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Lecture 6

BIO120H1 Lecture Notes - Lecture 6: Net Reproduction Rate, Survivorship Curve, Fecundity


Department
Biology
Course Code
BIO120H1
Professor
Jon Abbatt
Lecture
6

Page:
of 3
x: age specific variables
nx : the number of individuals of age x in a population.
bx: female offspring produced per reproductive season (b
for birth)
lx: probability of being alive at age x
dx: death rate, proportion of individuals of age x dying by
age x+1
mx: mortality rate; proportion of individuals of age x
dying by age x+1
Lecture 6: Age-structured populations and life histories
Age structure: the distribution of individuals among age classes within a population.
Geometric rate of population growth the ratio of the population size after one year to
that the beginning of the year:
 
o Will eventually reach a stable age distribution; each age class grows or declines
at the same rate
Fecundity: The number of offspring produced per reproductive episode.
o Reproductive period usually preceded by resource-accumulation phase
o Fecundity-survivorship trade-offs = cost of reproduction
Shapes of survivorship curves
Type II survivorship curveconstant survival rate with age. Thus, survivorship declines
exponentially with age.
Type I survivorship curve high survival rate at the beginning, falls off abruptly with age
as the age-specific mortality rate increases (human; mortality is low early in life and
then increases rapidly later in life) .
Type III survivorship curvehigh mortality rate in early life, survival rate increase later
in life. (fishes; young individuals are extremely vulnerable to predation and other risk
factors, which they escape as they grow larger and mature).
Net reproductive rate (R0): the expected total number of female offspring produced by
an average female over the course of her life span.
 
o would be the total # daughters produced by a mother who doesn’t die early;
multiplying by discounts expected production by the probability that some
mothers do die early
Generation time (T): the average period between the birth of an individual and the birth
of its offspring; average age at which a female gives birth.
 
o This is a formula for a weighted average. X is a female’s age. Multiplying x by
weights x by how many offspring are produced at that age; dividing the sum of
the weighted x’s by the total production of daughters () gives a weighted
average that specifies when a female gives birth on average.
Relationship between and
Since   , then,
  .
o If t represents the generation time T, then the ratio
 is the net reproductive
rate.
Hence,   and   
Organisms with higher ’s have higher fitness…So why aren’t all plants annuals?
Constraints and tradeoffs: Reproduction is costly. Longer prereproductive periods allow
time to accumulate more resources.
Life Histories
semelparous (“big bang”) organism a life history characterized by a single, terminal
reproductive episode
Why synchrony?
Semelparity & Predator satiation
o Frasera speciosa (“Monument Plant”) Semelparity plus local synchrony
o Ipomopsis aggregate (“Scarlet Gilia”)Flexible semelparity based on resources.
o Some bambooExtremely synchronized semelparity
iteroparous organism a life history characterized by multiple reproductive episodes.
o Blue OakIteroparity plus local synchrony = “masting”
Life expectancy,” ex
Definition: Expected years left to an individual of age x
Reproductive value, vx
Definition : Expected # further daughters left to an individual of age x (usually
normalized to a newborn individual)
o Effects
Success of captive breeding/release programs for conservation: should
release animals with highest reproductive value
Prospective success following dispersal to new habitats: roaming
behaviour should coincide with age of high vx
Age of high vx should maximize attractiveness to potential mates
Antagonistic pleiotropy
Pleiotropy: one gene may have multiple different functions
“Antagonistic pleiotropy”: a gene may have opposite effects on survival at different
ages
o A gene with positive value in young animals but negative value in old animals
will be favoured by natural selection…because reproducing early increases
fitness
Accumulation of such genes causes senescence
o Example: p53 suppresses tumours in youth, but later destroys stem cells