Alligator Gar 1 June 2003 32 days post-hatch (approx. 90 mm TL). Demographic Techniques – Chapter 10. Life Tables - Mortality. Mortality is one of the four key parameters that drive population changes.
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1 June 2003
32 days post-hatch
(approx. 90 mm TL)Demographic Techniques – Chapter 10
X = age
nx = number alive at time t
lx = proportion of organisms surviving from the start of the lifetable to age x (ex: l1 = n1/n0, 0.217 =25/115; l2=n2/n0, 0.165=19/115)
dx = number dying during the age interval x to x + 1 (ex:d0=n0-n1, 90 = 115-25; d1=n1-n2, 6=25-19)
qx = per capita rate of mortality during the age interval x to x + 1 (ex: q0=d0/n0, 0.78 =90/115; q1=d1/n1)
Cohort Life Table:
A plot of nx on a Log scale from a starting cohort of 1,000 individuals.
These curves are models. Most real curves are intermediate.
Calculated by taking a cross section of a population at a specific time:
Balanus can affect the survival of Chthamalus as determined by survivorship curve
Based on 584 individuals plus observed estimated mortality for age 1 and 2 individuals
This data proves our simple theory of senescence is not correct
Population net reproductive rate
0.6% increase each generation
bx = natality
(lx)(bx) = reproductive output for that age class
R0 < 1 population is declining, R0 = 1 population is stable, R0 > population is increasing.
This animal lives three years, produces two young at exactly one year, and one young at exactly year two, and no young year three, then dies at end of year 3.
If a population starts with one individual at age 0, the age distribution quickly becomes stable: 60% age 0, 25% age 1, 10% age 2, and 4% age 3.
Written in integral form Nt = N0ert
dtStable Age Distribution
When a population has reached the stable age distribution, it will increase in numbers according to:
Nt = number of individuals at time t
N0 = number of individuals at time 0
e = 2.71828 (a constant)
r = intrinsic capacity for increase for the particular environmental conditions
t = time
This equation describes the curve of geometric increase in an expanding population (or geometric decrease to zero if r is negative).
Any population on a fixed age schedule of natality and mortality will change geometrically.
This geometric change will dictate a fixed and unchanging age distribution – the stable age distribution.
0.824 per individual per year
Calculating r from a life table:
Gc = 4.0/3.0 = 1.33 years
lxbxx = 4.0
r > 0 population increasing, r = 0 population stable, r < 0 population decreasing
lx = proportion of original individuals surviving to each age class.
bx = number of offspring produced per individual for the given age class (often refers to females only)
R0 = net reproductive output (lxbx)
> 1 pop increasing, = 1 pop stable, < 1 pop decreasing
Gives us a multiplier to see how much the population increases each generation
Gc= generation time
this is an approximation because not all births occur at once.
r = the populations intrinsic capacity for increase
each r is for a specific set of environmental conditions
environmental conditions may affect survival/reproduction
> 0 pop increasing, = 0 pop stable, < 0 pop decreasing
Temperature and moisture effects on r value for a wheat beetle (Store wheat in cool dry place).
Comparison of r value’s for two species of wheat beetle.
l beetle (Store wheat in cool dry place).tbt
t and x are age and w is age of last reproduction
Females begin breeding beetle (Store wheat in cool dry place).
Males protect harems
V beetle (Store wheat in cool dry place).x =
Residual reproductive value
= number of progeny that on average will be produced in the rest of an individuals lifetime
If the population is growing (not stable), then this value must be discounted because the value of one progeny is less in a larger population.
Reproductive value is important in the evolution of life-history traits because natural selection acts more strongly on age classes with high reproductive values (cancer in humans).
Predation has more of an effect if acting on individuals with high reproductive value.
Natality Rates beetle (Store wheat in cool dry place).
Rate of increase or decrease of the population
Populations of vole grown in the lab.
Age structure can differ strongly year to year in plant and animal species (dominant fish year classes).
Neither has an age structure representative of a stable age distribution.
At high levels of reproductive effort, a small increase in effort is more beneficial for big-bang reproduction than for repeated reproduction
Repeated reproduction may be an evolutionary response to uncertain survival from zygote to adult stages.