Lecture 18

Question 1

possible ways to add more complexity or reality to exponential or growth models

Answer 1

• different forms of density dependence (allee effects)
• time lags
• incorporate species interactions (eg effects of competitors, predators, mutualists)

Question 2

per capita growth rate is fastest when… what is an exception to this?

Answer 2

population is near zero; sometimes more density may be beneficial

Question 3

what are Allee effects?

Answer 3

negative effects of low density, arising from social benefits such as mate finding, group living, group defence

Question 4

meerkats

Answer 4

cooperate to avoid predators and rear young, so their populations require a minimum population density to grow

Question 5

when Allee effects are in force

Answer 5

• populations may fluctuate between carrying capacity, K, and another, lower limit
• dropping below the lower limit goes to extinction
• very important in conservation

Question 6

age-structured populations

Answer 6

• exponential and logistic models of population growth treat all individuals in a population the same
• but in real populations, not all individuals have the same probability of giving birth or dying
• fecundity and survivorship depend on age
• how these depend on age varies among species; species have different life history strategies

Question 7

key components of a life history strategy include

Answer 7

lifespan, the timing of reproduction, number of offspring, and parental investment in offspring

Question 8

typical life history for many plant and animals

Answer 8

• start life at small size
• grow for a period without reproducing (for resource accumulation)
• when have enough resources, become mature, start spending resources on reproduction
• organisms show various lifestyles after sexual maturity
• some expend all resources at once, see spread them out
• need to consider age structure of population to better predict population trajectories

Question 9

elephants

Answer 9

low fecundity
long lifespan
late 1st reproduction
big investment in each individual offspring

Question 10

pika

Answer 10

high fecundity
medium lifespan
fast first reproduction (within 1st year of life)
1-13 babies per reproduction cycle

Question 11

salmon

Answer 11

very high fecundity
medium lifespan
late first reproduction
return to natal rivers at end of lives to have offspring then die right after
female can lay 1000s of eggs when she spawns

Question 12

variation in fecundity and survivorship with age is summarised by

Answer 12

life tables of age-specific rates

Question 13

life tables have important implications for

Answer 13

• evolution of life histories
• conservation of populations
• understanding the changing structure of human populations (human demography)

Question 14

age-sex pyramid

Answer 14

males left, females right, height of bar Indicates how many individuals there are of that population

Question 15

demographic transition undergone in Canada

Answer 15

pyramidal shape -> stable age structure with similar number at each age class

Question 16

which sex is usually only used in age structures?

Answer 16

females - these are assumed to invest the most time and energy into rearing offspring, and so limit the amount of children

Question 17

age-class intervals

Answer 17

• arbitrary units of time chosen to give a reasonable number of age classes for the organism in question
• for microbes, minutes to hours
• most insects, weeks
• most mammals and birds, years
• humans, typically 5 year intervals

Question 18

life tables

Answer 18

• data that summarise the life events that are statistically expected for the average individual of a specified age in a population
• age of death
• age and timing of reproduction
• for modelling, these are treated as constants
• usually consider females only

Question 19

age classes denoted by

Answer 19

subscript x

Question 20

lx =

Answer 20

probability of being alive at age x

Question 21

l0 =

Answer 21

1.0 by definition

Question 22

survivorship curve

Answer 22

graph of lx vs x

Question 23

lx necessarily declines with

Answer 23

x

Question 24

shape of lx curve

Answer 24

characteristic of species

Question 25

draw and describe types of survivorship curves

Answer 25

type II - if mortality is constant with age, you will get an exponential decline; usually graph lx curves as log plots, where type II is a straight line
type I - individuals survive really well until middle age
type III - really high mortality early in life, but if you make it into adulthood you have a high chance of surviving

Question 26

real shapes of survivorship curves + example diagram

Answer 26

more complex

Question 27

real human data example from Statistics Canada

Question 28

fecundity schedules

Answer 28

• mx (or bx) = number of daughters born to a female of age x during the interval x to x+1
• shape of mx curve is characteristic of species
• reproductive period usually preceded by resource-accumulation phase
• fecundity-survivorship trade-off = cost of reproduction

Question 29

net reproductive rate

Answer 29

• average (expected) number of daughters a female has in her lifetime = R0
• R0 = Σlxmx

Question 30

why does net reproductive at work?

Answer 30

Σmx would be the total number of daughters produced by a mother who doesn’t die earl; multiplying by lx discounts expected production by the probability that some mothers do die early

Question 31

R0 is like

Answer 31

λ, but in time units of one generation rather than one time interval

Question 32

in epidemiology, R0 is

Answer 32

the average number of secondary infections that a single infection gives rise to

Question 33

generation time, T

Answer 33

average age at which a female gives birth
T = Σxlxmx/R0
- this is a formula for weighted average. x is a female’s age; multiplying x by lxmx weights x by how many offspring are produced at that age; dividing the sum of the weighted x’s by the total lifetime production of daughters (R0) gives a weighted average that specified when a female gives birth, on average

Question 34

relationships among R0, λ, r

Answer 34

• these parameters indicate the factor by which a population changes during a discrete interval of time, but those intervals are different
  r = ln(R0)/T = ln(λ)

Question 35

how are growth rate and fitness related?

Answer 35

generally, organisms with higher growth rates have higher fitness

Question 36

why aren’t all plants annuals? why aren’t all mammals mice? why aren’t all lives short and fast?

Answer 36

constraints and trade-offs: reproduction is costly. longer pre-reproductive periods allow time to accumulate more resources

Question 37

plant life history category table

Question 38

example of obligate semelparity

Question 39

when does natural selection favour semelparity?

Answer 39

when reproductive output is increased by accumulating resources for longer, for example if:
- reproductive output depends strongly on size
- in plants, massive flower/fruit displays attract more beneficial animals (pollinators or seed dispersers)
- or massive seed crops satiate seed predator populations, allowing more seeds to go uneaten

Question 40

semelparous fish lay larger eggs, but only if

Answer 40

they grow large enough

Question 41

example of extremely synchronised semelparity

Answer 41

• bamboo
• long lived
• long reproductive period when growth of offspring is highly synchronised
• thought to satiate the bamboo seed predators so the predators can’t eat all of the offspring

Question 42

advantage of synchrony

Answer 42

infrequent pulses of reproduction = predator satiation tactic

Question 43

iteroparity plus local synchrony

Answer 43

masting
eg quercus douglasii

Question 44

K strategy vs r strategy

Question 45

ex

Answer 45

life expectancy: expected years of life left to an individual of age x

Question 46

vx

Answer 46

reproductive value - expected number of future daughters left to an individual of age x

Question 47

draw and label a graph for reproductive value in humans