1. Population parameters (Chp. 9)
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

2. Primary characteristic: density

3. Secondary characteristics
Age distribution
Genetic composition and variability
Distribution in time and space

4. Approximate densities of organisms in nature

5. Fig. 9.3 (p. 120): Relationship between body side and density for mammals (red) and birds (blue)

6. 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

7. Measurement of absolute density
Total counts
count every individual in the population
census
not possible for many species

8. 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

9. 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

10. Quadrat sampling

11. Quadrat sampling

12. Quadrat sampling

13. Quadrat sampling

14. 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

15. 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

16. 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

18. 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

19. 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

20. Natality: birth rate Recruitment or addition to population live birth
hatching
fission
germination
budding

21. Natality: birth rate Fertility Fecundity
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

22. 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

23. 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

24. Mortality: death rate Physiological longevity Ecological 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.

25. 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

26. Fig. 9.5 (p. 129): Catch curve for bluegill sunfish; descending curve after Age 2 can be used to estimate the adult mortality rate.

27. 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

28. 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

29. Fig. 9.1 (p. 117): Examples of modular organisms.
Fescue grass
Wheatgrass
Sandwort

30. 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

31. 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

32. Composition of populations
Secondary differences
color
markings
behavior

33. 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

34. Table 10.1 (p. 134): Cohort life table for the song sparrow on Mandarte Island, British Columbia.

35. Elements of a life table
x: age interval
nx: number of survivors at the beginning of age interval x
lx: proportion of individuals surviving to the start of age interval x
dx: number dying during the period between one age class (x) and the next (x+1)
qx: mortality rate during age interval x to x+1
ex: mean expectation of further life for individuals alive at the start of age interval x

36. Formulas for life table elements
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 bottom of table]
T2 = 46.5 ex
ex = Tx / nx
e3 = 0.75

37. Reworked life table (Table 10.1) for song sparrowsx
(Age in years)
nx (Observed number of birds alive) lx
(Proportion surviving at start of age interval x) dx
(No. dying within age interval x to x+1) qx
(Rate of mortality) Lx
(No. alive on average during age interval x to x+1) Tx
(Individual x time factor) ex
(Average expectation of further life)
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
0.017
0.50 5
0.009
1.00
0.000 -

38. Reworked life table (Table 10.1) for song sparrowsx
(Age in years)
nx (Observed number of birds alive) lx
(Proportion surviving at start of age interval x) dx
(No. dying within age interval x to x+1) qx
(Rate of mortality) Lx
(No. alive on average during age interval x to x+1) Tx
(Individual x time factor) ex
(Average expectation of further life)
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 4
0.017
0.50
1.5 5
0.009
1.00
0.5
0.000 -

39. Reworked life table (Table 10.1) for song sparrowsx
(Age in years)
nx (Observed number of birds alive) lx
(Proportion surviving at start of age interval x) dx
(No. dying within age interval x to x+1) qx
(Rate of mortality) Lx
(No. alive on average during age interval x to x+1) Tx
(Individual x time factor) ex
(Average expectation of further life)
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
9.0 4
0.017
0.50
1.5
2.0 5
0.009
1.00
0.5
0.000 -

40. Reworked life table (Table 10.1) for song sparrowsx
(Age in years)
nx (Observed number of birds alive) lx
(Proportion surviving at start of age interval x) dx
(No. dying within age interval x to x+1) qx
(Rate of mortality) Lx
(No. alive on average during age interval x to x+1) Tx
(Individual x time factor) ex
(Average expectation of further life)
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
9.0
0.75 4
0.017
0.50
1.5
2.0
1.00 5
0.009
0.5
0.000 -

41. Fig (p. 134): Survivorship curves for all males (red) and females (blue) in the U.S. in 1998 from a starting cohort of 1000.

42. Fig. 10.2 (p. 135): Hypothetical survivorship curves (nx) and mortality curves (dx).

43. 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

44. Table 10.2 (p. 136): Static life table for human female population of Canada, 1996.

45. 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

46. 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

47. Fig (p. 137): Survivorship curves of the barnacle Chthamalus with and without its competitor barnacle Balanus.

48. Types of data used for life tables
BIOL 4131 Lecture 05
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)

49. Fig (p. 138): Mortality rate per year (qx) for African buffalo; age at death determined from skulls.

50. Fig. 10. 5 (p. 138): Age-specific mortality rates for cohort of 1
Fig (p. 138): Age-specific mortality rates for cohort of 1.2 x 106 Mediterranean fruit flies.

51. 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

52. 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

53. 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

54. rm: innate capacity for increase
Estimates for rm ra
observed reproductive rate for population r0
net reproductive rate
calculated from life table

55. 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

56. rm: innate capacity for increase
Estimation of rm from r0 calculation using life table
lx age-specific survivorship column from
life table
bx number of female offspring produced per female of age x
Vx = (lx) (bx) = age-specific reproductive rate

57. r0 = Vx 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