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

Primary characteristic: density

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

Approximate densities of organisms in nature

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

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

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

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

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

Quadrat sampling

Quadrat sampling

Quadrat sampling

Quadrat sampling

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

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

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

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

Composition of populations Secondary differences color markings behavior

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

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

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

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

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) 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 -

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) 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 -

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) 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 -

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) 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 -

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.

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

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

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

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

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

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

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)

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

Fig. 10. 5 (p. 138): Age-specific mortality rates for cohort of 1 Fig. 10.5 (p. 138): Age-specific mortality rates for cohort of 1.2 x 106 Mediterranean fruit flies.

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

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

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

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

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

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

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