lec 17 Flashcards
what is a population
collection of living things in an area
formula for pop density
N(pop size)/area
why is N(pop size) important
natural resource management
-size of fish stocks in ocean
-abundance of outbreaking insect pests in forests
conservation
-pop declines of species
health
-monitoring pop of viruses or bacteria in humans
Myotis lucifungus bats and white-nose
devastated bat population
malthus theory
human pop cant grow faster than resources produced
Paul Ehrlich
published “the population bomb”
argued that the explosive growth in the human pop would have catastrophic social and environ. consequences
what is the goal of most pop models
-predict the path of pop growth thru time
what are time steps in a pop model
use concept of limits and calc to ensure growth is smooth and best suited for species with cont. reproduction
E meaning
number who emigrate during one time step
I meaning
number who immigrate during one time step
birth and what are equiv
birth and immigration are equivalent (i.e. individuals added to pop)
death and what are equiv
death and emigration are equivalent (i.e. individuals removed from pop)
treat birth and death during one time step as ____ that are…
per-capita rates; fixed constants
lambda
multiplicative factor by which pop changes over time
if births exceed deaths..
pop grows
if deaths exceed births…
pop shrinks
relationship b/w lambda and r
ln(lambda)=r
dN/dt
slope of the growth curve at any point
what does a constant positive growth rate represent
produces a pop size that isnt constant but rather exploding in an exponential way
explain why species can’t stay as lambda greater or less than 1
lambda>1 births exceed deaths, no species can sustain that for a long period
lambda<1 deaths exceed births, no surviving species can maintain that due to going extinct
density-dependent regulation
growth depends on pop size
In such systems, factors that limit population size become more intense as the population density increases.
This means the population’s growth and survival are affected by how crowded the population becomes
e.g. competition for resources, predation
density-independent regulation
refers to factors that affect population size or growth regardless of the population’s density
density-independent factors do not intensify or diminish based on how crowded a population is
Instead, these factors act uniformly, impacting a population no matter its size.
e.g., natural disasters, weather
what happens if N gets too big
-pop growth stops
-reaches carrying capacity since pop size is too big
logistic braking term
models the simplest form of density dependence
at low density…
no braking
complete braking when…
N approaches K
logistic model produces…
s-curve (sigmoid)
when are logistic trajectories truly s-shaped?
only when starting from low numbers
at carrying capacity, slope is
0
pros of logistic model
simple(only 1 extra parameter, K)
-model of intraspecific competition for resources
cons of logistic model
too simple (specifies 1 kind of density dependence)
-likely to be non-linear, which overshoots K
