Question

Question 2. Consider the following figure representing the theoretical relationships between patch area (size) and isolation (distance from one another) and the equilibrium proportion of occupied habitat patches in a metapopulation: 0.25 0.20 0.15 0.10 0.05 0.2 0.4 0.6 0.8 1.0 Given the metapopulation equation (dP/dt- cP1-P eP), at equilibrium, what is the predicted change in patch occupancy from one year to the next for a metapopulation with large patches located relatively far from one another? Show your work.

Just one question please answer ASAP!! Please explain and I will rate :) thank you!!!!

Answer 1

                                 DEFINITATION OF METAPOPULATION

It persist due to the balance between extinction and colonization of local populations. Each population in a patch has its own local dynamics, which are not dependent on the state of other patches as in structured populations, nor on immigration from other patches as sink-populations do.

DIFFERENT PATCHES INCLUDES-

1) continuous populations with approximately instantaneous immigration among its sub-populations

2) structured populations, with sub-populations, whose dynamics depend on the     others in the landscape

3) metapopulations whose populations receive some immigrants

4) isolated populations too far apart for effective immigration.

                                       EXPLAINATION

In order to focus our attention on migration we will focus only on the presence of absence of the species and ignore other aspects of population growth. Instead of keeping track of the number of individuals within each patch we will be concerned only with the proportion of occupied patches, P, which can vary from zero to 1.

1. The proportion of occupied patches will change by only two processes. The proportion of occupied patches will increase through colonization decrease through extinctions. So, € dP dt = Colonization rate ? Extinction rate Already we can see that the system will be at equilibrium when colonizations exactly balance extinctions

We will start by assuming that there are a large number of patches which are identical. Each patch has an equal probability of going extinct in a particular time interval, and each occupied patch is equally likely to be a source of colonists for unoccupied patches. The simplest model assumes no spatial structuring of the landscape and no variation in the size or quality of the habitat patches.

The number of new colonizations will depend on the colonization rate, the proportion of occupied patches that can serve as a source of colonists, and the proportion of unoccupied patches. There must be a source of colonists (probability =P) AND a colonization must occur (probability = c) AND there must be an empty patch to colonize (probability=(1-P)).

Events are independent, then we multiply those probabilities. That means that colonizations will occur at a rate cP(1-P). Extinctions will occur at a rate eP.

This the extinction rate per patch (e) times the probability that a patch is initially occupied (P). Puttingthat all together we get: € dP dt = cP(1? P)? eP

In equilibrium, we set dP/dt=0 and get: € cP(1? P) = eP € (1? P) = e c so the equilibrium is: € P ˆ =1? e c eq.6.2 At equilibrium, some of the patches will be occupied ( € P ˆ > 0) as long as the colonization rate is greater than the extinction rate.

DISTANCE BETWEEN PATCHES AND SIZE OF THE PATCH , DOES IT REALLY MATTERS-

1.The simple metapopulation model did not do a good job of predicting the patch occupancy of thE butterflies.

2.The population surveys show more populations going extinct each year than are being colonized, and therefore predicts that the whole metapopulation should BE collapsed.

3. Although the occupancy rate is declining, there is still a high frequency of occupied patches

4.When our observations don’t match the model predictions, it usually means that one or more of the model assumptions were violated during metapopulation.