In this first module of chapter 4 on reproduction,
Module 4.1, I will cover reproductive terms, concepts,
patterns and Lexis diagrams. Reproduction can be
characterized in two ways, either physiological,
in other words the process that results in offspring,
or demographic, which is the per capita rate
of offspring production in a given period of time.
The terms reproductive rate, renewal rate,
recruitment rate, and natality rate all
denote the same reproductive concept
and are frequently used synonymously.
In biology, fecundity and fertility are sometimes
used interchangeably with reproductive rate,
but we will use the convention from formal
demography of defining fecundity as the total
number of offspring a female is capable of
producing in a specified age interval,
and fertility as the total number of offspring
a female actually produces in the interval.
Patterns of Reproduction
One way to classify the reproductive diversity
of organisms is by the number of
reproductive events in an individual’s lifetime.
Semelparous species reproduce once.
This pattern is often termed “big bang” reproduction
because individuals die after reproduction.
Examples of semelparous reproduction include
Pacific salmon, American eels, octopods, and bamboo.
Iteroparous species, on the other hand,
breed more than once and thus exhibit
age-specific patterns of reproduction.
Examples include most vertebrates
mammals, birds, reptiles, amphibians and fish
but also humans, of course, and most species of insects.
The shape of the age schedule of reproduction
is generally classified into three groups including
uniform—an age-independent or constant
level of offspring production with age;
asymptotic—an increasing reproductive output
with age, a pattern that often occurs in plants and ectotherms
and increase in size after reproductive maturity;
and triangular—an age-dependent reproductive pattern
that starts low, increases to a peak typically
in early middle age, and decreases with age.
Some Basic Concepts
A reproductive age schedule is the per-capita age-specific fecundity and fertility rates
over specified age intervals or over a cohort’s lifetime.
A gross schedule is one in which mortality is not taken into account,
and a net schedule weights reproduction by the proportion, or number,
in the cohort that survive to each age class.
Parameters that express various aspects of this heterogeneity include the following:
reproductive interval, which gives the daily frequency
of offspring production among individuals;
daily parity, or it could be yearly parity,
which denotes the fraction of the cohort
that produce specified numbers of offspring
at a given age; cumulative parity,
which expresses the fraction of living individuals
within a cohort that have had a specified sum total
of offspring at given age; and, the concentration
of reproduction, which gives the frequency distribution
of lifetime reproduction ranked by individual.
Offspring produced by females are often produced
as clutches, for example in insects,
or litters, for example in rodents,
this clutch or litter size designate offspring groupings
that can be also expressed as an age schedule.
Most organisms produce more than one offspring type,
of which the most common type category is gender or sex,
male or female. All of the reproductive relations discussed
here pertain to females and are thus maternity functions.
Although only limited effort has been directed towards
reproductive rates of males, a number of paternity functions
can be patterned after these same maternity concepts.
Birth Intervals and Rates
Variation in reproduction among individuals
within a cohort can be quantified by comparing
birth intervals and birth rates. Birth intervals provide order
that is an age sequence, duration, that is the width of age class
and timing, that would be period.
And birth rates can be expressed
as age or period-specific or as total reproductive rates,
without adjustments for mortality is a gross rate,
or with adjustments for mortality would be a net rate.
Basic age-specific birth metrics
If all individuals in a cohort are exactly the same age,
period effects on birth rates will, at least in theory
and with respect to statistical analysis,
have the same impact on all individuals.
The schematic shown here in this figure illustrates
how a number of reproductive metrics are
measured and computed. The hypothetical raw data
include the number of offspring by age for each
individual in the rows, that is Individuals A to D,
and columns, Ages 0 to 4. The summary data include
total births by individual, exposure time which
refers to the duration of life for an individual
and average births per epoch, which are the births
divided by exposure time,
so this would be 9 divided by 4.0 equal 2.3 for Individual A.
The summary metrics for the total group of individuals
are computed from the sums of each of three columns
which shows a total of 24 offspring, 12 epochs exposure,
that is average lifetime, and thus, 7.3 total births.
From these sums, averages can be computed
such as the average lifetime births,
24 divided by 4 individuals equal 6 lifetime births per individual,
the average lifetime, 12 epochs and 3 individuals equal 4 epochs,
and the average reproduction per epoch,
that is 7.3 time units or epochs
divided by 4 individuals equal 1.8.
Lexis diagrams: Births by age and period
The Lexis diagram can be used to illustrate
the measurement of three different categories
of birth rates in humans when both
age and period are considered. We have the Lexis square.
This is the number of births within a single period for
two cohorts in the same age class. In the figure,
this total equals the number of births from the cohort
prior to Cohort A, which is 25 births, plus the total from Cohort A,
or 32 births, that occurred in the year 2000,
when individuals were between 31 and 32 years old.
The total is 57 births.
Lexis horizontal parallelogram
This is the number of births through the time
that a cohort is a particular age and that age covers two periods.
In the figure here, Cohort A produced 32 births in 2000
and 19 births in 2001 when individuals in this cohort
were between 31 and 32 years. The total is 51 births.
Lexis vertical parallelogram
This is the number of births for a cohort during
a single period. In the figure for the year 2000,
some individuals from Cohort A were between
30 and 31 years and they produced 27 births
and other individuals from Cohort A were between
31 and 32 years and produced 32 births. The total is 59 births.
This all for this first module, Module 4.1 of Chapter 4 on reproduction.