Bio Ch 13 - population growth and regulation

Demography

the study of populations (their structure and dynamics)

uses mathematical techniques to predict the growth of populations

-emphasis on causes of population fluctuations and effects of crowding on birth/death rates

Effects on population size

populations increase due to births and immigration

populations decrease due to deaths and emigration

B + I - D - E = ΔN

Growth rate

in a population, the number of new individuals that are produced in a given amount of time minus the number that die

Geometric growth model for population

a model of population growth in which the population increases at regular time intervals

often used for species with discrete generations and discrete reproductive bouts

N(t+1) = N(t)λ

N(T+1) = number of individuals after 1 time unit

N(t) = population size at time, t

λ = N(t+1)/N(t) or (number present now)/(number present then)

for multiple time intervals: N(t) = N(0) λ^t

Exponential population growth

a population exhibiting exponential growth has a smooth curve of population increase as a function of time

model of population growth where the population increases continuously at an exponential rate

N(t)= N(0) e^rt

N(0) = initial population size

r = exponential growth rate (per capita births minus per capita deaths)

e = base of the natural log

Rate of growth

using the exponential model, we can determine the rate of growth

dN / dt = rN

this equation tells us that the rate of change in population size at any point in time depends on the population’s intrinsic growth rate and the population’s size at that time

Comparing r and λ values

when a population is decreasing, λ < 1 and r < 0

when a population is constant, λ = 1, and r =0

when a population is increasing, λ > 1 and r > 0

Density independent factors

factors that limit population size regardless of the population’s density

Density dependent factors

factors that affect population size in relation to the population density

Negative density dependence occurs when the rate of population growth decreases as population density increases

Self-thinning curve

a graphical relationship showing how decreases in population density over time lead to increases in the mass of each individual in the population

Positive density dependence

when the rate of population growth increases as population density increases; also called inverse density dependence or the Alee effect

typically occurs when population densities are low, which makes it hard to find mates

Positive and negative density dependence

populations are often regulated by both positive and negative density dependence

increased densities provide more individuals for breeding, but above some density, resources become limiting and negative density dependence begins to play a role

Logistic growth model

a growth model that describes slowing growth of populations at high densities

Carrying capacity (K) is the maximum population size that can be supported by the environment

dN / dt = rN (1- N/K)

S-shaped curve

the shape of the curve when a population is graphed over time using the logistic growth model

the inflection point is the point on the s-shaped growth curve where the population achieves its highest growth rate

Effect of population size on the rate of increase & per capita rate

as populations grow from a small number to their carrying capacity, the rate of population growth increases until it reaches the inflection point, after which it decreases

on a per capita basis, the rate of population increase continually declines

Age structure

the proportion of individuals that occurs in different age classes in a population

usually in human demography this is visualized as an age structure pyramid

Life tables

tables that summarize a population’s age structure and fecundity

allow prediction of population characteristics for future generations

x = age interval

sx = survival from age class x to x+1

lx = survival to age x

bx = fecundity, number of offspring per adult at age x

Stable age distribution

when the age structure of a population does not change over time

Survivorship curves

Type I - depicts a population that experiences low mortality early in life and high mortality later in life

Type II - depicts a population that experiences constant mortality throughout lifespan

Type III - depicts a population with high mortality early in life and high survival later in life

most populations exhibit a curve that combines features of types I & III

Net reproductive rate (R(0))

the total number of female offspring that we expect an average female to produce over the course of her life

Generation time (T)

the average time between the birth of an individual and the birth of its offspring

expected number of births for a female / net reproductive rate

Cohort life table

a life table following a group of individuals born at the same time from birth to death of the last individual

Static life table

a life table that quantifies the survival and fecundity of all individuals in a population during a single time interval

serves as a snapshot in time