BIO 262 Population Structure and Dynamics + Population Growth

Negative density dependence

PCGR is a negative function of N (i.e., PCGR decreases as N increases).

Sex ratio

males per female (♂/♀)

Primary sex ratio

sex ratio of all individuals at birth; may change overtime because of differential survival

Primary sex ratio example

In polygynous species, ♂ mortality is greater than ♀mortality. As population ages, sex ratio decreases.

Secondary sex ratio

sex ratio at reproductive maturity

Sex ratios tend towards

50:50

R.A. Fisher's argument for maintenance of 50:50 sex ratios

I. In diploid species, every organism has ♂ and ♀ parent that contribute equally to future generations.

II. If mutation changes sex ratio, the rarer sex becomes more valuable than the more common sex.

III. Since rarer sex is more valuable, selection favors rarer sex.Increased production of rare sex leads back to 50:50.

Fisher Complications

I. If one sex is more costly to produce per individual (larger, etc.),fewer of that sex will be produced. As a result, total cost of ♂production should equal total cost of ♀ production.

II. If ♂s and ♀s experience different mortality rates between birth and maturity, primary sex ratio should shift in order to produce 50:50secondary sex ratio at maturity

Fisher examples

A. Crocodiles

B. Atlantic silversides

C. Polygynous Anolis lizards

D. Polygynous wood rats

A. Crocodiles

sex of hatchlings determined by temperature of eggs

B. Atlantic silversides

I. Sex ratio controlled by both genetics and environment.

a. At low water temperatures, ♀s produced.

b. At high water temperatures, ♂s produced

II. If silversides are kept in only warm water, strong selective pressure for individuals capable of producing ♀s. Quickly restores50:50 sex ratio in the population

C. Polygynous Anolis lizards

I. Large offspring have higher fitness as ♂s. Small offspring have higher fitness as ♀s

II. Mothers in good condition (i.e., capable of producing large offspring) should produce ♂ offspring; mothers in poor condition (i.e.,can only produce small offspring) should produce ♀ offspring.

III. Also occurs in stressed rats and mice; does not occur in stressed deer

D. Polygynous wood rats

I. When food supply reduced to mothers, mothers did not nurse ♂offspring and pushed sex ratio from 1:1 to 0.5:1

When might larger ♀s be advantageous?

Larger mothers may be able to carry more eggs, raise better offspring

When might larger ♀s be advantageous? Examples

A. Seychelles Warblers

B. Parasitic wasp Lariophagus sp. (Charnov)

When might larger ♀s be advantageous?

A. Seychelles Warblers:

♀s in high-quality territories raise more ♀offspring; ♀s in low-quality territories raise more ♂ offspring.

When might larger ♀s be advantageous?

B. Parasitic wasp Lariophagus sp. (Charnov):

♀ wasps parasitize weevils that have bored into corn kernels. 10.16-10.17

I. Large weevil larvae (large resource for wasp larvae) bore large hole into corn kernel; small weevil larvae (small resource for wasp larvae) bore small hole into corn kernel.

II. So... hole size determines weevil size, which determines size of emerging wasp.

III. Eggs laid in corn kernels with large holes produce more ♀s; eggs laid in corn kernels with small holes produce more ♂s.

IV. How is it done?

a. In a haplodiploid species, ♀ wasp may be able to choose whether to fertilize the egg (producing ♀) or not (producing ♂)

b. Short answer... nobody knows

Age Structure

% of individuals in different age classes

Survivorship curves: Type I

Low initial mortality, with most mortality occurring at older ages (not common:humans, some large mammals and lizards)

Survivorship curves: Type II

Equal chance of dying at all ages(uncommon: characterizes most birds, lizards, some mammals).

Survivorship curves: Type III

High initial mortality, lower mortality in older organisms (most common: most invertebrates, plants, many fishes, etc.)

Cohort:

those individuals in the population born during a specific time interval (e.g., 1/1/1987 through 12/31/1987)

Lx:

% of individuals in a cohort surviving to age X (i.e., probability of surviving from birth to age 3).

Mx:

'fecundity,' the number of offspring produced by an individual of age X while at that age (a number, not a probability)

Net reproductive rate, R0:

The average number of offspring per female over the course of its lifetime, averaged across all ages.

Net reproductive rate, R0 equation

R0 = Σlxmx

If R0 > 1, population is _________; if R0 < 1, population is ___________

growing, decreasing

Generation time:

Average age of reproduction

Generation time simple calculation

- generation time = (α + ω)/2

- α = age at first reproduction

- ω = age at last reproduction

- so... if α=12 years and ω=52 years, then gen time = (12+52)/2 = 32

Generation time complex calculation

generation time = Σxlxmx /R0

Generation time complex calculation: Why add complexity?

Organisms may differ in likelihood of reaching different ages, or in # offspring produced at each age

Reproductive value, VA:

the number of offspring expected to be produced by an organism of age A over the rest of her life

Reproductive value, VA: Why does VA initially increase over time?

Because newborn organisms may die before reproducing, an organism just entering reproductive maturity is more valuable than an infant (VA takes into account both mortality and offspring production)

Reproductive value, VA: Applications to conservation and resource management

I. conservation of organisms with type III survivorship curves(e.g., sea turtles) should focus on mature females rather than infants.

II. Both young and very old individuals can be culled (removed) from the population without harming it.

Population:

individuals of a given species in a given place

λ =

Geometric rate of increase, the ratio of population size at two points in time

- (i.e, Nt+1/Nt)

R0 will not equal λ if species has overlapping generations and/or continuous ___________

reproduction

T =

Average generation time per population

r =

Intrinsic rate of increase for a population (r = per capita births - per capita deaths) (r = lnR0/T)

Geometric population growth equation

Nt = N0 λ^t

Nt =

number of individuals at time t

N0 =

number of individuals at t = 0 (the starting point)

Geometric population growth models

population growth for organisms that experience pulsed reproduction

- (i.e., insects that produce a single generation per year, annual plants) (note: in order for this to be the appropriate model, generations cannot overlap)

Exponential population growth

Used to model continuous population growth in an unlimited environment

Exponential population growth equation

Nt = N0e^rt

Exponential growth expressed as a differential equation

dN/dt = rN = the rate of change in N with t

Logistic population growth equation

dN/dt = rN[1-(N/K)]

Characteristics of the logistic population growth equation

A. If N is small, then N/K ≈ 0 and 'drops out'.dN/dt = rN(1-0) = rN(1) = rN = exponential growth

B. If N is large, then N/K ≈ 1dN/dt = rN(1-1) = rN(0) = 0 = no growth

C. r, the intrinsic rate of increase, is highest when N is lowest and declines as a linear function of N... reaches zero when N=K.

D. The maximum value (i.e., slope) of dN/dt is at K/2. 11.20I. Optimum yield (AKA maximum sustained yield, 'MSY')

a. N at which the population growth rate, dN/dt, is highest.

b. Population size that should be maintained for maximum harvest rate.

When is the logistic growth equation appropriate?

A. Best fit with small, rapidly-reproducing organisms with uniform populations (i.e.,individuals are very similar to each other).

B. In larger organisms, population age structure creates oscillations. Individual large organisms are also more variable (i.e., population is less uniform)

Logistic growth equation with time lag

dN/dt = rNt[1-{Nt-L/K}]

Per capita growth rate (PCGR) equation

(dN/dt)/N = PCGR

If per capita growth rate (PCGR) is

A. Negatively density-dependent, PCGR decreases as N increases

B. Positively density dependent, PCGR increases as N increases

C. Density-independent, PCGR unrelated to N

Negative density dependence: How might this happen?

I. Competition for resources

II. Competition for territories

III. Increased crowding increases disease prevalence

Positive density dependence

PCGR is a positive function of N

Positive density dependence: How might this happen?

I. More mating opportunities if more individuals around

II. Large groups defend against predators and get resources more efficiently

Density independence

PCGR is not a function of N

Density independence: How might this happen?

Weather, catastrophes (volcanoes, etc)

Density independence: Exponential growth example

dN/dt = rN; PCGR = (dN/dt)/N = r

I. r is not a function of N

Negative density dependence: Logistic growth examples

A. dN/dt = rN(1-(N/K))

B. PCGR = (dN/dt)/N = r(1-(N/K))