LECTURE 07 CH 11 POPULATION GROWTH AND DYNAMICS 1
BRING to lecture…PRINT-OUT of THIS
Read Pgs 222-226; 235-239
MAJOR CONCEPTS
1. Populations grow by multiplication rather than addition.
2. In the presence of abundant resources, populations can grow at geometric or
exponential rates.
3. As resources are depleted, population growth rate slows and eventually stops; this is
known as logistic population growth.
4. The environment limits population growth by changing birth and death rates that
become density-dependent.
5. Population growth models are built upon several assumptions.
BIDE model of population growth
Growth = (birth + immigration) – (death + emigration)
Growth in unlimited environments p. 224-225
Difference model (geometric growth)
discrete (seasonal) reproduction 11.3
N / t = g N
 = Nt+1 / Nt
Growth over many time intervals Nt = t No 11.4
Values of : population increases if  >1, decreases <1, and is stable 0 top p. 226
Differential equation model (exponential growth) p. 225-226
Continuous reproduction (overlapping generations)
dN / dt = rN, r = instantaneous rate of (birth – death)
Nt = No e rt 11.4
Values of r: population increases if r >0, decreases <0, and is stable 0 top p. 226
Species characteristics and environment set limits on r
tends to be large in disturbed habitats; small in stable habitats
Population growth increases inversely with mean generation time.
Model assumptions
1. population changes as proportion of current population size
2. constant birth and death rates so constant rate of change
3. no resource limits
4. all individuals are the same ( no age or size structure)
Growth in limiting environments: growth limited by extrinsic factors p. 236-239
Logistic (sigmoidal) growth model dN/dt = rN (K – N) / K
Several assumptions of exponential model are violated.
Resources now limiting
Birth and death rates change as population size (density) changes. 11.12; p. 239-244
Negative Density-Dependence
Density-dependent factors lower survival. 11.17
Density-dependent factors lower reproduction. 11.19, 11.20
Decreases growth of plants  size hierarchies 11.24
Decreases some components of reproduction; increases others
Decreases survival  population ‘self-thinning’ 11.25
r decreases as a linear function of population size. 11.13
Positive Density-Dependence 11.22
Allee effect: fining maters easier in larger populations
Population growth slows as population size increases. 11.14, 11.15
Population growth becomes density-dependent and reaches point of zero growth.
Population size reaches equilibrium when birth rate = death rate (at K).
K = carrying capacity; as N approaches K, dN/dt gets smaller and moves to 0.
(K – N) K as environmental brake; amount of unused resources
Inflection point of curve at K/2 separates acceleration and deceleration of growth.
Pop size of maximum sustainable growth (and harvest)
Assumptions of logistic model
Pop. growth is proportional to remaining resources.
All individuals can be represented by an average.
Continuous resource renewal (constant environment).
Instantaneous responses to crowding; no time lags.
K and r are specific to particular organisms in a particular environment.
Doubling time: amount of time in which population size doubles p. 235-6
t2 = ln2 / ln 
t2 = ln2 / r
Summary: 1-5, 11-16.