Increasing Reality

• Modeling Improvements– Linking migration and local extinction– Accounting for habitat destruction

• Conceptual Improvements– Continuous rather than categorical population

structure

• Linking to landscape ecology• Empirical studies

Modeling Improvements (Hess 1996)

• Assumption 1: colonization and extinction are assumed independent by Levins, but are both likely linked to connectivity– Corridors could bring immigrants as well as pathogens,

predators, etc that increases extinction

– Modeling this adjustment shows that metapopulation extinction increases if negative effects of connectivity increase faster than positive effects

Fixing Assumption 1

• r(c) is recolonization rate as function of connectivity– Substitute r for c in original formula so c can indicate function of connectivity

• x(c) is local extinction rate as function of connectivity

ePPcPdtdP )1(/

PcxPPcrdtdP )()1()(/

c

eP 1ˆ

)(

)(1ˆ

cr

cxP Now, r(c) > x(c) for nonzero

equilibrium (metapopulation not going extinct)

Focus Now Shifts to Effects of Connectivity on Extinction and Colonization

The relationship of extinction and colonization with connectivity is key to understanding if the metapopulation will survive or go extinct.

Assumption 2

• Simple model assumes that a patch is immediately available for recolonization after deme goes extinct there, but often extinction occurs because habitat is destroyed and recolonization cannot occur until patch regenerates.

Fixing Assumption 2

• Proportion of patches available for recolonization is not 1-p, but h-p, where h is fraction of total patches that are suitable (regenerated)

• Local extinction is now a function of normal stochastic events (demographic and environmental) PLUS patch destruction

c

dehP

)(ˆ (where d = extinction

rate due to patch destruction)c

eP 1ˆ

Focus Now Shifts to Relative Importance of

Stochastic Events vs Habitat Loss to Extinction

Note, in Levin’s terminology, m=c and x=e.

Removing risk of extinction to habitat destruction is critical, but eliminating stochastic events that cause extinction does little

Multi-species response to habitat Destruction

• Liu et al. 2007

• Model metapopulation dynamics of a plant community looking at how instantaneous versus constant habitat destruction affects colonization and extinction of patches and competitive interactions among an assemblage of species

Which means that the proportion of habitat occupied by species I is a function of colonization, mortality, competitive effects of other species, and a direction reduction in abundance due to habitat destruction

• Survival is affected by competitive ability (dominants go extinct because of poor colonization ability) and is initially greater in response to continuous destruction (top), but in long term complete extinction is predicted in response to continuous

• Intermediately competitive species (6, 7, 8, 9) end up surviving instantaneous disturbance)

• Metapopulation dynamics determine community composition

(Liu et al. 2007)

Fine-tuning How We Conceptualize Population Structure (Thomas and Kunin 1999)

• Continuous function of Immigration (I), Emigration (E), Birth (B), and Death (D), rather than categories

• Process, not pattern is what is important

Populations are Not Fixed on Compensation Axis

• Depends on balance of internal (B, D) vs. external (E, I) processes– Density dependence and stochastic variation in B, D, E,

or I can affect position through time

– May depend on location relative to other demes (central areas more likely to be sources, fringe areas more likely to be sinks, but this changes as central areas become fringe areas due to deme extinctions; Stacey et al. 1997)

– Investigation of the change in processes through time or with respect to density would be fruitful investigation

Plotting Metapopulations to View Processes

A Butterfly (Hesperia comma) Example

Result is a “Process-oriented” fingerprint of population structure.

Two Study sites:Surrey has many small patches, close together with lots of E, I and some importing and some exporting populations.East Sussex has a few large patches with low E and I.

Getting Real

Thinking about metapopulations in actual landscapes (Wiens 1997)•distances are not Euclidean

•Patch permeability and edge effects may affect travel and hence functional distance between patches)

Need to understand and quantify individual movements and how individuals in a population vary in their within- and between-patch movements

When Can We Ignore Aspects of the Landscape?

• The pattern of the landscape may be relatively unimportant until habitat loss exceeds the “percolation threshold”– Percolation thresholds vary with vagility of organism (Wiens

1997; Fig. 4) and as they are approached, the landscape perspective is more important to metapopulation modeling

• Landscape view is less needed when:– Abundant and widespread suitable habitat– Less isolated patches– Transition probabilities among patches are relatively equal and

high regardless of patch type– Habitat pattern is ephemeral

What Can We Learn from Empirical Studies?

• Metapopulations with “Strong Rescue Effects” are more common than thought (Stacey et al. 1997)– “Strong rescue effects” occur when dispersal prevents

local extinctions (as opposed to rescuing occupancy of a patch after extinction)

• Butterflies, small mammals (pikas, voles, prairie dogs, mice, chipmunks, rats, squirrels), amphibians (red-spotted newts, natterjack toads, pool frogs)

– Individual demes can vary from being source in one year to sink in the next due to stochastic or landscape-mediated changes in survival and reproduction

Modeling Isolates Importance of Rescue(Stacey et al. 1997)

Modeling also Indicates the Detriments of Spatial Autocorrelation

Do not want to have all demes function as sinks in the same yearImplications for reserve design?

Long-distance Rescue from Dispersal may also be Important for Birds

• Naturally fragmented populations of Ptarmigan

• Lot of turnover in breeders, especially females

(Martin et al. 2000)

Recruitment was from

Outside of Area Studied

• Recruitment most conspicuous in females

• More than 50% of females new each year, most of those from outside study area

More is Not Necessarily Better• Dispersal and population

persistence in butterflies (Thomas 2000)

• Apparent disruptive selection– Small populations and high

colonization of intermediate dispersers not as good as larger populations (despite lower colonization) of poor dispersers

– Large populations and high colonization by most mobile species

Intermediate spp survive at median = 60% of regions, sedentary at 95%, mobile at 100%

Sinks Matter

• Greater Reed Warblers (Netherlands) live in metapopulations with sinks and sources (Foppen et al. 2000)

• Growth of sources increases with number of, and connectivity to, sinks

Beyond Sources and Sinks: The Sponge (Marzluff et al. 2001)

• Crow demographics suggest that populations in urban areas have lambda=1, yet populations continue to grow

• Perhaps urban areas “soak up” non-breeders from wildland and suburban sources to fuel growth

Projections indicate local breeding population not responsible for growth

An exponentially increasing population?

0

20

40

60

80

100

1970 1980 1990 2000

Seattle CBC

Cro

ws/

pa

rty-

ho

ur

Projected growth

Do suburban and exurban fledglings become young urban crows?

• Method: radiotracking dispersing juveniles

56 crows radiotagged as fledglings at 8 sites: urban, suburban, fringe, and exurban

Benefits of Moving to the City

living dead failed unknownsurburban (14) 21.4% 21.4% 28.6% 28.6%

fringe (21) 19.0% 52.4% 9.5% 19.0%exurban (8) 12.5% 37.5% 12.5% 37.5%

subtotal (43) 18.6% 39.5% 16.3% 25.6%

urban (13) 38.5% 23.1% 23.1% 15.4%

Of known-fate crows, 38% of urban and 68% of other crows died

45% of crows dispersing from suburbs and exurbs became more urban and 36% showed no change

result of dispersal:

disperserstotal

caughtpercent

totalincreased

urbanization no changedecreased

urbanizationsuburban 2 14 14.3% 1 0 1fringe 5 21 23.8% 3 1 1exurban 4 8 50.0% 1 3 0Subtotal 11 43 25.6% 5 4 2

urban 3 13 23.1% 0 2 1

0%

20%

40%

60%

80%

100%

175 275 375 475 575 675

days since 1st day of birth year

lan

d c

ov

er

>3

5%

pa

ve

d in

1k

m2

are

a

165.534 164.444 165.684

One non-disperser tried city life and came back home as a helper

Is dispersal enough to explain the gap?

•Five of 43 (12%) suburban and exurban crows moved to more-urban areas during dispersal

•Sufficient to replace crows emigrating and add to population?

0 1 0 2 0 3 0 4 0 5 0 6 0

1 0

1 0 0

1 0 0 0

S e a t t l e C B Cp r o j e c t e d u r b a n g r o w t h

Y e a r0 1 0 2 0 3 0 4 0 5 0 6 0

1 0

1 0 0

1 0 0 0

S e a t t l e C B Cp r o j e c t e d g r o w t h w i t h ( I - E )

A .

Stan

dard

ized

Cro

w C

ount

Is dispersal enough to explain the gap?

Effect of adding 12.3% to local production explains some - but not all - of the gap between predicted and observed population growth

More precise modeling of contribution of suburban and exurban areas worthwhile

0 1 0 2 0 3 0 4 0 5 0 6 0

1 0

1 0 0

1 0 0 0

S e a t t l e C B Cp r o j e c t e d u r b a n g r o w t h

Y e a r0 1 0 2 0 3 0 4 0 5 0 6 0

1 0

1 0 0

1 0 0 0

S e a t t l e C B Cp r o j e c t e d g r o w t h w i t h ( I - E )

B .

Stan

dard

ized

Cro

w C

ount

Sociality and Metapopulations (Marzluff and Balda 1989)

Sex-ratio based dispersal leads to metapopulations of Pinyon Jay flocks

Metapopulations of Metapopulations?

•Butterflies in Britian (Wilson et al. 2002)

•Very long-distance dispersal is critical to persistence (longer than empirically-recorded max dispersal distances

•Connectivity within patch networks and proximity to networks to other networks discriminated occupied from unoccupied networks

Small networks near large, persistent networks

A Word of Caution

• Seduction of reduced risk of extinction in metapopulations relative to single, panmictic populations can be taken too far

• Creation of small populations of captive Puerto Rican Parrots with human-mediated dispersal among the demes was recommended – But increased risk of disease spread with exchange of

individuals among demes, and– Reduced mating success in small groups– Makes this recommendation unsound (Wilson et al. 1994)

References• Wilson, R. J., Ellis, S., Baker, J. S., Lineham, M. E., Whitehead, R. W., and C. D. Thomas. 2002. Large-scale patterns of

distribution and persistence at the range margins of a butterfly. Ecology 83:3357-3368.• Wiens, JA. 1997. Metapopulation dynamics and landscape ecology. Pp. 43-62. In: (Hanski, IA and ME Gilpin, eds.)

Metapopulation biology: ecology, genetics, and evolution. Academic Press. San Diego.• Stacey, PB, Johnson, VA, and ML Taper. 1997. Migration within metapopulations: the impact upon local population

dynamics. Pp. 267-291. In: (Hanski, IA and ME Gilpin, eds.) Metapopulation biology: ecology, genetics, and evolution. Academic Press. San Diego.

• Wison, MH, Kepler, CB, Snyder, NFR, Derrickson, SR, Dein, FJ, Wiley, JW, Wunderle, JM Jr., Lugo, AE, Graham, DL, and WD Toone. 1994. Puerto Rican parrots and potential limitations of the metapopulation approach to species conservation. Conservation Biology 8:114-123.

• Foppen, RPD, Chardon, JP, and W. Liefveld. 2000. Understanding the role of sink patches in source-sink metapopulations:reed warbler in an agricultural landscape. Conservation Biology 14:1881-1892.

• Martin, K, Stacey, PB, and CE Braun. 2000. Recruitment, dispersal, and demographic rescue in spatially-structured white-tailed ptarmigan populations. Condor 102:503-516.

• Thomas, CD. 2000. Dispersal and extinction in fragmented landscapes. Proceedings of the Royal Society (London) 267:139-145.

• Thomas, CD and WE Kunin. 1999. The spatial structure of populations. J. Animal Ecology 68:647-657.• Hess, GR. 1996. Linking extinction to connectivity and habitat destruction in metapopulation models. American

Naturalist 148:226-236.• Marzluff, J. M., K. J. McGowan, R. E. Donnelly, and R. L. Knight. 2001. Causes and consequences of expanding

American Crow populations. Pages 331-363. In: Marzluff, Bowman, and Donnelly Eds., Avian conservation and ecology in an urbanizing world, Kluwer, Norwell, MA.

• Marzluff, J. M. and R. P. Balda. 1989. Social, demographic, and evolutionary consequences of dispersal in a group-living bird, the pinyon jay. Ecology 70:316-328.

• Liu, H. Y., Z. S. Lin, and T. Wen. 2007. Responses of metapopulation dynamics to two different kinds of habitat destruction caused by human activities. Plant Ecology 188:53-65.