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> li:before{content:"■ "}.lst-kix_mzut7oq5dfmn-6 > li:before{content:"● "}.lst-kix_7r0iqw6axd7v-0 > li:before{content:"● "}ul.lst-kix_6sh74ra0vqye-0{list-style-type:none}.lst-kix_6iatcabomujx-1 > li:before{content:"○ "}.lst-kix_6iatcabomujx-0 > li:before{content:"● "}.lst-kix_6iatcabomujx-2 > li:before{content:"■ "}.lst-kix_6iatcabomujx-3 > li:before{content:"● "}.lst-kix_xme5rgipjnwj-4 > li:before{content:"○ "}.lst-kix_xme5rgipjnwj-3 > li:before{content:"● "}.lst-kix_xme5rgipjnwj-5 > li:before{content:"■ "}.lst-kix_xme5rgipjnwj-0 > li:before{content:"● "}.lst-kix_xme5rgipjnwj-8 > li:before{content:"■ "}.lst-kix_xme5rgipjnwj-1 > li:before{content:"○ "}.lst-kix_xme5rgipjnwj-2 > li:before{content:"■ "}.lst-kix_xme5rgipjnwj-7 > li:before{content:"○ "}.lst-kix_xme5rgipjnwj-6 > li:before{content:"● 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li:before{content:"○ "}.lst-kix_44mhsmprtci8-1 > li:before{content:"○ "}.lst-kix_44mhsmprtci8-3 > li:before{content:"● "}.lst-kix_g8xdiz3z3l86-2 > li:before{content:"■ "}.lst-kix_gg1w9mlqvd9s-8 > li:before{content:"■ "}.lst-kix_6sh74ra0vqye-8 > li:before{content:"■ "}.lst-kix_gg1w9mlqvd9s-6 > li:before{content:"● "}.lst-kix_g8xdiz3z3l86-0 > li:before{content:"● "}.lst-kix_lisonpfivbvu-8 > li:before{content:"■ "}.lst-kix_gg1w9mlqvd9s-4 > li:before{content:"○ "}.lst-kix_6sh74ra0vqye-4 > li:before{content:"○ "}ul.lst-kix_reyxdo4aqzhy-0{list-style-type:none}ul.lst-kix_6iatcabomujx-1{list-style-type:none}ul.lst-kix_6iatcabomujx-0{list-style-type:none}ul.lst-kix_reyxdo4aqzhy-3{list-style-type:none}ul.lst-kix_reyxdo4aqzhy-4{list-style-type:none}ul.lst-kix_reyxdo4aqzhy-1{list-style-type:none}.lst-kix_4wq636ye34jh-3 > li:before{content:"● 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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 = N0
1
N2 = N0
2
N3 = N0
3
> Nt = N0
t 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