Lecture 19 population growth and regrowth

Population, Population size, Population density, and population ecology

1. Individual of a species within a given area

2. the number of individuals in a pop.

3. The number of individuals per unit area

4. spatial and temporal dynamics of population density

pgr (per capita growth rate)

1/Nt * dN/dt

pgr = 0, no change in population size

pgr < 0 leads to the extinction of the population (N_t+1 < Nt)

pgr > 0 exponential growth (N_t+1 > Nt)

Density dependent vs independent growth rate

Density independent - pgr does not depend on population density

Density dependent - pgr capita reduction in survival or fecundity depends on population density (competition, paracitism, predation)

the second along aside population regulation by negative feedback (slowing population growth as population increases) is most likely

Discrete generation model vs Continuous population growth model

1. N_T = N_intial (lambda)→rate of increase

2. dN/dt = N(b-d) = rN

3. → so N_t = N_0 (e^rt)

The continuous population growth model is best for a small population or one new to the environment

Discrete is best for →specific breeding seasons

Instrinsic rate of growth ( r ) is…

the maximum per capita growth rate a population can ahcieve under ideal conditions, with unlimited resources, and no enviormental limitations

pgr is influenced by…

Survival and Fecundity

Demographics

IF growth rate depend on age structure then we need to know age strucuture to predict overall popluation dynamic.

Demographics age gender,

Changing enviormental conditions changes Resource allocation

1. Normal Conditions - Maintence needs must first be met. Remaining resources divided among other activies

2. Adudant conditions - When reosurces are abudant more resources are gained and more availble to go into growth and reproduction after matainence

3. Stress conditions - mean more roesurces on maintainance

Logistic equation (continuous growth model)

dN/dt = r_max * N[1- N/K)

K is carrying capacity

N<K growth

N>K negative population change

N=K no change

Occurs under normal conditions of limited resources and potential predators (long term)

Examples of logistic equation growth

bacterial cultures, animal population limits. As it reaches the K it slows down

Allee Effect

Per capita growth rate Increases with N at low density

→Mate finding, detection, and defense against predators, pack hunting

levels of and decrease with high capacity as it reaches K (carrying capacity)

Ecological allometry

1. Lifespan as a function of body mass in animals

2. II. Intrinsic rate of increase (r) as a function of body mass

Discrete logisitc equation

dN/dt = r_d * N_T[1- N/K)

difference is it is at a discrete time T

completely deterministic relationship

if r is large, it will overshoot and ossolate

after a certain amount it will ossolate chaotic

Chaos in biological systems

1. Based on determinstic functional relationship (rd at specfic time

2. Negative feedback system (self regulates)

3. End, aperiodic oscillations

4. Sensitive to intial conditions

5. Unpredictable long-term dynamics, bc one can’t determine exact starting conditions