Studied by 1 personpopulation dynamics is…
population is an important unit of organization
basic unit w management and conservation
population definitions
a group of individuals of one species that live in a particular geographic area
a collection of inter-breeding organisms of a particular species
tell four basic population dynamic processes
why defining the unit is important
bc it will affect the unit / manner of management
bc it will affect the status of the population
evolutionary significant unit (ESU)
from salmon managment
commonly used for the purpose of conservation of “protected species”
Distinct population segment (DPS)
language in Endangered Species Act
smallest unit of species to be protected under ESA
Stock
unit of management in fisheries
the Magnuson-Stevens Fishery Conservation and Management Act
State Variables
variables that represent the state of a population
population dynamics (definition)
changes in the state of a population
what are the state variables
measures of the state of the population
population abundance
population density (number of individuals per unit area)
biomass
incidence (presence-absence)
Vital rates
facts that change population abundance
what are the vital rates
birth
death
immigration
emigration
Constant per-capita birth rate
number of offspring born and survive between time t and t+1 per individual parent
assume no immigration and no emigration
b (in equation)
Constant per=capita death rate
a portion of individuals alive at time t dying before t+1
rate of death of individuals from time t to time t+1
d (in equation)
geometric growth equation
n(t+1) = lambdan(1)
per-population meaning
2.2
natural log of density changes w geometric growth
grows (declines) linearly ( straight line )
constant number or birth rates + constant number of death rates =
geometric growth/decline
finite per-capita population growth rate
lambda
lambda > 1 = geometric growth
lambda = 1 pop. density remains the same
1>lambda>(-) = geometric decline
fertility term
fecundity (# of offspring per adult) x Offspring survival until age 1
lifecycle graph
circle/node = age class
arrows = potential transitions of individuals from t to t+1
solid: aging/death
dashed: reproduction / fecundity per parent c the survival of the offspring over one time unit
how to read/label a(ij)
contribution of age class J to age class I
OG age class is second script
how to deal with females and males in a model
how to write a matrix w a(ij)
first subscript = row on matrix
second subscript = column in matrix
vector
matrix with one column
matrix
3 x 3 matrix
scalar
a matrix with one row and one column (n)
ordinary product
multiplication of matrix and vector product
component of a vector
each parameter/variable in a vector
element of a matrix
each parameter/variable in a matrix (vital rates)
location is indicated by 2 numbers (i,j)
how to multiply matrices
row 1 and column 1 x row 1 and column 1
row 1 and column 2 x row 2 and column 1
etc
only matrices of same size can be multiplied
number of columns of a matrix and the number of components of a vector must be the same
how to refer to an elemet of matrix (indices)
how to multiply a popultion matrix and population vector
n(t+1) = An(t) (?)
how to enter transition rates into a population matrix
a(ij)
i = the row
j = the column
population vector
the ith component of the vector is the number/density of individuals in the ith stage
the number of components is the same as the number of age classes in the model
when does the natural log of population density grows/declines linearly with time?
when the elements of a population matrix are constant over time = expo. growth
what happens to a population when per-capita rates are constant ?
geometric / exponential growth
what is the difference between transient and asymptotic dynamics when vital rates are constant?
asymptotic = population grows/declines exponentially (here all stages have the same slope w same rate)
transient = each stage grows/declines exponentially after some transient period.
difference between state variables and vital rates ?
what’s asymptotic per-capita population growth rate ?
each stage density grows geometrically and the coefficient is the same for all stages
describe stable stage (age) distribution
under asymptotic dynamics, distribution of individuals amongst stage remains constant
differences in the characteristics of lifecycle graphs associated with lesilie matrix (age structured) and lefkovitch mitch (stage structured)
leslie matrix:
age progress w time
lefkovitch mitch:
assume age is a special type of stage
stage does not necessarily progress w time
can remain in same stage for years (self-loops)
both have asymptotic population growth rate and stable stage distribution (properties are the same)
how to draw lifecycle graphs for stage-structured populations
time unit is the same for all
they are stages that can hold multiple ages
how to write population matrix for stage-structured population
just know
3 things you can calculate from constant population projection matrix
asymptotic population growth rate (lambda)
stable stage distribution (w)
reproductive value (v)
stable stage distribution
where the proportion of individuals in each stage remains constant
reproductive value
measures relative expected contribution of individuals in different stages to future population abundance
denoted by vector v
difference between reproductive value and fertility
fertility = contributions of individuals in the present
reproductive value = measure of future potential asymptotic contribution of individuals
what is sensitivity ?
how sensitive lambda is to changes in population parameters aka transition rates
shows measures of how important vital rates are to the asymptotic population growth rate
be able to calculate sensitivity from stable stage distribution and reproductive values
W = stable stage distribution // V = reproductive value
vw (T) / v (T)w
interpret the sensitivity results
use (i,j) to see how sensitive lamda is to a(ij)
the ith row of the sensitivity matrix is high if the “reproductive value” of a stage i is high
the jth column of the sensitivity matrix is high if the stable stage distribution of stage j is high
loggerhead sea turtles basic info:
5 stages:
eggs
small juveniles
large juveniles
subadults
adults
more younger individuals in the population
reproductive value of older individuals is high
we should allocate more effort to protect juveniles
how is sensitivity matrix related to reproductive value and stable stage distribution
the product of reproductive value and stable stage distribution is the sensitivity matrix
high sensitivity
if the sensitivity of lamda is to a(ij) is high
relatively large number of individuals is in stage j and or
reproductive value of stage i is high
instantaneous population growth rate:
the natural log of the finite population growth rate (lambda)
instantaneous and finite population growth rates are both per-capita population growth rates
what affects vital rates (transition rates) ?
lack of food
habitat deterioration
human interventions (e.g conservation activity)
describe the steps in conducting matrix population model analysis?
v =
reproductive value
w =
stable stage distribution
simpsons paradox
a trend appears in several groups of data but disappears or reverses when the groups are combined
difference between longitudinal data and census data
longitudinal data: the individual capture-recaptured data are a type data collected
identified individuals are followed over time
census data: just count individuals
meaning of 95% confidence intervals
if we repeat the analysis, the estimated value is expected to fall within the confidence intervals 95% of the time
the cause of increased morality of north atlantic right whales
individuals are dying with a higher stage specific per-capita mortality rate
changes in vital rates
collision with ships
the 4 qualities calculated from the population matrix
growth rate
reproductive values
stable stage
sensitivity matrix
why a population growing in its abundance can have a reduced survival rate?
because stage distribution may be different
because the population may consist of more individuals in a stage with lower survival rate
elasticity
how lambda changes from proportional changes in transition rates a(ij)
what is the shape of a graph representing population abundance if the same proportion 0.3 of individuals ( 30% ) dies and each individual in the population contributes to the birth of 0.2 individuals on average and these per-capita rates remain constant ( the same ) ?
exponentially decreasing density
shape of the graph representing population density of both per capita birth rate and per. capita death rates are constant over time?
exponentially increasing density
which one of these statements are not true ?
there is no variable in statistical analysis
the proportional of individuals died over one year is 0.8. this value represents
per capita death/mortality rate
geometric/exponential growth results from
constant per-capita survival and per-capita birth rate
why do we need to structure a population based on age?
bc survival rate may be different among age classes and bc reproductive rate may be different among age classes
a(21)
the first number = the destination / the row
the second number = the OG / the column
the first step to build a population matrix
to draw a lifecycle graph
the size of leslie matrix for a population is determined by
the oldest individuals in the population
the number of rows of leslie matrix and the number of component of an associated population vector must be the same
true
which is the correct way of multiplying a population matrix and population vector
nt+1 = Ant
( lambda ) weird Y
represents population growth rate
if all of the per capita rates ( birth rate, death rate, developmental rate ) are constant over time, population density should change
exponentially with time
the asymptomatic population growth rate and stable stage distribution are the properties of age-structured populations but they are not the properties of stage - structured population?
false
sensitivity in the matrix population model analysis measures how sensitive lambda is to the same magnitude changes in vital rates whereas the elasticity measures how sensitive lambda is to the same proportional changes in vital rates
true
in each experiment, we start with the same number of individuals in each stage and introduce two additional individuals either adults or juveniles. on average which will have the greater number of individuals in the future?
both populations
what does lambda = .95 imply?
the population is expected to decrease by 5% per year on average
why does stage 2 have a greater number of individuals than stage 1 ?
bc stage 2 includes multiple age classes
why does stage 5 loggerhead sea turtles have high relative reproductive value?
bc stage 5 have high survival rate
bc stages 1-3 have low survival rate
bc stage 5 has high fecundity
according to the figure, which of the following is expected to make the population to start growing?
50% reduction in mortality of large juveniles
what does reproductive value measure?
relative contribution of individuals in a given stage to future population abundance
according to the sensitivity matrix, which parameter has the most impact on the asymptotic population growth rate?
a (43)
you administer medication to individuals and keep track of their symptoms/fate over time ( a record for each individual is kept ) the data are
longitudinal data
the average survival rate for population can be decline when a population abundance is increasing (assuming no immigration and emigration)
TRUE
case mortality rate appears to be declining. it is still plausible that that disease is becoming worse ( according to simspons paradox ) bc
more younger people ( who previously did not develop symptoms before ) are developing symptoms and they tend to recover.
population is
a group of individuals of one species that live in a particular geographic area
semelparous means
individuals reproduce at most once in their life time
suppose a population of frogs consisted of 100 individuals on March 1, 2021 and 94 individuals on April 2021. We know there was no birth. we also know there is no immigration and emigration because the population is isolated. Which of the following is the best answer?
The monthly mortality rate was 0.06
suppose X=500-Ns where Ns is the variable in the script. what is X Suppose you survey deer in national park ( all of the individuals in population is in the park ) and count how many individuals died in a given year. the total number of death is
not sufficient information to calculate a per-capita annual death rate
which of the following is correct
individuals can start reproducing at age 4, and some individuals can live beyond age 5
fertility rate for matrix population model is
the product of fecundity per parent and the survival rate of offspring
lifecycle graph tells
number of stage/age classes and how individuals can be transition among them
why does population density fluctuate over time ?
is it because vital rates are not constant
which of the following is correct
x(1) = a11n1 + a12n2+a13n3
Note
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