#3 Conservation Biology Exam 2: Review of Population Growth Models

metapopulation

each habitat patch contains a different sub-population of the species and the sub-populations are linked by occasional dispersal

metapopulations are also referred to as

a population of sub-populations

what are the different types of meta-populations

shifting-mosaic and core-satellite

shifting-mosaic metapopulation

no sub-population is permanent, but the metapopulation persists because establishment of new sub-pops balances extinction of existing sub-pops

example given for shifting-mosiac metapopulations

desert mountain sheep

shifting-mosaic metapopulations have lots of

turnover

core-satellite metapopulation

one or more sub-populations is permanent and maintains smaller, more ephemeral sub-
populations through dispersal

core-satellite metapopulation example

bay checker butterfly

rescue effect

in a core-satellite metapopulation, the satellites persist because they are being
maintained by dispersal from the core; without the regular input of individuals from the core, the satellites would go extinct

first reason why satellite sub-pops may be ephemeral

they occur on small patches of high quality habitat with low carrying capacity. If the sub-population is always small then it is vulnerable to the perils of small population size

second reason why satellite sub-pops may be ephemeral

They occur on patches of low quality habitat that can support positive population growth in only a minority of years; local extinction is inevitable regardless of chance events

sink sub population refers to the

second reason why satellite sub-pops may be ephemeral

first conservation implication of metapopulation structure

For a core-satellite metapopulation, preserving the core sub-
population should be top priority

second conservation implication of metapopulation structure

For a shifting-mosaic metapopulation, preserving unoccupied but suitable habitat is essential because current sub-populations are ephemeral

third conservation implication of metapopulation structure

Dispersal is a critical process, so intervening habitat between sub-populations must be maintained to allow dispersal of the species

example of third conservation implication of metapopulation structure

removing fences for sheep, limiting off-road vehicles, no raising domestic sheep

fourth conservation implication of metepopulation strucuture

Metapopulation dynamics provides a framework for understanding functioning of populations in a fragmented landscape

What is the most likely result of the interaction between con-specific individuals in a fragmented landscape?

reduces dispersal but won’t eliminate entirely

environmental stochasticity

random variation in parameters that measure habitat quality such as climate, nutrients, pollutants, interactions with other species

preserves that have subpopulations close together maximizes

dispersal

downside of preserves that have metepopulations close together

subjected to same environmental variation like drought or natural disasters

it is important to preserve examples of

most different habitats for one species because they respond differently to environmental variation ex. more vs less resistant to drought

why is a realistic population growth model not the most efficient

lots of data and parameters; expensive and time consuming

population growth models need a balance between

simplicity and realism

N=

population size

N0=

initial population size

N1

population size one time unit in the future

N2018

population size in the year 2018

t=

time in years

Nt=

population size at some unspecified time

Nt+1=

population size one time unit beyond t

delta N=

change in population size, expressed as number of individuals gained or lost

net rate of change in population size

delta N/delta t

per capita rate of change in population size

delta N/delta N0/delta t

per capita rate of change definition

number of individuals added or lost from the population per individual in the population at the start per unit time

predicting population size one time unit in the future

Nt+1= Nt+(delta N/delta t) OR Nt+1=Nt+(1+delta N/N0/delta t)

finite range of population increase

lambda=(1+delta N/N0/delta t)

lambda or finite range of population increase can also be calculated as

Nt+1/Nt

if lambda is greater than 1

population increasing

if lambda is 1

population stable

if lambda is less than 1

population decreasing

if r is greater than 0

population increasing

if r is 0

population stable

if r is less than 0

population decreasing

exponential population growth

population growth or decline at a constant proportional rate over time; constant value for finite rate of population increase

discrete-time exponential growth model

Nt=N0lambda^t

exponential population growth if lambda=1.2 per capita growth rate =

0.2

exponential population decline if lambda=0.8 per capita growth rate =

-0.2

continuous time exponential growth model

dN/dt=rN

dN/dt=

rate of change in a population size over a very small time interval; the slope of a line tangent to the population growth curve at one time point

if you want to predict continious time population size in the future

Nt=Noe^rt

r=

intrinsic rate of population increase

ln lambda=

r

e^r=

lambda

Nt=N0e^rt equation is not

discrete; time occurring in chunks; lambda

continuous time population growth time does not occur in

chunks; continuous change over time; r

first reason why it is unrealistic to assume a constant per capita population growth rate through time

environment in which the species exists changes in time-environmental stochasticity

second reason why it is unrealistic to assume a constant per capita population growth rate through time

density of the population will affect per capita population growth rate

would you expect the per capita population growth rate to slow or increase as the population becomes more dense? why?

slow; resources become more limited with increased population size

third reason why it is unrealistic to assume a constant per capita population growth rate through time

density of populations of species with which our species interacts change through time