Population dynamics and models Flashcards
what are stochastic models?
represent the inherent randomness and uncertainty that drive ecological systems. they incorporate the element of chance and account for the unpredictable fluctuations and variability in the natural world. shows a range of possible outcomes. scatter plot instead of smooth graph.
important in capturing population dynamics/probability distribution, understanding species persistence, predicting disease outbreak patters, and exploring climate change impacts
ex: predicting how a forest fire might spread depending on wind direction and fuel availability
what are stochastic models?
represent a more predictable picture of ecological systems and predict one exact outcome for a given set of conditions. they could predict the precise trajectory of both populations over time and provide a smooth and predictable graph.
important for providing baseline predictions, simplifying complex systems, and as education tools
ex: simulating how a deer population grows with a fixed food supply and birth rate.
intrinsic rate of increase “r”
the personal growth rate of an individual within a population that tells us how quickly (on average) an individual contributes to a population’s growth. measured per unit of time (like a year)
usually expressed as births - deaths per individual per time unit
ex. like the engine’s power in a car – higher r, faster population grows (plus other resources/conditions)
finite rate of increase “lambda”
the population growth factor/finite rate of increase over a specific time interval that tells us how much bigger the population will be at the end vs the beginning of that interval. (ex. two consecutive time intervals year 1 and year 2).
dimensionless numbers, so no specific units, it is more like a multiplier.
ex. cars’ actual speed on a specific road. even with a powerful engine, other factors (environmental limitations) can slow down the car (aka population growth)
r vs lambda
r focuses on continuous, per capita rate, lambda focuses on overall population growth in discrete time steps.
they are related. r is the natural log of lambda.
predict future pop size if growth is continuous - r
predict pop size if growth is discrete - lambda
equation for exponential growth
differential form (good for comparing with logistic):
dN/dt = rN
integrated form (solution to differential form):
Nt = e^rtN0
deterministic vs stochastic models
deterministic models offer simpler interpretations of long-term trends but can miss real-world fluctuations and uncertainty.
stochastic models embrace the real-world randomness of populations, providing a more nuanced understanding of short-term dynamics, extinction risks, and impacts of unpredictable events.
fundamental equation
ΔN = B-D + I -E
N is number of individuals/pop size
closed populations
fixed: no new members are immigrating or emigrating from group
open populations
not fixed: account for immigration and emigration
discrete model
model populations with non-overlapping generations that reproduce in certain periods of time (ex. seasons)
continuous model
model populations with overlapping generations and year-round reproduction
exponential growth
occurs when the per capita rate of increase stays constant regardless of population size, causing a population to grow faster and faster as it gets larger.
seen in nature most often when organisms enter novel habitats with abundant resources, such as invasive species or introduced species.
all populations tend to exponential growth, but limiting factors reduce it
a pop will only grow exponentially when the ecosystem has an unlimited supply of resources. in these conditions, only limit is biotic potential or reproductive capacity of individuals in pop
logistic growth
as a population gets closer to carrying capacity (K), the growth rate will slow down - more accurate for most populations.
if N is greater than K and resources can accommodate for, the growth rate will slow
equation: dN/dT = rN (1-N/K)
density-independent growth
growth rates not regulated by the density of a population
density-independent factors are abiotic (weather, natural disasters)
