BIOL204-STATS III

Quadrat population formula

area x density

Line transect formula + area

area x density | area = 2W x L

Area formula

length x width

Density formula

number of individuals / unit area

Mark recapture formula + steps

M/N = m/n

1. cross multiply

2. isolate N

3. plug in

N = Mn/m

What do M, m, N, and n represent?

M= number of marked individuals

m= number of marked individuals from the recapture

N= total population

n= total individuals in recapture

How do you calculate change in population size generally?

(b-d) + (i-e) BIDE principals

What represents survivorship?

lx

What represents age-specific fecundity?

mx

What does lx(mx) give you?

avg. number of female offspring produced per original female at that age class

What is R0?

net reproductive rate

sum of avg. female births per year per female

for life tables

• <1 decreasing population

• =1 stable population (each female is replacing itself)

• >1 increasing population

Life history

how an individual allocates resources to growth, reproduction, and activities or structures that are related to survival

Life history traits

survivorship, age-specific fecundity, growth rate, age at first reproduction, lifespan

What does N/t represent? What about dN/dt?

population size per unit time — change in population size per change in unit time

What is exponential growth?

when a population grows faster and faster over time because the per capita growth rate (r) stays constant and there are no limiting factors.

Conditions of exponential growth

• Unlimited resources

• Constant per-capita growth rate (r)

• Density independent

Steps of calculating exponential growth

1. Calculate per capita growth rate (r) = (births-deaths)

2. Multiply r by N

3. X individuals per unit time

Exponential growth rate formula

N/t = rN

What is survivorship?

proportion of individuals that survive on average to a certain age

What is fecundity?

number of female offpsirng produced by each female in a population

r interpretation

• b>d then r>0

• b<d then r<0

• r=0 population is stable and doesn’t change

What is r and how do you calculate it?

per capita growth rate—(b-d)

rmax

intrinsic rate of increase: when conditions are optimal for a species (high b low d) r reaches this max value

Logistic growth

population growth that starts exponentially but slows as the population approaches carrying capacity (K) due to limiting factors.

Logistic growth conditions

• resources are finite

• growth becomes density dependent

Logistic growth formula

dN/dt = rN |K-N/K|

What is K?

carrying capacity: maximum number of individuals in a population that can be supported in a particular habitat over a sustained period of time

What is |K-N/K|?

the proportion of unused resources and space in the habitat

What happens to growth if N = 900

a high N means there is a low |K-N/K|, meaning there is a low amount of unused resources, such as habitats and food, meaning population growth will see a decline/ slow growth, as we are closer to carrying capacity

At what population size is growth = 0

when N=K, meaning the population reached carrying capacity

Why does growth slow as N approaches K

because we are reaching closer and closer to carrying capacity, meaning there isn’t enough resources and room for more growth

What is age-specific fecundity?

avg. number of female offspring produced by a female in each age class

1 in context of exponential growth

closer to 1, closer to exponential

r

How fast a population grows per individual, under ideal conditions

Draw survivorship curves