E.U2: Population Growth

What do life tables do?

Depict how vital rates (survival, reproduction) vary with age/stage/size

What can life tables be used to project?

N (population size)

What 2 times can population growth be modeled in?

Discrete time and Continuous time

Populations can grow exponentially forever. True or false?

False

What can population size be constrained by?

density dependence

What does logistic growth do?

Incorporates density dependence and shows how a population can stabilize at K (carrying capacity)

What can population models do for conservation efforts?

Help to inform them to make better decisions

What is a survivorship curve a measure of?

The # of survivors over time

What is type I survivorship?

Survivorship is high until old age. Young that are born have a high survival rate, then as they age, it drops down. 0.8→0.3

What are examples of type I survivorship?

humans and elephants

What is type II survivorship?

Survivorship is constant over time. The mortality of individuals stays the same throughout their lifetime 0.5→0.5

What are some examples of type II survivorship?

birds and squirrels

What is type III survivorship?

Survivorship is low for young. Survivorship starts low and becomes more constant over their lifetime. 0.3→0.8

*Which survivorship curve is most common in nature?

type II

What do life tables provide?

A summary of survival and reproductive rates as a function of age/stage/size

What is survival rate?

The chance that an individual at age X lives to age X+1

What is survivorship?

The proportion of individuals from age 0 that live to age X

What is fecundity?

The average # of offspring produced by a female at age X

If the survival rate for an organism goes from 0.3 at age 0 to 0.8 at age 1 to 0.0 at age 2, what survivorship type is the organism?

type III

Each life stage of a population fluctuates in the beginning, but reaches what when fluctuations stop?

stable age distribution

Estimation of what is allowed due to knowledge of N (population size) over time?

population growth rate

Why are population equations important?

They provide a framework for testing and understanding wild populations, capture natural dynamics well, and inform conservation decisions.

Does the following equation measure growth rate or future size? Nt+1=Nt+births-deaths+immigrants-emigrants

future size

When can you use the discrete time population equation?

when reproduction occurs over regular time intervals or for species with non-overlapping generations

Wha does discrete time population equation assume?

no immigration or emigration

What does lambda stand for in population equations?

finite rate of increase

What is the value of lambda is the population is constant, growing, and shrinking?

>1 grows exponentially, =1 is constant, <1 declines to extinction

What does it mean when time is continuous?

each time step is infinitely small

When is continuous time used?

Breeding organisms in an environment lacking seasons where there is an overlap of generations

What is this equation? dN/dt=B-D

Population growth over continuous time

What does dN/dt mean?

Change in number (population size) over change in time

What is B? How is it calculated?

Birth rate, B=bN

What is D? How is it calculated?

Death rate, D=dN

What is b?

instantaneous birth rate (births per individual per unit time)

What is d?

instantaneous death rate (deaths per individual per unit time)

We assume that b and d are?

constant

What is this equation? dN/dt=rN

exponential population growth equation

What does the constant r represent?

birth rate-death rate (b-d) since they are considered constant

What is r called?

intrinsic rate of increase aka instantaneous rate of increase

What is the value of r if N is growing, constant, and shrinking?

>1 grows exponentially, =1 is constant, <1 declines to extinction

What are the two cases when the exponential growth equation predicts a population does not grow?

Intrinsic growth rate (r) is zero or when N=0

What is Nt?

The population size at some infinitely small future time step

What are the details of discrete growth?

interval based time (age, stage), parameterized by lambda (finite rate of growth), “geometric” growth

What are the details of continuous growth?

infinitely small time steps, parameterized by r (intrinsic rate of growth), “exponential” growth

On a population size over time graph with a line and with dots, which one represents discrete time?

dots

What is a sensitivity analysis?

Seeing how population growth rate responds to changes

What is doubling time?

The time it takes for a population to double in size

What is this equation? tdouble=ln(2)/r

doubling time

No matter the population size, if this occurs, the population will double at some point, what is this?

if it is growing exponentially

What is the relationship between body size and doubling time?

As body size increases, so does the species’ doubling time

Does r increase or decrease with greater body size?

decrease

Does doubling time increase or decrease with greater body size?

increase

What are the assumptions of exponential growth?

population is closed, no immigration or emigration (fish in pond, species on island, limited dispersion species like snail), no genetic structure (all indiv. have the same birth and death rates aka functionally equivalent), no age or size structure (indiv. are reproductive when they are born), continuous growth with no time lags

Are the assumptions of exponential growth reasonable?

sometimes

What are density independent ecological processes?

weather

What does density dependence assume?

Instantaneous birth and death rates change as a function of population size

What are density dependent ecological processes?

Any process that depends on the density of the population (population size). For example disease.

What is this equation? b’=b-aN

instantaneous density dependent (DD) birth rate

What is the constant a?

measures the strength of DD birth effect

If a=1, what does this mean?

For every new indiv., there is a strong density dependent effect

If a=0, what does this mean for the density dependent effect?

It is not as strong

Why do we subtract aN but add cN ? (b’=b-aN and d’=d+cN)

We expect DD effects to decrease b’ and increase d’

What is this equation? dN/dt=rN[1-N/K]

logistic population growth

What part of the logistic growth equation is the unused carrying capacity?

[1-N/K]

As N increases in the unused carrying capacity, what happens to the growth rate?

It starts to go negative