Consider an ecological network consisting of three interconnected habitats (A B C A). Ecologists want to model the occupancy dynamics of a particular species "Species" across these habitats over time using a discrete time discrete state stochastic process. State Space: State 0: Species X is absent from all habitats. State 1: Species X is present in Habitat A State 2 : Species X is present in Habitat B. State 3: Species X is present in Habitat C. State 4: Species X is present in Habitats A&B State 5: Species X is present in Habitats A&C. State 6: Species X is present in Habitats B&C. State 7: Species X is present in All Habitats. Transition Probabilities: Rule 1: The probability of colonizing an adjacent habitat is 0.2. Rule 2: The probability of extinction from a habitat is 0.15. Rule 3: The probability of recolonization of a random habitat is 0.1 A) Draw a schematic diagram of the Markov Process illustrating states and transitions. Define the transition rate matrix forthis discrete time discrete

BIOLOGY:CONCEPTS+APPL.(LOOSELEAF)
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Chapter41: Community Ecology
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Consider an ecological network consisting of three interconnected habitats (A BCA). Ecologists want to model the
occupancy dynamics of a particular species "Species" across these habitats over time using a discrete time discrete state
stochastic process. State Space: State 0: Species X is absent from all habitats. State 1: Species X is present in Habitat A State 2
: Species X is present in Habitat B. State 3: Species X is present in Habitat C. State 4: Species X is present in Habitats A&B
State 5: Species X is present in Habitats A&C. State 6: Species X is present in Habitats B&C. State 7: Species X is present in
All Habitats. Transition Probabilities: Rule 1: The probability of colonizing an adjacent habitat is 0.2. Rule 2: The probability
of extinction from a habitat is 0.15. Rule 3: The probability of recolonization of a random habitat is 0.1 A) Draw a schematic
diagram of the Markov Process illustrating states and transitions. Define the transition rate matrix forthis discrete time discrete
state stochastic process. Here is a sample of what diagrams of a Markov Process look likefor reference (attached picture). B)
Suppose that species presents an important ecosystem service. If as a scientist you can either support recolonization (upping
the probability to 0.2) or reducing extinction probability to 0.1 what would be a better conservation strategy? strategy?
0.3 A
0.8
ÿ
0.4
0.3
0.3
0.1
с
0.1
B
0.5
0.2
Transcribed Image Text:Consider an ecological network consisting of three interconnected habitats (A BCA). Ecologists want to model the occupancy dynamics of a particular species "Species" across these habitats over time using a discrete time discrete state stochastic process. State Space: State 0: Species X is absent from all habitats. State 1: Species X is present in Habitat A State 2 : Species X is present in Habitat B. State 3: Species X is present in Habitat C. State 4: Species X is present in Habitats A&B State 5: Species X is present in Habitats A&C. State 6: Species X is present in Habitats B&C. State 7: Species X is present in All Habitats. Transition Probabilities: Rule 1: The probability of colonizing an adjacent habitat is 0.2. Rule 2: The probability of extinction from a habitat is 0.15. Rule 3: The probability of recolonization of a random habitat is 0.1 A) Draw a schematic diagram of the Markov Process illustrating states and transitions. Define the transition rate matrix forthis discrete time discrete state stochastic process. Here is a sample of what diagrams of a Markov Process look likefor reference (attached picture). B) Suppose that species presents an important ecosystem service. If as a scientist you can either support recolonization (upping the probability to 0.2) or reducing extinction probability to 0.1 what would be a better conservation strategy? strategy? 0.3 A 0.8 ÿ 0.4 0.3 0.3 0.1 с 0.1 B 0.5 0.2
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