1 Population parameters (Chp. 9) Population –group of organisms of the same species occupying a given space at a particular time –ultimate constituents:

1

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

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Primary characteristic: density

DENSITY

Immigration

Natality Mortality

Emigration

+ +

- -

3

Secondary characteristics

• Age distribution

• Genetic composition and variability

• Distribution in time and space

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Approximate densities of organisms in nature

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

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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

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Measurement of absolute density

• Total counts– count every individual in the population– census– not possible for many species

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• Population sampling– count proportion of population and use to

estimate size of total population– quadrat sampling

• plants• sessile animals

– mark-recapture sampling• motile animals

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• 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

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Quadrat sampling

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Quadrat sampling

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Quadrat sampling

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Quadrat sampling

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• Mark-recapture sampling– Lincoln-Peterson method– used to estimate

• one-time density of population• changes in density over time• natality• mortality

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• 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

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Mark-recapture sampling

N = nM/xwhere 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

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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

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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

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Natality: birth rate

• Recruitment or addition to population– live birth– hatching– fission– germination– budding

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• 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

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• 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

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• 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

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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.

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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

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

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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

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• 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

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Fig. 9.1 (p. 117): Examples of modular organisms.

Fescue grass

Wheatgrass

Sandwort

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• How do differences in community pressures and stresses influence populations?– negative influence on density– positive influence on density

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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

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Composition of populations

• Secondary differences– color– markings– behavior

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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

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

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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

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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 bottom of table]

T2 = 46.5

ex ex = Tx / nx e3 = 0.75

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Reworked life table (Table 10.1) for song sparrows

x

(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)

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 - -

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x

(Age in years)


lx


dx


interval x to x+1)

qx

(Rate of mortality)

Lx


to x+1)

Tx


ex


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 - - -

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x

(Age in years)


lx


dx


interval x to x+1)

qx

(Rate of mortality)

Lx


to x+1)

Tx


ex


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 - - - -

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x

(Age in years)


lx


dx


interval x to x+1)

qx

(Rate of mortality)

Lx


to x+1)

Tx


ex


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 - - - - -

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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.

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

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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

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

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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

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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

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Fig. 10.3 (p. 137): Survivorship curves of the barnacle Chthamalus with and without its competitor barnacle Balanus.

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• 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)

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Fig. 10.4 (p. 138): Mortality rate per year (qx) for African buffalo; age at death determined from skulls.

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Fig. 10.5 (p. 138): Age-specific mortality rates for cohort of 1.2 x 106 Mediterranean fruit flies.

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• 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

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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

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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

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• Estimates for rm

ra• observed reproductive rate for population

r0• net reproductive rate• calculated from life table

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• 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


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• Estimation of rm from r0 calculation using life tablelx 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


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• Estimation of rm from r0 calculation using life table

r0 = Vx

r0 = 1: population replacing itselfr0 > 1: population growingr0 < 1: population declining

• r0 = rm only under lab conditions that are optimal for every factor that affects the reproductive rate

Net reproductive rate

Documents

1 Population parameters (Chp. 9) Population –group of organisms of the same species occupying a given space at a particular time –ultimate constituents: