integrated lec 17 Flashcards
pop dynamics and their importance
Definition: Study of how and why population size (𝑁) changes over time (t)
Relevance:
Natural resource management: E.g., fish stocks, pest control.
Conservation: Monitoring endangered species (e.g., bats with white-nose syndrome).
Health: Tracking diseases (e.g., SARS-CoV-2, HIV).
Human population growth: Historical and modern challenges.
geometric growth (discrete-time) formula and example
N(t+1)=lambdaN(t)
lambda>1= growth
lambda<1=decline
e.g. stepwise growth observed in organisms with episodic reproduction
exponential growth formula and example
dN/dt=rN
r: intrinsic rate of increase (r>0=growth, r<0=decline)
e.g. smooth growth observed in continuously reproducing species
what does it mean if lambda=1 or r=0
pop remains constant
density-dependent regulation
-growth depends on pop size (N)
examples:
-Competition for resources.
-Disease spread.
-Predation
logistic growth model:
-dN/dt=rN(1- N/K)
-K: carrying capacity (max sustainable pop size)
-Produces an S-shaped curve (sigmoid)
density-independent regulation
Growth influenced by factors unrelated to population size.
Examples:
Natural disasters (fires, floods).
Climate events.
logistic growth model
Key features:
-Accounts for resource limitations.
-Growth slows as population approaches K due to competition.
Formula:
N(t)= K/ 1+((K-N0)/N0)e^-rt
Graph Interpretation:
-Low N0: Logistic growth starts with exponential growth, then slows as N–>K
-High N0>K: Pop overshoots K, then stabilizes
Strengths and limitations:
-Pros: simple, models intraspecific competition
-Cons: assume gradual approach to K; real pop may overshoot or oscillate
What is the difference between geometric and exponential growth models?
- Time Scale
Geometric Growth:
-Describes population growth in discrete time intervals (e.g., generations or specific time steps).
-Appropriate for organisms with distinct breeding seasons or generations (e.g., annual plants, insects with seasonal reproduction).
-Lambda is the finite rate of increase
growth rate= finite rate
Exponential Growth:
-Describes population growth in continuous time.
-Suitable for organisms with overlapping generations and continuous reproduction (e.g., bacteria, humans).
-r is the per capita growth rate
growth rate=intrinsic rate
How does carrying capacity (K) affect population growth in the logistic model?
- Limits pop size:
-K represents the upper limit for the population size due to resource constraints such as food, space, or other environmental factors.
-As N approaches K, pop growth slows down, eventually stopping when N=K - Regulates growth rate
-At small pop sizes (N<K), the term (1- N/K) is close to 1, and the pop grows exponentially
-As N increases (1- N/K) decreases, reducing the effective growth rate
-When N reaches K, (1- N/K)=0 and growth stops - Stabilizes the Population:
-K acts as a stabilizing force, creating a dynamic equilibrium where population size oscillates around K due to environmental fluctuations or other factors. - Population Overshoot:
-If the population temporarily exceeds K (due to delayed effects of resource depletion or other dynamics), it can result in a decline or crash, followed by stabilization around K.
What are examples of density-dependent factors affecting population dynamics?
Density-dependent factors
- Competition for Resources:
-Food shortages due to higher population densities.
-Space limitations for nesting or shelter.
-Water scarcity in crowded populations. - Predation:
-Predators are more likely to target prey in densely populated areas because prey is easier to find.
-Example: A wolf pack targeting dense deer populations. - Disease and Parasitism:
-Higher population density facilitates the spread of contagious diseases or parasites.
-Example: Influenza outbreaks in crowded human cities - Waste Accumulation:
-In dense populations, waste products can accumulate, leading to unsanitary conditions and increased mortality.
-Example: Ammonia build-up in dense fish populations in aquaculture tanks.
5.Territoriality and Aggression:
-Increased competition for territory can lead to aggression and reduced reproduction.
-Example: Songbirds defending limited nesting sites.
What are examples of density-independent factors affecting population dynamics?
These factors affect populations regardless of their density. They are often abiotic and involve environmental changes or catastrophic events.
Examples:
1. Natural Disasters:
Hurricanes, floods, earthquakes, and wildfires can destroy habitats and reduce populations irrespective of their density.
Example: A flood wiping out a population of mice, regardless of how many are present.
- Climate and Weather:
Extreme temperatures (heatwaves, cold snaps) or seasonal changes can affect survival.
Example: A sudden frost killing plants or insects.
- Human Activities:
Habitat destruction, pollution, or pesticide application affects populations without considering density.
Example: A pesticide spray killing both small and large populations of insects.
- Availability of Resources Independent of Density:
Drought or water scarcity affecting an area equally, regardless of population size.
Example: A prolonged drought reducing plant populations.
- Catastrophic Events:
Volcanic eruptions or tsunamis that impact all organisms in the affected area.
Example: A volcanic eruption eliminating all species in the vicinity.
What is population dynamics?
the study of how and why pop size size (N) changes over time (t)
why do we study pop dynamics
To manage natural resources, conserve species, track disease outbreaks, and understand human population growth
what does pop size (N) represent
the number of individuals in a pop
how is pop density calculated?
pop density= N/area
what is the formula for geometric growth
N(t)=N(0)λ^t, where λ is the finite rate of increase.
what is the formula for exponential growth
dN/dt=rN, where r is the intrinsic rate of increase
how are lambda and r related
lambda=e^r and r=ln(lambda)
what is carrying capacity(K)?
the max pop size that an environ can sustain
what is density-dependent regulation?
Population growth depends on population size (N), often involving competition, predation, or disease.
what is the logistic growth equation?
dN/dt= rN(1- N/K)
how does logistic growth differ from exponential growth?
logistic growth includes a “braking term” (1- N/K) to account for resource limitations
how is pop change modelled in discrete time
N(t+1)=N(t)-D+B-E+I
D=deaths
B=births
E=emigration
I=immigration
what does the per-capita growth rate (r) represent?
the instantaneous rate of pop growth per individual
how do you calculate doubling time t(d) for exponential growth
t(d)=ln(2)/r
Name a situation where exponential growth occurs.
Bacteria in a nutrient-rich medium (short-term).
When does logistic growth occur?
When a population grows initially but levels off as it approaches carrying capacity(K)
Why is exponential growth unrealistic long-term?
Resources are limited, and populations eventually encounter density-dependent constraints.
What happens if a population overshoots K?
Population size declines due to resource depletion.
Why does the logistic curve level off?
as N approaches K, the growth rate slows because resources become limited.
What determines K in the logistic model?
The environment’s resources and conditions
What is the key similarity between geometric and exponential growth models?
Both describe populations growing without resource limitations.
how is the logistic model used in conservation bio?
to predict pop recovery or decline and set sustainable harvesting limits
