Animal Population Dynamics

8/13/2019 Animal Population Dynamics

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ANIMAL POPULATION DYNAMICS

The constituents that influence the rate of change in

the numbers of a particular species found in the

wild include such density-dependent factors.

Environmental aspects such as weather,

temperature, flooding, snowfall, all of which are

density-independent will also affect populationdynamics.


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FIVE BASIC COMPONENTS

Birth

Death

Gender Ratio

Age Structure

Dispersal


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A number of components affect a populations

birth rate:

The amount and quantity of food Age at first reproduction

The birth interval

The average number of young born per pregnancy


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BIRTHor NATALITY RATE

Is the total number of births per 1000 of apopulation each year.


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DEATH or MORTALITY RATE

Is defined as the number of animals thatdie per unit time divided by the number

of animals alive at the beginning of that

time period.


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GENDER RATIO

Is the proportion of males to

females within a population.


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AGE STRUCTURE

Percentage of the population at

each age level in a population.


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DISPERSAL

Is defined as the movement of an animal

from the location of its birth to a new area

where it lives and reproduces.


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The simplest (exponential) model assumes that the

resources necessary for population growth are unlimited.

Therefore, the population grows at an exponential rate,which is the maximum rate possible for that particular

species:

= rN (Eq.1)

where

-the change in numbers of animals within a

certain population per unit timerthe specific rate of change

Nnumber of animals within a certain population


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If Nois the no. of organisms attime zero, the no. of organisms

at any particular time, N can be

determined by integrating Eq.1over that particular time period:

N = Noexp(r) Noer


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Growth occurs in discrete intervals describedby the term .

(+)() = =

where N(+1) - population after (+1) no. in yearsNpopulation after years

rthe specific growth rate (net new organisms per

unit time)


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Example 1: Use the ff. data along with the exponential

model to determine the population of the predicted

eastern gray wolf in the state of Wisconsin in the year

2005. Compare that result with that obtained with the

geometric model.

Year 1975 1980 1990 1995 1996 1997 1998 1999

Number 8 22 45 83 99 148 180 200


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Solution:

N() = N(0)e0.123()= 8e0.123(30)

= 320 wolves


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For year 0 to year 1: 8 x = a

For year 1 to year 2: a x = b

For year 2 to year 3: b x = c

And so on until we get

year 4 to year 5: x = d


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8 x 5

= N(5)

where N(5) is the no. of

individuals 5 years later; and

is equal to 22. So

8 x 5= 22


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Solving for yields = 1.224

=

where is the year of calculation and 0is the firstyear for which data is available.


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YEAR NUMBER 0 8

5 22 1.224

15 45 1.122

20 83 1.124

21 99 1.127

22 148 1.142

23 180 1.145

24 200 1.144

Average: 1.147


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N(30) = N(24) x (1.1476)

= 455 individuals


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The population change can be represented

by the model:

= rN[

]

N() =

+()


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Example 2: Assume that the population of the greater

roadrunner in the Guadelope Desert was 200 per

hectare at the beginning of 1999. If the carryingcapacity, K, is 600 and r = 0.25 . year-1, what is the no.

of roadrunners one, five & ten years? What happens

when the no. of roadrunners equals K?

SOLUTION:

N(1) =

+()^(.)

= 234 roadrunners

N(5) = 381 roadrunners

N(10) = 515 roadrunners


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Numerous more complex models exist. These include

phenomena known as monotonic damping, damped oscillations,

limiting cycles, or chaotic dynamics. A number of these models

can also be used to describe plant population dynamics.

Much more complex models describe the interactions between

species by considering predator-prey relationships. These

models show how the interactions between two species result

in periodic behavior.


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The models use the following two differential equations to describe

the numbers of predators, K, and prey, P:

=

=

where a = growth rate of the prey

b = mortality parameter of the prey

c = growth rate of the predator

d = mortality parameter of the prey

These equations are often referred to as the LOTKA-VOLTERRA

MODEL.


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HUMAN POPULATION DYNAMICS

Human population dynamics also depend on birth, death,

gender ratio, age structure, and dispersal. In humans,

cultural factors play a significant role. In human populations,dispersalis referred to as immigrationand emigration.

The effect of cultural differences can be easily illustrated

using population pyramids. Population pyramids display theage by gender data of a community at one point in time.


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Population pyramids


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Assuming an exponential growth rate, the population can be

predicted using the equation:

P(t) = Po

where P(t) - the population at time, t

Po- population at time, 0

r - rate of growthttime

The growth rate can be determined as a function of the birth rate

(b), death rate (d), immigration rate (i), and emigration rate (m):

r = b - d + im

where the rates are all expressed as some value per unit time.


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Example 2: A population of humanoids on the island of

Huronth on the planet Szacak has a net birth rate (b) of 1.0

individuals/(individual x year) and a net death rate (d) of 0.9

individuals/(individual x year). Assume that the netimmigration rate is equal to the net emigration rate. How many

years are required for the population to double? If in year zero,

the population on the island is 85, what is the population 50

years later?Solution:

r = 1.00.9 =.

tdouble=

=

.

= 6.93 years

No= 85

t = 50 years

r = 0.1N50= No

= 85 . ()

= 12,615 humanoids


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TOTAL FERTILITY RATE

Is the number of children a woman will have over herentire lifetime.

Animal Population Dynamics

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