Bio120#5 final

Why do we care about N (population size)?

1. Resource management

2. Conservation

3. Human Health (ex. HIV population dynamics)

4. Understanding and predicting human population growth

What do most graphs looking at N have in common

y-axis: N or log N | x-axis: time

What is the first and most simple formula for population change?

What is common in both geometric and exponential models?

the growth rate (lamda or r) is a constant that reflects biology, where a constant positive growth rate will have an exploding population size not constant

What are the pros and cons of a logistic model

what are the two models of population growth

1. deterministic — b and d are fixed outcomes

2. stochastic — b and d (and so r) are based on probabilities

average b and d (r) approximates reality, where in small populations fluctuations in b and d can be more consequential (stochastic models may be better)

What do the different values of λ suggest

• >1.0 → positive growth; births exceed death

• <1.0 → negative growth; deaths exceed birth

what are examples of density dependent and independent factors

Dependent:

• food shortage

• social agression

• scarcity of mates

• predation

Independent:

• weather

• predation

which model is used to describe a density dependent growth

logistic equation

Population Size (N)

Number of individuals

Deterministic Model

Same inputs always give same outputs

Stochastic Model

Includes randomness

Finite Rate of Increase (λ)

Multiplicative growth factor

Intrinsic Rate of Increase (r)

Continuous per-capita growth rate

Density-Independent Growth

Growth unaffected by population size

Density Dependence

Growth changes with population size

Carrying Capacity (K)

Maximum sustainable population size (when b = d)

Logistic Growth

Density-dependent growth toward K

Population Irruption

Rapid outbreak followed by crash

Chaos

Unpredictable fluctuations from deterministic rules

Allee Effect

Positive effects of higher density at low population sizes

Allee Threshold (A)

Critical minimum population size

Genet

Genetic individual

Ramet

Clonal physiological individual

What is population size (N)?

The number of individuals in a population.

What is a genet?

A single genetic individual.

What is a ramet?

A clonal physiological individual derived from a genet.

What is a deterministic model?

A model that always produces the same outcome from the same inputs.

What is a stochastic model?

A model that includes randomness.

What does λ represent?

Finite rate of increase.

What happens when λ > 1?

Population increases.

What happens when λ < 1?

Population declines.

What does r represent?

Intrinsic rate of natural increase.

What happens when r = 0?

Population remains constant.

What is density-independent growth?

Growth unaffected by population size.

What is carrying capacity (K)?

Maximum sustainable population size.

What shape does logistic growth produce?

Sigmoidal (S-shaped) curve.

At what population size is logistic growth fastest?

N = K/2.

What is a population irruption?

Rapid outbreak followed by crash.

What causes many insect population crashes?

Food depletion, disease, and weather changes.

What did May's model introduce?

Delayed density dependence and population oscillations.

What is chaos in population ecology?

Deterministic but unpredictable population fluctuations.

What is an Allee effect?

Positive effect of higher density at low population sizes.

What is the Allee threshold (A)?

Population size below which extinction becomes likely.

Difference between heuristic and management models?

Heuristic models explain concepts; management models predict real populations.

Population Size (N)

Number of individuals in a population

Deterministic Model

Model that always produces the same outcome from the same starting conditions

Stochastic Model

Model that incorporates randomness and produces multiple possible outcomes

Finite Rate of Increase (λ)

Multiplicative factor by which a population changes each time interval

Intrinsic Rate of Increase (r)

Continuous per-capita population growth rate

Density-Independent Growth

Population growth unaffected by population size

Density Dependence

Population growth changes as population density changes

Carrying Capacity (K)

Maximum population size that an environment can support indefinitely

Logistic Growth

Density-dependent growth that approaches carrying capacity

Population Irruption

Rapid population outbreak followed by a crash

Chaos

Deterministic but unpredictable population fluctuations

Allee Effect

Positive effects of increased population density at low population sizes

Allee Threshold (A)

Critical minimum population size below which extinction becomes likely

Genet

Single genetic individual

Ramet

Physiologically independent clone derived from a genet

Age Structure

Distribution of individuals among different age classes

Life Table

Summary of age-specific survival and reproduction

Survivorship Schedule (lx)

Probability that an individual survives to age x

Fecundity Schedule (mx)

Average number of daughters produced by a female at age x

Net Reproductive Rate (R₀)

Expected number of daughters produced by a female during her lifetime

Generation Time (T)

Average age of a mother when she produces her offspring

Leslie Matrix

Matrix used to project future population growth and age structure

Reproductive Value (vx)

Expected future reproductive contribution of an individual of age x

Semelparity

Reproducing once and then dying

Iteroparity

Reproducing multiple times throughout life

Annual Plant

Plant that completes its life cycle in one growing season

Biennial Plant

Plant that grows one year and reproduces in the second year

Monocarpic Perennial

Long-lived plant that flowers once and then dies

Cost of Reproduction

Reduction in survival or future reproduction caused by current reproduction

Size-Number Tradeoff

Tradeoff between producing many small offspring or fewer large offspring

r-Selected Species

Fast-growing species with high fecundity, short generation times, and poor competitive ability

K-Selected Species

Slow-growing species with lower fecundity, long lifespans, and strong competitive ability

Predator Satiation

Strategy where synchronized reproduction overwhelms seed predators

Mast Year

Year of unusually high seed production in trees

Stochastic Population Model

Population model that incorporates random variation in demographic parameters

Extinction Risk Analysis

Using repeated stochastic simulations to estimate the probability of extinction

what is population density

N/area