • Predators, parasites, diseases
   • Density-independence: effects from habitat factors bear no relation to the density of the population; effects on mortality and fecundity are not responsive to changes in population density
     • Weather: temperature, rainfall and snow, freezing
     • Floods
   • Examples of Density-Dependence in Animals

8. Self-Thinning
• Log-log plot of plant weight against density gives a straight line (is linear)
• Slope of line = -3/2
9. Summary
• Populations tend to match carrying capacity
• Environmental conditions influence the magnitude of the carrying capacity
• Only density-dependent factors can "regulate" a population
• Density-independent factors can cause catastrophic impacts on population density but cannot "regulate" the population

II. Temporal and Spatial Dynamics

1. Introduction
   • Populations tend to reach a steady-state where number of births = number of deaths
   • External factors: environmental factors affect mortality and fecundity
   • Internal factors: originate from the population itself
   • Dispersal links subpopulations together

2. Fluctuations in Natural Populations
   • Variation in density is related to environmental fluctuations and inherent stability of the population
     • Sheep: relatively large homeotherms have long life spans: results in small ratio between high and low densities
     • Phytoplankton have short life spans, are small and sensitive to environmental fluctuations: leads to large variations in densities
     • Moths in Germany seem to fluctuate independently of each other with ratios intermediate between phytoplankton and sheep
     • Small mammals and birds of high latitudes, e.g. Clethrionomys rufocanus, exhibit regular fluctuations in density

3. Population Variation and Age Structure
   • The history of a population is reflected in its age structure
     • Lake Erie whitefish: size of 1944 age class implied excellent spawning and recruitment in that year relative to others
     • Trees: sporadic recruitment over 400 years; white pine recruitment was especially high between 1650 and 1710; beech showed an even age distribution
     • Human population showed the effects of the Depression (1929) and World War I and II (Fig. 15.5)

4. Key Factor Analysis
   • Search for the environmental factors that have the greatest influence on population birth and death rates
   • Which factors are density-dependent?
     • Life table mortality and fecundity are determined by environmental factors; therefore, answer could be found by analyzing life tables
   • Conclusions about factors affecting natural species
     1. Those that cause a relatively constant mortality from year to year and contribute little to population variation
     2. Those whose affects on the population vary with population density; may cause less mortality; can regulate population density ("has predictive value") and is a "key factor"
     3. Larval parasitism was a key factor for the black-headed budworm, Acleris variana

5. Tracking of Environmental Change
   • Carrying capacity changes with fluctuations in resources and environmental conditions
   • Populations with high intrinsic rates of increase (r > 1) tend to respond most quickly to changing environments (they track the environment closely)

6. Population Cycles and Intrinsic Demographic Processes
   • Environmental fluctuations tend to be irregular rather than periodic, i.e., they are random
   • Population changes seem periodic
   • Sunspot cycle of 11 years did not match population cycles: not a cause of periodic population fluctuations
   • Population models with time lags produced oscillations in population density
   • Nicholson's blowflies (Lucilia cuprina): increasing the effect of density on mortality and fecundity of adults reduced oscillations and increased population density of both adults and larvae

7. Metapopulations
   • Definition: subpopulations linked by emigration and immigration between habitat patches
   • The smaller the patch and the population, the higher the probability of extinction
   • Rescue effect: immigration prevents a subpopulation from declining to extinction

8. Stochastic Processes: Greatest impact is on small populations
   • Models
     • Deterministic models: birth and death rates are stable and predictable
     • Stochastic models: variations in birth and death rates are unpredictable
   • Relevancy
     • Habitat fragmentation is increasing
     • Changing environmental conditions are reducing populations
     • Endangered species face competitors
   • Island populations provide examples
     • California's Channel Islands: extinction of birds
     • New Guinea's Karkar Island, West Indies islands: extinctions
   • Conclusions
     • Small populations are more susceptible to extinction
     • Spatial structure of populations is important for survival

When you have completed this lesson, go on to Review Questions