Transcript L x

Population parameters (Chp. 9)
• Population
– group of organisms of the same species
occupying a given space at a particular time
– ultimate constituents: species
– demes
• local populations
• smallest collective unit of a population
– boundaries of populations are usually vague
1
Primary characteristic: density
Immigration
Natality
+
+
DENSITY
-
Mortality
Emigration
2
Secondary characteristics
• Age distribution
• Genetic composition and variability
• Distribution in time and space
3
Approximate densities of organisms in nature
4
Fig. 9.3 (p. 120): Relationship between body side
and density for mammals (red) and birds (blue)
5
Measurement of density
• Absolute density
– estimate of the actual number of individuals in
the population
• Relative density
– collection of samples that represent some
relatively constant, but unknown relationship
to population size
– provides index of abundance, not an estimate
of actual density
6
Measurement of absolute density
• Total counts
– count every individual in the population
– census
– not possible for many species
7
Measurement of absolute density
• Population sampling
– count proportion of population and use to
estimate size of total population
– quadrat sampling
• plants
• sessile animals
– mark-recapture sampling
• motile animals
8
Measurement of absolute density
• Quadrat sampling
– uses area of known size, any shape (quadrat)
– count total in quadrat and extrapolate
– quadrats usually rectangle, square or core
– reliability dependent on
• accurate count of population in each quadrat
• exact area of quadrats and total site known
• quadrat representative of whole site to ensure
random sampling
9
Quadrat sampling
10
Quadrat sampling
11
Quadrat sampling
12
Quadrat sampling
13
Measurement of absolute density
• Mark-recapture sampling
– Lincoln-Peterson method
– used to estimate
•
•
•
•
one-time density of population
changes in density over time
natality
mortality
14
Measurement of absolute density
• Mark-recapture sampling
– collect, mark and release animals 
population will consist of both marked and
unmarked animals
– population size is estimated from determining
the proportion of the total population that is
marked
15
Mark-recapture sampling
N = nM/x
where
N = total population size
M = number marked in 1st sampling
n = number captured in 2nd sampling
(marked + unmarked individuals)
x = number of marked individuals
recaptured in 2nd sampling
16
17
Mark-recapture sampling
• Assumptions
– marked and unmarked individuals are
captured randomly (versus trap-happy or
trap-shy)
– marked individuals are subject to the same
mortality as unmarked
– marks are not overlooked or lost
18
Measurements of relative density
•
•
•
•
•
Traps
Number of fecal pellets
Vocalization frequency
Pelt records
Questionnaires
•
•
•
•
•
Aerial photography
Roadside counts
Feeding capacity
Catch per unit effort
Number of artifacts
19
Natality: birth rate
• Recruitment or addition to population
– live birth
– hatching
– fission
– germination
– budding
20
Natality: birth rate
• Fertility
– measure of actual number of viable offspring
• Fecundity
– potential reproductive performance of a
population
– realized fecundity: rate based on actual
numbers
– potential fecundity: potential level of
reproductive performance
21
Natality: birth rate
• Fecundity of human population
– realized fecundity:
1 birth / 8 years / female of child-bearing age
– potential fecundity:
1 birth / 10 months / female of child-bearing age
22
Natality: birth rate
• Number of offspring born per female per unit time
• Dependent on number of reproductive events and
number produced per event
• Species dependent
– breeding seasons: 1/yr, 2/yr, continuous
– number of offspring per breeding period
•
•
•
•
oysters: 114,000,000 eggs
fish: 1000 eggs
birds: 1-20 eggs
mammals: generally <10, usually 1-2
23
Mortality: death rate
• Physiological longevity
– average lifespan of individuals of a population
living under optimal conditions
– individuals die of senescence
• Ecological longevity
– empirical average lifespan of individuals of a
population under natural conditions
– individuals die of predation, disease,
parasites, etc.
24
Mortality: death rate
• Measurement of mortality rates
– direct: mark-recapture experiments over time
– indirect: catch curves
• survival rates estimated from decreases in relative
abundance from age group to age group
• survival rate between two years (e.g., Age 2-3) =
relative abundance of Age 2 / relative abundance
of Age 3
25
Fig. 9.5 (p. 129): Catch curve for bluegill sunfish;
descending curve after Age 2 can be used to estimate
the adult mortality rate.
26
Limitations on methods used to
estimate population density
• What constitutes a population of a
species?
– determining the boundary of the population
– distributions along continuums with no
distinct boundaries
– overlapping populations
27
Limitations on methods used to
estimate population density
• What constitutes an individual in the
population?
– problem in grasses, colonies of social insects,
corals, hybrids, clones, etc.
– unitary organisms versus modular organisms
– the individual may be the original zygote
– biomass or coverage often used to determine
density in these populations
28
Fig. 9.1 (p. 117): Examples of modular organisms.
Fescue grass
Wheatgrass
Sandwort
29
Limitations on methods used to
estimate population density
• How do differences in community
pressures and stresses influence
populations?
– negative influence on density
– positive influence on density
30
Composition of populations
• Primary differences
– sex ratio
• most populations close to 50:50
• determines reproductive potential of population
and many social interactions
– age structure
• physical size
• reproductive rates
• disease resistance
• social interactions
31
Composition of populations
• Secondary differences
– color
– markings
– behavior
32
Demographic techniques (Chp. 10)
• Life tables
– age-specific summary of mortality rates
– makes predictions base on past history of
the population
– adapted from human actuarial formats
33
Table 10.1 (p. 134): Cohort life table for the song
sparrow on Mandarte Island, British Columbia.
34
Elements of a life table
x:
nx:
lx :
dx:
qx:
e x:
age interval
number of survivors at the beginning of age
interval x
proportion of individuals surviving to the start
of age interval x
number dying during the period between
one age class (x) and the next (x+1)
mortality rate during age interval x to x+1
mean expectation of further life for
individuals alive at the start of age interval x
35
Formulas for life table elements
Element
Formula
Example
nx
Observed data
n0 = 115
lx
lx = nx / n0
l4 = 0.017
dx
dx = nx – nx+1
d2 = 7
qx
qx = dx / nx
q1 = 0.24
Lx
Lx = (nx + nx+1 )/2
L5 = 0.5
Tx
Tx = Lx + Tx+1 or
Tx = Lx [summed from
T2 = 46.5
bottom of table]
ex
ex = Tx / nx
e3 = 0.75
36
Reworked life table (Table 10.1) for song sparrows
x
nx
lx
dx
qx
Lx
Tx
ex
(Age in
years)
(Observed
number of
birds alive)
(Proportion
surviving at
start of age
interval x)
(No. dying
within age
interval x to
x+1)
(Rate of
mortality)
(No. alive on
average during
age interval x
to x+1)
(Individual x
time factor)
(Average
expectation
of further
life)
0
115
1.000
90
0.78
1
25
0.217
6
0.24
2
19
0.165
7
0.37
3
12
0.104
10
0.83
4
2
0.017
1
0.50
5
1
0.009
1
1.00
6
0
0.000
-
-
37
Reworked life table (Table 10.1) for song sparrows
x
nx
lx
dx
qx
Lx
Tx
ex
(Age in
years)
(Observed
number of
birds alive)
(Proportion
surviving at
start of age
interval x)
(No. dying
within age
interval x to
x+1)
(Rate of
mortality)
(No. alive on
average during
age interval x
to x+1)
(Individual x
time factor)
(Average
expectation
of further
life)
0
115
1.000
90
0.78
70
1
25
0.217
6
0.24
22
2
19
0.165
7
0.37
15.5
3
12
0.104
10
0.83
7
4
2
0.017
1
0.50
1.5
5
1
0.009
1
1.00
0.5
6
0
0.000
-
-
-
38
Reworked life table (Table 10.1) for song sparrows
x
nx
lx
dx
qx
Lx
Tx
ex
(Age in
years)
(Observed
number of
birds alive)
(Proportion
surviving at
start of age
interval x)
(No. dying
within age
interval x to
x+1)
(Rate of
mortality)
(No. alive on
average during
age interval x
to x+1)
(Individual x
time factor)
(Average
expectation
of further
life)
0
115
1.000
90
0.78
70
116.5
1
25
0.217
6
0.24
22
46.5
2
19
0.165
7
0.37
15.5
24.5
3
12
0.104
10
0.83
7
9.0
4
2
0.017
1
0.50
1.5
2.0
5
1
0.009
1
1.00
0.5
0.5
6
0
0.000
-
-
-
-
39
Reworked life table (Table 10.1) for song sparrows
x
nx
lx
dx
qx
Lx
Tx
ex
(Age in
years)
(Observed
number of
birds alive)
(Proportion
surviving at
start of age
interval x)
(No. dying
within age
interval x to
x+1)
(Rate of
mortality)
(No. alive on
average during
age interval x
to x+1)
(Individual x
time factor)
(Average
expectation
of further
life)
0
115
1.000
90
0.78
70
116.5
1.01
1
25
0.217
6
0.24
22
46.5
1.86
2
19
0.165
7
0.37
15.5
24.5
1.29
3
12
0.104
10
0.83
7
9.0
0.75
4
2
0.017
1
0.50
1.5
2.0
1.00
5
1
0.009
1
1.00
0.5
0.5
0.50
6
0
0.000
-
-
-
-
-
40
Fig. 10.1 (p. 134): Survivorship curves for all males
(red) and females (blue) in the U.S. in 1998 from a
starting cohort of 1000.
41
Fig. 10.2 (p. 135): Hypothetical survivorship curves (nx)
and mortality curves (dx).
42
Types of life tables
• Static life tables
– stationary, time specific, vertical life tables
– calculated on basis of a cross-section of the
population at a specific time
– must be able to determine age of individuals
in the population
43
Table 10.2 (p. 136): Static life table for human female
population of Canada, 1996.
44
Types of life tables
• Cohort life tables
– generational, horizontal life tables
– calculated on basis of a cohort of organisms
followed from birth through entire life
– must be able to track individuals from birth to
death
45
Types of data used for life tables
• Survivorship observed directly
– lx of cohort is monitored closely over the
entire life period
– e.g., Connell’s study of barnacles
46
Fig. 10.3 (p. 137): Survivorship curves of the barnacle
Chthamalus with and without its competitor barnacle
Balanus.
47
Types of data used for life tables
• Age at death observed
– assumes population is stable over time and
birth and death rates remain constant
– e.g., Sinclair’s study of buffalo (Type I)
– e.g., Carey et al. study of fruit flies (Type III)
48
Fig. 10.4 (p. 138): Mortality rate per year (qx) for
African buffalo; age at death determined from skulls.
49
Fig. 10.5 (p. 138): Age-specific mortality rates for
cohort of 1.2 x 106 Mediterranean fruit flies.
50
Types of data used for life tables
• Population age structure observed
directly
– requires some way to determine age
• annular rings on fish scales
• bird plumage
• tree rings
– not always possible to construct a life table
using this kind of data
51
Innate capacity for increasing density
• Combines reproduction and life table data
• Dependent on environmental conditions
– favorable conditions: positive capacity for increase, numbers
increase
– unfavorable conditions: negative capacity for increase, numbers
decrease
• In nature, the actual rate of increase varies
continuously from positive to negative in
response to changes within population
–
–
–
–
age distribution
social structure
genetic composition
fluctuations in environmental factors
52
rm: innate capacity for increase
• Maximum rate of increase attained at any
particular combination of environmental
conditions when niche requirements are
optimal and other species are entirely
excluded from the experiment
• Determined only in lab experiments
• Changes with different environmental
conditions
53
rm: innate capacity for increase
• Estimates for rm
ra
• observed reproductive rate for population
r0
• net reproductive rate
• calculated from life table
54
rm: innate capacity for increase
• Population innate capacity for increase
dependent on
– fertility
– longevity
– speed of development of individual organisms
• Natality > mortality  population increases
• Since natality and mortality rates vary with
age structure, quantitative estimates of
population growth rates are difficult
55
rm: innate capacity for increase
• Estimation of rm from r0 calculation using
life table
lx
bx
age-specific survivorship column from
life table
number of female offspring produced
per female of age x
Vx = (lx) (bx) = age-specific reproductive rate
56
Net reproductive rate
• Estimation of rm from r0 calculation using life
table
r0 = Vx
r0 = 1: population replacing itself
r0 > 1: population growing
r0 < 1: population declining
• r0 = rm only under lab conditions that are optimal
for every factor that affects the reproductive rate
57