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Determining Density / Population GrowthWe also discuss several other topics like What is psychology neuromuscular theory?

Review:

Lincoln - Peterson index assumes:

• Random sampling (each individual has an equal chance of being caught)
• Marked animals are distributed throughout the environment

If you want to learn more check out What is the definition of a cosine?

Determining Density Requires Sampling

• Other methods may used to estimate abundance that use observations about the presence of organisms rather than direct counts
• Signs of the presence of animal include:

• Vocalization counts (bird song)
• Scat counts along a length of trail
• Track counts

• If there is a relatively constant relationship between the observations and the total population, we can track animals

We also discuss several other topics like What can make a free woman detrimental?

PopulationsDon't forget about the age old question of ucsc math 3

Populations sizes arranges as a function of several factors:

• Birth rate
• Death rate
• Fertility rate
• Age structure
• Sex ratio
• Immigration / Emigration and possible others…

• Age structure affects population growth,

Importing age classes:

• Pre productive
• Reproductive
• Post productive

• Each age group = a cohort
• Populations with a higher % of younger cohorts will expand more rapidly

If you want to learn more check out Who was a Russian physician who conducted biological research on the nervous system from about 1890 to 1936?

Sex Ratio

• Sex ratio affects populatiin growth
• Primary sex ratio = ratio at conception
• Secondary sex ratio = ratio at birth
• (These may be different)

If you want to learn more check out What are the eight steps of forecasting?

Population Growth

• Populations can grow in several ways:

• Linear growth = the population increases steadily
• Exponential growth = population growths at an exponential rate
• Logistic growth = population experiences exponential growth, and then levels off (sigmoidal)

Exponential growth leads to:

• Crowding, less shelter
• Starvation
• Increased disease risk
• Increased predation risk

• Fewer offspring, lower survival
• Small offspring, reduce adult survival, fertility

Populations

A real - life example → equation →

Exponential Growth Equation

You want to look at the overall trend

Nt=Noert

N0 = initial population size

Nt  = # of individuals after”time”

E = ~2.72 (natural log base)

R = instantaneous per capita growth rate

In an exponential growth situation, the rate at which individuals are added to the population is:

This is the derivative of the exponential equation,

        Nt= Noert r = instantaneous per capita growth rate

 varies according to population size

Geometric Growth

• Most populations don’t grow continuously
• They aren’t seasonal: increases and decreases depending on the season

geometric growth  = population change over discrete time intervals

Rate of geometric growth =  =

 = Nt+1/Nt where t = time

Rearrange:          Nt = Nt+1

• To project the growth rate at a specific time:

N1 = N01

N2 = N02

N3 = N03

> Nt = N0t geometric growth equation

Populations

•  > 1.0, population will increase
•  < 1.0, population will decrease
•  = 1.0, population remains stable

•  = net reproductive rate
•  = (# of offspring) x (probability that kids survive childhood)

• Total # of kids produced = fertility

Intrinsic rate of increase

Ym = intrinsic rate of increase (malthusian parameter)

• Maximum possible growth rate under ideal conditions
• The exponential rate of increase of a population with a stable age distribution

• Rm is more useful identifying environmental conditions affecting population growth that is an accurate predictor of population growth

• Most populations do not have a stable age distribution

R0 = net reproductive rate (fecundity x  survival of newborn)

Survival and Fertility Decline in Crowded Populations

Survival is reduced by:

• Limited food
• Increase waste
• Increased vulnerability to predators
• Increase stress
• Disease

Fertility is reduced by:

• Limited food for adults
• Increased behavioral interaction (fight, stress)
• Smaller adults due to competition during adolescence

References: