Population Growth



Turkey Population S’math

Integrated Science Meleagris gallopavo

Populations have the biotic potential to reproduce and thus increase at an exponential rate over time. This is because as a population grows, not only are there more individuals added to the population, but more and more individuals are adding to the population. Of course, biotic potential is never reached; factors such as competition between species, mortality and resource availability act to limit the growth of, and ultimately, size of populations.

Merriam's Turkey is a wild bird native throughout the Western United States. Their habitat is primarily pine forest at elevations from 3,500’ to 10,000’. By 1935, Merriam’s turkeys were extinct in Wyoming. A decision was made to attempt to re-establish a population, and a small number of turkeys were introduced to a mountainous part of the state. The Wyoming Game and Fish Department estimated the population of Merriam's turkey after five years at 2,500 birds. The population has continued to thrive, so much that they now support a large turkey hunting industry.

Merriam’s hens lay two eggs every three days or so until a clutch of 10 to 13 is produced. After about 28 days of incubation, the chicks meet the world. Within a week the chicks start flying and roost in trees thereafter. Hens and their brood, often joined by like combos, stay together until the next breeding season.

Wyoming Fish and Game Department. Turkey Holiday Puts Spotlight on Wyoming’s Bright Turkey History. 11/17/2006. 10/13/2008.

A. Quantitatively predict the growth of a population over five years that originated with 46 introduced turkeys. Base your predictions on the following assumptions:

• An equal number of males and females were introduced/born

• All females hatched a clutch of 10 eggs each year

• No immigration, emigration, or disease affects the population size

Record your results in a data table (Table A).

B. No immigration, emigration, or disease affecting the population size? That's not terribly realistic! To increase the accuracy of your predictions calculate population size reflecting the following additional assumptions:

• Turkeys are sexually mature after one year

• All introduced turkeys were 1 year old and thus sexually mature

• All turkeys died their sixth year of life, after hatching fifth clutch

To complete the calculations, use the steps outlined on the back of this page. Complete Table B, checking your figures with your lab partner’s (and the teacher’s) as you go.

Line 1. Begin with the introduced 46 turkeys.

1a. Subtract from the beginning population the members that died (5+ years old).

1b. Also subtract those too young to reproduce (last years hatch, from row 3).

1c. This equals the breeding population.

Line 2. Divide the breeding population by two to determine the number of breeding pairs (row 1c divided by 2)

Line 3. Each breeding pair produces, on average, 10 eggs per clutch, so multiply the number of breeding pairs by 10, to determine the number of chicks hatched (row 2, times 10)

3a. To the number of chicks hatched, add back in the breeding population (from 1c),

3b. and add last years hatch, now old enough to breed (from 1b)

Line 4. Sum to find the end-of-season total population.

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• Graph the results in Line 4, using population increments of 2000.

• Analyze the turkey growth pattern in both Table A and Table/Graph B. What accounts for the differences in growth rate?

Turkey Growth

Follow Up

1. Were all the assumptions in the model equally valid? Discuss.

2. Are Merriam’s turkey populations exploding in size all over the western US, as your data suggests? What factors might be limiting the biotic potential of the Merriman's turkey?

3. Propose two ways the Wyoming Game &Fish Department might have made their estimate of a turkey population size of 2,500.

4. Rabbits are even more fecund that these turkeys, with the potential to double their population size every month. From one breeding pair, what would the potential rabbit population size after 6 years? (hint: since growth is exponential, use an exponent!)

5. Another way to plot exponential growth is to employ an exponential, rather than linear, scale on the Y axis of the graph. Graph your data in Table A using an exponential scale. How does using this scale change the appearance of the graphed line?

TABLE B

| |Generation 1 |2 |3 |4 |5 |6 |

|1) Start population (from line | | | | | | |

|4) |46 |276 |506 | | | |

| a) minus 5 yr olds |0 |0 |0 |0 |-46 |-230 |

| b) minus last years |-0 |-230 |- |- |- |- |

|hatch (from line | | | | | | |

|3) | | | | | | |

| c) equals breeding |=46 |= |= |= |= |= |

|population | | | | | | |

|2) Breeding pairs |23 | | | | | |

|(line 1c/2) | | | | | | |

|3) chicks hatched |=230 |= |= |= |= |= |

|(line 2 x 10) | | | | | | |

|plus breeding population (from |+46 |+ |+ |+ |+ |+ |

|line 1c) | | | | | | |

|plus last years |+0 |+ |+ |+ |+ |+ |

|hatch (line 1b) | | | | | | |

|4) New population |= 276 |=506 |= |= |= |= |

|(verify each gen.) | | | | | | |

TABLE B

| |Generation 1 |2 |3 |4 |5 |6 |

|1) Start population (from line | | | | | | |

|4) |46 |276 |506 | | | |

| a) minus 5 yr olds |0 |0 |0 |0 |-46 |-230 |

| b) minus last years |-0 |-230 |- |- |- |- |

|hatch (from line | | | | | | |

|3) | | | | | | |

| c) equals breeding |=46 |= |= |= |= |= |

|population | | | | | | |

|2) Breeding pairs |23 | | | | | |

|(line 1c/2) | | | | | | |

|3) chicks hatched |=230 |= |= |= |= |= |

|(line 2 x 10) | | | | | | |

|plus breeding population (from |+46 |+ |+ |+ |+ |+ |

|line 1c) | | | | | | |

|plus last years |+0 |+ |+ |+ |+ |+ |

|hatch (line 1b) | | | | | | |

|4) New population |= 276 |=506 |= |= |= |= |

|(verify each gen.) | | | | | | |

Teacher ref

ADD G = rN calc for one of the generations (follow up?)



• How many more turkeys would be added to the population in year 7?

Use: G = rN, Where G = the number of offspring

r = rate of increase (slope between gen. 5 & 6)

N = Population size (gen 6)

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