Espm 114 Lec 12

Front 1

Limitations to exponential growth model and logistic growth model b/c of close populations. In the next few flash cards name the four limitations. What is the first Limitations

Back 1

**comes from the Bay Checkerspot Butterfly

****notice that population went extinct and then reestablish again in a
close population

*• Problem for close populations model b/c once your population crash it
doesn’t come back according to the population model (you need to have some
kind of immigration)

Front 2

Limitation 2:

Back 2

Huffaker’s Experiment (1958)
Patchy landscape w/ 2 mite species: 1 prey and 1 predator
**when you have well-connected habitats they end up being unstable from a
predator and prey stand points b/c predator (and sometimes prey) are
driven to extinction.

**

Front 3

If you added a spatially subdivided habitats (allowing prey species to
float/move to diff. habitats)
--system is different
--but same amount of food
What is the result?

Back 3

**Result: Spatial heterogeneity allowed for coexistence of predator and
prey populations
--fluantuations

Front 4

Limitation 3

Back 4

some populations have d>b

***long-term persistence of some local populations depends on
immigration known as Sink population = A breeding group that does not
produce enough offspring to maintain itself in coming years without
immigrants from other populations
***closed population models inadequate for describing maintenance of sinks

Front 5

SINK POPULATIONS

Back 5

• Low reproductive success and high mortality (births < deaths)
• Population receives immigrants from other populations (immigration >
emigration)
• Population would face extinction if absence of dispersal coming in
• Sink population is often found on the PERIPHERY (boundary) OF a species
RANGE particular IN HABITAT QUALITY is NOT AS GOOD

Front 6

SOURCE POPULATIONS

Back 6

• High reproductive success and low mortality (births > death)
• Excess individuals emigrate to adjacent areas (emigration > immigration)
• Population would exceed carrying capacity in the absence of dispersal
• Often in the core of a species’ range in areas w/ optimal habitat quality
• 12:15 lecture 14

Front 7

Limitation 4: closed population models do not refects...

Back 7

the increasingly fragmented nature of Earth's habitats

Front 8

Summary what are the 4 limitations of closed population models

Back 8

1. local population extinctions and recolonizations
2. Unstable predator-prey cycles
3. Sources and Sinks
4. Increasing habitat fragmentation

Front 9

Solution to these limitations

Back 9

Include space in our population model and look explicitly at immigration rate and emigration rate

Front 10

[Therefore that's what's Metasis comes from]

META comes from the Greek word

Back 10

(meta) meaing "beyong" or after

**addressing some of these problems that weren't address by close population models

Front 11

Metapopulations =

Back 11

a population of populations, coined by levins (1970)

Front 12

What makes it a metapopulation?

Back 12

**local breeding populations in relatively discrete habitat patches surrouned by an unsitable matrix
------matrix = Where an individual might be able to disperse through, but couldn't breed

**Limited dispersal necessary for recolonization

**Dynamics of local populations are asynchronous (independent)

---- meaning that if one population is doing really bad that doesn't mean that the other population is doing bad b/c you might have local factor in each patch that are diff.

Front 13

There are three types of Metapopulations Models (discussed in lecture) what are they?

Back 13

1. Linked closed-populaation models

2. Spatially implicit patch occupancy models

3. spacially realistic patch occupancy models

Front 14

[linked closed-population models] what is included in this model

Back 14

**Models abundance (N) of all local populations
--link a bunch of population models we can monitor through time

**Complex and data intensive

**Local populations have density-dependent growth

Front 15

Why is this model difficult and didn't fully describe the population

Back 15

**Complex and data-intensive: must estimate b, d, i, e for each local population

**not enough data to accurately describes these parmeters (d, b, etc)

Front 16

(2) spatially implicit patch occupancy models

Back 16

We should think about the patches instead and lets look at how patch occupancy might changepopulation

**---instead of modeling living and dying individuals we should measure local populations in these patches and see how the occupied patches change over time. - This is know as spatially implicit it’s a patch occupancy models b/c were looking at patches not an individual animal.

**this model is simple and not data-intensive its an example of Levein's model

Front 17

Spatially implicit means

Back 17

Spatially implicit means were just assuming all of the patches are the same size, shapes and there’s and infinite number of them.

Front 18

Occupied patches (P) is also know as

Back 18

occupancy

Front 19

What is the difference b/c individuals-based models and Patch occupancy models? start w/ individual-based models

Level of interest:
Measurement units:
What drives changes in the system:

Back 19

Level of interest: individual

measurement unts: Abundace (N)

What drives changes in the system: Births, immigration, deaths, and emigration

Front 20

Patch occupancy models:
Level of interest:
Measurement units:
What drives changes in the system:

Back 20

Level of interest: patch (local population)

Measurement units: Proportion of occupied patches (P)

What drives changes in the system: Patch colonizations, and Patch extinctions

Front 21

[Levin's patch occupancy modell]

Back 21

proportion of occupied patches (P) is modeled over time as a function of colonization and extinction rates

dP/dt = cP(1-P) - eP

dP/dt = change in patches occupied over time
c = probability of colonization
e = probability of extinction
cP(1-P) = colonization rate

Front 22

What are the limitations to this model?

Back 22

**This model is very simple, so were not taken any into account about patch size, how connected the patches are.
**also this is a deterministic model
---run this model ten or a thousand times u'll just get the same answer every time and we know that nature is not like that there's a lot of variabilities.

**Spatially realistic patch occupancy models tries to address these things

Front 23

3. Spatially realistic patch occupancy models

Back 23

**models proportion occupied patches (P)

**incorporate spatial structure of a finite patch network (only a limited number of patches)

**moderately data-intensive

Front 24

Give an example of Spatially realistic patch occupancy models discussed in class

Back 24

Incidence function model (IFM), Hanski

Front 25

What are the two ideas of IFM?

Back 25

1. Patch colonization probability is positively related to CONNECTIVITY

****connectivity how closely related are the patches. If a site is more connected more likely to recieve colonist.

2. Patch EXTINCTION PROBABILITY is negatively related to AREA

**How big the pathc is
----the bigger the patches --> bigger population more individuals tougher to drive to extinctions

Front 26

Small isolated patch ____

Back 26

increase probablity
decrease colonization

Front 27

Large well-connected patch ____

Back 27

decrease extinction probability

increase colonization probability

Front 28

Connectivity is a function of _______

Back 28

how close the focal patch is to other patches and how large the neighboring patches are

Front 29

How can you use metapopulation models to make predictions about persistence?

Back 29

Do some stochiastic stimulations and run the model a number of times and see what happen as the population changes w/ time

Procedure for this:

*Caculate area and connectivity for all patches

*Set initial occupancy
--data collected in the field

*Calculate COLONIZATION and EXTINCTIONs probabilities.
--base on big they are and how connected they are

**once you collect the probabilites you can stimulate
the population through time
by assign stochastic colonizations and extinctions to patches (using a random number generator)

**Re-calculate connectivity

**Simulate again...
--
**Re- calculate connectivity

**Simulate again...

Front 30

Persistenc =

Back 30

probability that the metaopulation persists (does not go extinct) over a given time scale

Front 31

local extinction:

Back 31

Extinction of an individual patch (local population)

Front 32

Regional extinction:

Back 32

Extinction the entire metapopulation (all local populaations)

Front 33

Colonization potential

Back 33

expected contribution a
patch makes in colonizing other patches

**Large, well-connected patches = high colonization
potential

**Relatively few key patches may
be responsible for the
persistence of the
metapopulation

Front 34

What are two examples for this model?

Back 34

CA Black Rails
American Pika (only lives in cold mountainous region)

Front 35

What factors cause local extinctions and colonizations?

Back 35

*West Nile virus
*Weather
*Competitors
*Irrigation water management
*Grazing
*Habitat quality

Front 36

What is the result of driving species to extinction?

Back 36

Area and isolation appear to drive extinction and colonization rates

Front 37

AS expected:
EXTINCTION probability _____ as sites became larger

Colonization probility ____ as sites became more isolated

Extintion probility _____ as sites became more isolated

Back 37

Decrease
decrease
increase

Front 38

What factors cause local extinctions and colonizations?

Back 38

*West Nile virus
*Weather
*Competitors
*Irrigation water management
*Grazing
*Habitat quality

Front 39

What is the result of driving species to extinction?

Back 39

Area and isolation appear to drive extinction and colonization rates

Front 40

AS expected:
EXTINCTION probability _____ as sites became larger

Colonization probility ____ as sites became more isolated

Extintion probility _____ as sites became more isolated

Back 40

Decrease
decrease
increase

Front 41

small Area and isolation drive

Back 41

extinction and colonization rates down

Front 42

What is the "rescue effect"?

Back 42

**patches that are well-connected will have a high immigration rate, even when they are already occupied

**Extra immigrants can reduce the chances of an extinction event or "rescue" a local populaion that has recently gone locally extinct

Front 43

[effect of fencing on souces vs. sinks] Describe a graph for each
1. Source population
2.. Sink populataion

Back 43

*source population: rapid increase followed by crash

**Sink population: steady decline towards extinction