For unlimited access to Textbook Notes, a Class+ subscription is required.
Chapter 10 (only pg 204-207)
Generally, the density individuals increases within an area in reference to the compatibility as determined by a species’
range of tolerance. It is important, from a standpoint of ecology and conservation, to understand the dispersion of species.
However, in some parts of the world this is difficult, for this purpose ecological niche modeling, a system of determining
where species in terms of dispersion and density, becomes useful. Ecologists can find dispersion within and area and
extrapolate the data based on patterns of temperature and precipitation within an area.
Ecological envelope: catalog of ecological conditions for a species.
Ecological niche modeling can be used to determine where an invasive species will establish itself by examining its
ecological envelope in its native area.
There are three main categories for dispersion: clumped, generally seen where resources are limited to certain areas or
species require communities for mating, hunting, protection, etc.; spaced, observed in species that are strongly
competitive; random, represents an environment where chances for survival are relatively equal across the entire area,
Demography: study of populations.
Population growth is usually modeled on a per capita (or per individual) basis, e.g. 10% growth rate adds 10 individuals
10 a population of 100 and 100 individuals to a population of 1000. Equally, it can be modeled in two ways:
Geometric growth over discrete time intervals (applies to most animals populations); equation is N(t+1) = N(t)χ; where
N(t) is the size of a population at time t; N(t +1) is its size one time interval later; χ is the ratio of a population size one
compared to its population size the next year, basically a growth rate, it cannot be negative, <1 indicates decline, >1
indicates increase in population.
Exponential growth over continuous-time (model which is really only accurate to depict humans); equation is N(t) =
N(0)e^rt; where r is the exponential growth rate; e = 2.72, natural log.
Changes in population size can likewise be determined for either model.
Geometric growth: ΔN = N(t+1) – N(t) or ΔN = N(t)χ - N(t) or ΔN = (χ – 1)N(t); <1 indicates decline, >1 indicates
increase in population.
Exponential growth; the derivative of the function for exponential growth, an instantaneous rate;
dN/dt = rN; where dN/dt is the rate of change in population; r is exponential growth rate; N number of individuals in the
Population growth rates can be calculated from birth and death rates. The per capita death rate is subtracted from the per
capita birth rate (expressed as probabilities) to give this value: r = b – d.
It is very important to consider age-structure when modeling population growth as not all individuals have equal chances
of reproduction or death. For this purpose, life tables, giving probability values of survival and numerical values for
fecundity are used. Assuming these rates remain the same over several interval, a stable age distribution will be reached,
meaning there are the same ratio of individuals from different age groups between intervals of time. Two important
equations used in conjunction with the values of life tables are:
R0 = ∑Lxbx ; where R0 is the growth factor; Lx is the probability of survivorship at age x; bx is the birthrate at age x.
T = ∑ Lxbxx / ∑ Lxbx ; where T is the time it takes from birth for a female to reach for average reproductive age,
generation time; x is the age of daughter.
Cohort life tables may be used for populations such as plants where their entire life span may be observed, but static life
tables are more often used for populations not easily tracked or may experience changes in environment pressures during
their life span.