18/19 Flashcards
possible ways to add more complexity or reality to exponential or growth models
- different forms of density dependence (allee effects)
- time lags
- incorporate species interactions (eg effects of competitors, predators, mutualists)
per capita growth rate is fastest when… what is an exception to this?
population is near zero; sometimes more density may be beneficial
what are Allee effects?
negative effects of low density, arising from social benefits such as mate finding, group living, group defence
meerkats
cooperate to avoid predators and rear young, so their populations require a minimum population density to grow
when Allee effects are in force
- populations may fluctuate between carrying capacity, K, and another, lower limit
- dropping below the lower limit goes to extinction
- very important in conservation
age-structured populations
- 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
key components of a life history strategy include
lifespan, the timing of reproduction, number of offspring, and parental investment in offspring
typical life history for many plant and animals
- 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
elephants
low fecundity
long lifespan
late 1st reproduction
big investment in each individual offspring
pika
high fecundity
medium lifespan
fast first reproduction (within 1st year of life)
1-13 babies per reproduction cycle
salmon
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
variation in fecundity and survivorship with age is summarised by
life tables of age-specific rates
life tables have important implications for
- evolution of life histories
- conservation of populations
- understanding the changing structure of human populations (human demography)
age-sex pyramid
males left, females right, height of bar Indicates how many individuals there are of that population
demographic transition undergone in Canada
pyramidal shape -> stable age structure with similar number at each age class
which sex is usually only used in age structures?
females - these are assumed to invest the most time and energy into rearing offspring, and so limit the amount of children
age-class intervals
- 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
life tables
- 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
age classes denoted by
subscript x
lx =
probability of being alive at age x
l0 =
1.0 by definition
survivorship curve
graph of lx vs x
lx necessarily declines with
x
shape of lx curve
characteristic of species
draw and describe types of survivorship curves
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
real shapes of survivorship curves + example diagram
more complex
real human data example from Statistics Canada
fecundity schedules
- 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
net reproductive rate
- average (expected) number of daughters a female has in her lifetime = R0
- R0 = Σlxmx
why does net reproductive at work?
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
R0 is like
λ, but in time units of one generation rather than one time interval