topic 2 Flashcards
what is absolute density
• Number of individuals per unit area or volume
• Can be a total count of the entire population
Can be estimated by sampling and extrapolating (must still conduct total counts within some defined area)
what is relative density
• Indirect measure of population size
• Use variable with relatively constant, but unknown relationship to population size
e.g. scat frequency, no. of individuals in timed count
when to use absolute density?
• Often impractical (especially for small or mobile organisms)
• May be possible for larger and/or immobile organisms
Ex. northern fur seal breeding colonies - larger, dont move too far
how to sample? types?
- Count a small proportion of population and extrapolate to estimate total population size or density
- Two types: quadrat sampling and mark-recapture sampling
describe quadrat sampling
○ Count the number of individuals in several quadrats of known size and extrapolate the average across the total area
ex. 11 individuals in 12m2 = 92 indviduals/100m2
what does quadrat sampling require?
§ Accurate counts within each quadrant
§ Didn’t miss any individuals
§ Known quadrat area
Quadrats must be representative of whole area (random sampling)
describe mark-recapture sampling
○ Important for mobile animals
○ Capture - mark individuals - release - recapture
Various models
two sampling periods: 1.capture then mark all individuals (record #)
2. recapture, assuming second sample will contain same % of marked animals as the whole pop.
how to calculate total pop size w mark recapture
marked animals in 2nd sample/ total caught in 2nd = marked animals in 1st/total pop size
cross multiply
assumptions of cross recapture and why
○ Closed population (no immigration or emigration)
○ No recruitment/births of new animals in sampling period
○ Marked and unmarked indiviuduals are captured randomly
§ Small mammals might become trap happy or trap shy
§ Trap happy = underestimation of pop sized
§ Trap shy: over estimation of pop size
○ Marked animals are neither lost or overlooked
§ May be stressed and have higher mortality
§ Some fishermen keep tags as good luck charms
Tags can fall off
how to calculate relative density
traps (#caught per day)
no of fecal pellets/ area (ex. hares, mice, deer, rabbits)
vocalization frew. (frogs, birds, calls per 30 mins ex)
pelt records (trappers)
how to choose a sampling tehnique
depends on organism density, size, and mobility
what determines pop abundance?
• Birth and immigrations, death and emigration
BIDE equation - balance of these four parameters
BIDE equation variables
- births (b or B)
-immigration (i or I): movement of individuals into area
-mortality: d or D
-emigration: e or E
uppercase = absolute #, lowercase = per capita rate
how to convert absolute values to rates and vise versa?
• Convert absolute values to rates and vice versa?
○ Convert to rate by dividing by number of individuals
○ Convert to absolute by multiplying by number of individuals
look at bide demopgraphic model infographic thing. what is the open pop. formula
Nt+1= Nt+ B+ I - D- E
• Nt+1 = number of individuals at a given time
• Nt = number of individuals at a previous time
bide demographic model for rates?
bNt = # of individuals added to the population via births (find it by multiplying b by N)
Nt+1=Nt+(b-d)Nt (closed)
describe importance of immigration and emigration
• Important to maintain gene flow, prevent inbreeding
• Sets limits to geographic distribution
• Basis of metapopulation (source/sink) dynamics
• Rarely accounted for in population studies
• Assumed to be equal (immigration = emigration) or absent
(closed population)
what are life tables? questions they answer?
• Populations are composed of different types of individuals with different vital rates
• Life tables: technique to summarize the mortality and reproduction schedules of a populations
• Originally developed by insurance
At what age are organisms most vulnerable? Most important for future survival and reproduction?
how to make a life table (general)
Classify - determine appropriate age intervals or stage intervals (ex. Insect life cycle)
describe cohort tables
• Identify individuals born at same time (cohort)
• Follow over time, recording deaths (& sometimes births)
• Easy to interpret
• Difficult (or impossible) to collect these data in nature
Assumes cohort represents population
describe static life tables
• Stationary; time-specific; cross section of population at a given time
• Can use age at death data
• Record age at death of large number of individuals (requires accurate estimate of age at death), ex. Trees, sheep (horns), coral (growth rings)
• Can use age distribution data (assumes differences between age classes is due to mortality)
Assumes population is stationary (b & d constant), which would lead to a stable age class distribution over time
what leads to a stable age class distribution
all pops with a constant schedule of b and d rates will approach a fixed/stable age distribution, no matter initial distribution - constant b and d rates lead to it
how could cohort and static tables be identical
• Would be identical if: • Cohort used represents population • Environment is constant • Population is at equilibrium (constant b & d, stable age-class distribution) — Almost never true; can vary widely
cohort table variables
x = age.chorot nx= # alive at age x = survivorship schedule lx = proportion of orgs. surviving from start of life table to age X = standardized survivorship dx= number of individuals dying during age interval x to x+1 qx= per capital mortality rate during interval x to x+1 = age-specific mortality rate
life table 0 find nx ?
# of individuals surviving at each age class/survivorship schedule n0 can only stay the same or decline in subsequent age classes
find lx on life table?
l0 is always 1, l(last age class) is always 0
find gx on life table?
probability that an individual who has already survived to a certain age (x) will survive to the next age class (x+1)
gx=1-qx
gx=nx+1/nx
gx= lx+1/lx
look at graph for n0, nx, and nx+1 under subscripts in notes
ok
find dx on life table?
dx=nx-nx+1
number dying at each cohort
find qx on life table
age specific mortality
qx=1-gx
qx=(nx-nx+1)/nx
qx= dx/nx
steps to build a static life table?
- determine # that die in each age class (dx)
- use (1) to determine # alive at beginning of age class (nx) - do nx=nx-1-dx-1
- use nx to find lx
- calculate qx and gx
what are survivor ship curves? what do they plot
common pop. demographic technique
plot (log) survivorship (nx or lx) on y axis vs age on x axis
if using nx data, n0 is standardized (100 or 1000)
3 common survivorship curves? look at graph in notes
type I: low mortality for most of lifespan; higher loss of older orgs.
type II: constant per capita mortality rate (independent of age)
type III: high mortality rates early in life, followed by lower and relatively constant mortality of older age classes (high adult survivorship)
what do we need to determine how likely a pop id to change in abundance over time?
Life tables give us lots of information about age-specific
survival/mortality
• To determine how a population is likely to change in
abundance over time, we also need:
Age-specific schedule of births (bx)
what is GRR - survivroship schedule
sum of bx column = gross reproductive rate
GRR = average # of offspring produced by an individual that survives through all reproductive ages classes
survivorship schedule - R0?
net reproductive/replacement rate
sum of per capita birth rates adjusted for mortality
average # of offspring per individual in their life time
increasing vs declining pop based on R0?
R bigger than 1 = increasing
R less than 1 = declining
R=1 = unchanged
what is reproductive value
contribution that an individual of a certain age makes to future pop
Vx = present progeny + expected progeny
significance of reproductive value irl?
• Conservation, wildlife and fisheries management, forestry, etc
• Tells us:
○ Which age classes contribute most to present and future population growth
○ Which age classes to focus on protectiong
○ For which age classes should we allow harvesting
• Pest management
○ Efficacy of the control agent will depend on the reproductive value of the targeted stage
○ e.g. if a biocontrol agent targets prey with low reproductive value (old individuals) it may not be effective as a biocontrol agent
• Implications for natural selection and evolution
○ Natural selection acts more strongly on age classes with higher Vx (bigger contribution to future population growth)
• Helps us understand the evolution of life history traits
Look at formula for Vx. what are the assumptions
• Assume population is stable in size
• In a growing population: present offspring will be worth more than future progeny (in terms of proportionate contribution to future pop growth)
Declining population: future progeny are worth more than present offspring (in terms of proportionate contribution to future pop. Growth)
Vx calculation - find present progeny
bx = # of offpsring produced per individual at age x
Vx calculation - find future progeny
it is the Residual reproductive value - avg. # progeny produced for rest of individuals lifetime sum of (lt*bt)/lx for age classes x+1 to last age class (w) after current age class
what is ltbt in the Vx equation
bt = # offspring produced per individual in each age class for ages (x + I) to w (last age class) Adjusted for mortality occurring in age classes (x+1) to w (multiplied by It)
what does lx do for Vx equation
adjust for mortality occuring in age class x denominator will always be the same for a given vx calc
