What is a population? Within a given area where the scale of the area is study-dependent Localised group of individuals of the same species e.g. population of aphids on a leaf e.g. population of baboons on the Cape Peninsula e.g. population of orchids in a 10km2 area of the Peninsula

Population Biology Describe Explain (Influencing factors) 50 100 150 200 250 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Year 10 Year 11 Year 12 Population size Time (t) Describe Explain (Influencing factors) Intrinsic Birth Mortality Death Emigration Extrinsic Environment Weather

Quantifying population growth Dependent on organisms life cycle Overlapping and non-overlapping Birth Death Immigration Emigration Population growth + - = Original population Nt+1 = Nt + B + I – D - E N = population size t = time period (eg. Days, months, years…depends on study organism) Populations grow IF (B + I) > (D + E) Populations shrink IF (D + E) > (B + I)

Non-overlapping (discrete) generations Life cycles Non-overlapping (discrete) generations Population growth potential Overlapping generations

Life cycles – discrete generations Often seasonally determined Pods Adults1 Generation 1 Eggs www.kidfish.bc.ca/caddis_cycle.htm Instar I Replace Instar II Instar III Adults2 Generation 2 Instar IV

Differential reproduction Differential survival Life cycles – overlapping generations R1 Time 1 Differential reproduction Differential survival R2 R1 Time 2 Individuals of different ages reproducing at the same time R3 R1 Time 3 R2

Overlapping generations Life cycles Overlapping generations Non-overlapping generations Population growth potential Frequency of reproduction Semelparous Iteroparous

Population Life Tables

Semelparous vs Iteroparous Life Cycles Reproductive phase Growth phase Post-Reproductive phase Single Reproductive Event One individual E.g. most invertebrates SEMELPAROUS: only one reproductive event in their lifetime Year 1 Reproductive phase Growth phase Post-Reproductive phase Multiple Reproductive Events One individual E.g. most birds & mammals ITEROPAROUS: multiple reproductive events over extended portions of their lives Year 1 Year 2 Year 3 Year 4

Differential reproduction Differential survival Quantifying population growth Dependent on organisms life cycle: Generation overlap & Semel/Iteroparous Age and stage specific Birth Death Immigration Emigration Population growth + - = Original population Differential reproduction Differential survival

Adults M F Pods Eggs Instar I Instar II Instar III Instar IV P=0 7.3 11 0.079 0.72 0.78 0.76 0.69 Adults Nt Nt+1 Seeds Nt.f Seedlings Nt.f.g Fecundity (f) Different ages and stage classes have different probabilities of survival and different probabilities of successful reproduction BIRTH Germinate (g) Survival (p) SURVIVAL Survival to maturity (s) Nt+1 = (Nt.p) + (Nt.f.g.s)

Tool for quantifying population growth Dependent on organisms life cycle: Generation overlap & Semel/Iteroparous Birth Death Immigration Emigration Population growth + - = Original population Tool for quantifying population growth Age and stage specific Differential reproduction Differential survival

Quantifying population growth LIFE TABLES a simple method for keeping track of births, deaths, and reproductive output in a population of interest Birth Death Immigration Emigration Population growth + - = Original population Number of young produced in each reproductive event Length of each generation Frequency of reproductive events

2 ways of constructing Life tables COHORT LIFE TABLE STATIC LIFE TABLE compares population size from different cohorts, across the entire range of ages, at a single point in time Snapshot in time Time 1 N of Age 1 N of Age 2 N of Age 3 Used to estimate population growth

Static tables make two important assumptions: Static Life Tables Static tables make two important assumptions: the population has a stable age structure (i.e. the proportion of individuals in each age class does not change from generation to generation) the population size is stationary , or nearly stationary lx Cohort 1 lx Cohort 2 Population size (n) lx Cohort 4 lx Cohort 3

2 ways of constructing Life tables COHORT LIFE TABLE follows a group of same-aged individuals from birth (or fertilized eggs) throughout their lives STATIC LIFE TABLE compares population size from different cohorts, across the entire range of ages, at a single point in time Less accurate than cohort tables Age 1birth Age 1death Time (t) Considers differential probabilities at each life stage Note: For organisms that have separate sexes, life tables frequently follow only female individuals.

Cohort Life Tables Simplest form: annual life cycle Semelparous (only one breeding season in its life time) no overlap of generations Animal with To make a life table for this simple life history, we need only count (or estimate) the population size at each life history stage and the number of eggs produced by the adults. www.kidfish.bc.ca/caddis_cycle.htm

From this raw data we can calculate several LIFE HISTORY FEATURES Cohort Life Tables Age classification From this raw data we can calculate several LIFE HISTORY FEATURES One generation COUNT DATA

Cohort Life Tables Calculated life history features Calculate by: Age classification Proportion of original cohort surviving to each stage lx Calculated life history features Calculate by: divide the number of individuals living at the beginning of each age (ax) by the initial number of eggs (a0) This data is STANDARDIZED therefore comparable between populations ...Raw data is NOT COUNT DATA

Proportion of original cohort surviving to each stage Cohort Life Tables Age classification Calculated life history features Proportion of original cohort surviving to each stage lx DISADVANTAGE: > ax = > lx and dx values ; Therefore dx does not indicate the stage where mortality is most INTENSE Calculate by: lx - lx+1 ADVANTAGE: Proportions can be added together to get a measure of mortality for different stage groups COUNT DATA

Proportion of original cohort surviving to each stage Cohort Life Tables Age classification Calculated life history features Proportion of original cohort surviving to each stage lx qx is the fraction of the population dying at each stage ADVANTAGE: qx does indicate the stage where mortality is most INTENSE Calculate by: dx/lx Stage specific ∑ CANNOT DISADVANTAGE: COUNT DATA

Cohort Life Tables Combining advantages of dx (can be summed) and qx (indicates mortality intensity) is K (killing power) K p age specific survivorship, calculated as 1 - qx (or ax+1 / ax): cannot be summed log

Proportion of original cohort surviving to each stage Cohort Life Tables Assessing the populations reproductive output Age classification Proportion of original cohort surviving to each stage lx Calculated life history features Age specific COUNT DATA COUNT DATA

Proportion of original cohort surviving to each stage Cohort Life Tables Assessing the populations reproductive output Age classification Proportion of original cohort surviving to each stage lx Calculated life history features Age specific mx is the eggs produced per surviving individual at each age or individual fecundity Calculate by: Fx/ax COUNT DATA COUNT DATA

Proportion of original cohort surviving to each stage Cohort Life Tables Assessing the populations reproductive output Age classification Proportion of original cohort surviving to each stage lx Calculated life history features Age specific The number eggs produced per original individual at each age (lxmx) Calculate by: lx*mx COUNT DATA COUNT DATA

Proportion of original cohort surviving to each stage Cohort Life Tables Assessing the populations reproductive output Age classification Proportion of original cohort surviving to each stage lx Calculated life history features R0 is the population’s replacement rate: If R0 = 1.0…no population growth If R0 < 1.0…the population is declining If R0 > 1.0…the population is increasing Age specific lxmx is an important value to consider in population studies basic reproductive rate ∑ lxmx = R0 individuals produced for every individual in every generation If only females in the life table then: individuals produced for every female in every generation COUNT DATA COUNT DATA

Calculating population features from life tables Raw count data Reproductive output Life history features R0 – the basic reproductive rate Tc = cohort generation time ex = life expectancy r = intrinsic growth rate Can use life tables to determine characteristics about the population: ∑ lxmx

Cohort generation time (Tc) Cohort generation time (Tc) can be defined as the average length of time between when an individual is born and the birth of its offspring. Tc is quite easy to obtain from our first example… But Tc is less obvious for more complex life cycles – must be calculated Calculate Tc: Calculate the length of time to offspring production for each age class Add all the lengths of time to offspring production for the entire cohort Calculate the total offspring produced by the survivors Divide by lengths of time to offspring production/the total offspring produced by the survivors BIRTH DEATH OFFSPRING Generation time semelparous annual life cycle (Tc =1 year) 610.32 1872.03 Tc = 3.1 TOTAL

Calculating population features from life tables Raw count data Reproductive output Life history features R0 – the basic reproductive rate Tc = cohort generation time ex = life expectancy r = intrinsic growth rate Can use life tables to determine characteristics about the population:

Time still to live (probability) Time still to live (probability) Life expectancy (ex) Life expectancy = the probability of living ‘x’ amount of time beyond a given age. Most commonly quoted as the life expectancy at birth, e.g., life expectancy for South Africans females = 50 yrs, and for South African males = 55 years (http://www.who.int/countries/zaf/en/) Note: time unit depends on organims being studied) We can also calculate the mean length of life beyond any given age for the population. Age 1 Age 2 Age 3 Time still to live (probability) Time still to live Death Any Age Time still to live (probability) Death

NB. Units of e must be the same as those of x Life expectancy (ex) Calculating ex: Calculate Lx - number of surviving individuals in consecutive stage/age classes Calculate Tx - the total number of living individuals at age ‘x’ Calculate ex NB. Units of e must be the same as those of x Thus if x is measured in intervals of 3 months, then ex must be multiplied by 3 to give life expectancy in terms of months

Calculating population features from life tables Non-overlapping generations R0 – the basic reproductive rate Tc = cohort generation time ex = life expectancy r = intrinsic growth rate Can use life tables to determine characteristics about the population: HOW?? Overlapping generations

Intrinsic growth rate (r) Non-Overlapping generations = ∑ lxmx R0 considers birth of new individuals Basic reproductive rate (R0) N0 NT 1 generation R0 converts the initial population size (N0) to the new size one generation later (NT) NT=N0.R0 If R0 remains constant from generation to generation, then we can also use it to predict population size several generations into the future. N0 N1 1 generation N2 N3 Nn 2 generations 3 generations n generations Constant R0

Intrinsic growth rate (r) Overlapping generations Rearrange Fundamental Reproductive Rate (R) Consider birth of new individuals + survival of existing individuals If R= 1.0…no population growth If R < 1.0…the population is declining If R > 1.0…the population is increasing As for R0 R=20/10 Nt = 10 Nt+1 = 20 R=2 Population size at t+1 = N0.R N1 = N0.R1 Nt = N0.Rt Population size at t+2 = N0.R.R N2 = N0.R2 Population size at t+3 = N0.R.R.R N3 = N0.R3

Intrinsic growth rate (r) Non-Overlapping generations Overlapping generations NT=N0.R0 Combine Nt = N0.Rt NT = N0.RT IF t = T, then Can now link R0 and R R0 = RT lnR0 = T.lnR lnR0/T = lnR But lnR = r Used to project population growth in population models r = average rate of increase/individual takes generation time into account

2 ways of constructing Life tables COHORT LIFE TABLE follows a group of same-aged individuals from birth (or fertilized eggs) throughout their lives STATIC LIFE TABLES is made from mortality data collected from a specified time period Problems: Most organisms have complex life histories (overlapping generations) Not always possible or feasible to follow a single cohort from birth to death

They have limited value in comparisons unless same units used Finite and instantaneous rates The values of p, q hitherto collected are FINITE rates…their units of time = units of time for x (months, days, three-months etc) They have limited value in comparisons unless same units used To convert FINITE rates at one scale to (adjusted) finite rates at another: Finite SURVIVAL rates [Adjusted FINITE] = [Observed FINITE] ts/to ts = Standardised time interval (e.g. 30 days, 1 day, 365 days, 12 months etc) to = Observed time interval e.g. convert annual survival (p) = 0.5, to monthly survival: Adjusted = Observed ts/to = 0.5 1/12 = 0.5 0.083 = 0.944 e.g. convert daily survival (p) = 0.99, to annual survival Adjusted = Observed ts/to = 0.99 365/1 = 0.99 365 = 0.0255

Finite and instantaneous rates INSTANTANEOUS MORTALITY rates = Loge (FINITE SURVIVAL rates) ALWAYS negative Finite Mortality Rate = 1 – Finite Survival rate Finite Mortality Rate = 1.0 – e Instantaneous Mortality Rate MUST SPECIFY TIME UNITS