Population Ecology Homework: Solving for N After Year One

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SUMMARY

The discussion centers on calculating the population size (N) of Kolea birds over multiple years after their introduction to a new habitat. The intrinsic growth rate (r) is established at 1.8 per year, with a carrying capacity (K) of 2,000 birds for similar islands. Participants are tasked with creating a table that includes parameters such as logistical correction and per capita growth rate. The primary challenge identified is determining the population size for subsequent years, particularly year two, which hinges on understanding the carrying capacity (K).

PREREQUISITES
  • Understanding of population ecology concepts, specifically intrinsic growth rate and carrying capacity.
  • Familiarity with logistic growth models and their mathematical applications.
  • Ability to perform calculations involving population dynamics over time.
  • Knowledge of ecological terms such as territoriality and its impact on population size.
NEXT STEPS
  • Study the logistic growth model in detail, focusing on the equation N(t+1) = N(t) + rN(t)(K-N(t))/K.
  • Research the implications of carrying capacity on population sustainability in ecology.
  • Explore case studies of Kolea birds or similar species to understand real-world applications of these concepts.
  • Learn about population dynamics simulations using software tools like R or Python for ecological modeling.
USEFUL FOR

Ecology students, wildlife biologists, and researchers interested in population dynamics and the effects of environmental factors on species growth.

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Homework Statement



A flock of 10 Kolea birds going back to its mating grounds in Alaska from Hawaii gets blown off course and lands on a small island in the Aleutian (with no other Kolea birds) that is 25 km2 and has tundra habitat. The birds are known to have an intrinsic growth rate of 1.8 per year. Islands of similar size and climate have a carrying capacity of 2,000 Kolea birds, as the birds do have some territoriality. Make a table with the following parameters assuming that these birds have founded a new population will return here year after year.:

- Population Size (N)
- Intrinsic Growth Rate (r)
- Logistical Correction (\frac{K-N}{K})
- Per Capita Growth Rate (r\frac{K-N}{K})
- Population Growth Rate (rN\frac{K-N}{K})

Homework Equations



Given above in parameters

The Attempt at a Solution



I don't have any issues plugging in values to fill out the first year, but I don't know how one determines the population size (N) of the following years. In this case, I'm stuck at year two and have no idea what the population should be.
 
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Depends on what "K" is, I suspect it's the carrying capacity.
 

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