Ecological Archives E091-040-A3

Steven E. McMurray, Timothy P. Henkel, and Joseph R. Pawlik. 2010. Demographics of increasing populations of the giant barrel sponge Xestospongia muta in the Florida Keys. Ecology 91:560–570.

Appendix C. Additional methods of life table response analysis and results for site summary matrices.

LIFE TABLE RESPONSE ANALYSIS

Life table response analyses were conducted to determine the contribution each vital rate had to differences in λ across temporal and spatial scales. In contrast to elasticity, which measures the potential effect of a change in a given transition on λ, a life table response analysis can be used to decompose the population effect of a treatment (i.e., time) into the effect on the underlying transitions (Caswell 1996, 2001).

In the first analysis, changes in λ from the 2000–2003 to the 2003–2006 Conch Reef summary matrices, A(00-03) and A(03-06) were examined. From the mean matrix of A(00-03) and A(03-06), a matrix of sensitivities was calculated. Then, with A(00-03) used as a reference matrix, a matrix of contributions was calculated by multiplying each element of the matrix of sensitivities by the respective element of A(03-06) - A(00-03) (Caswell 1996). In the second analysis, differences in λ between sites were examined. Analyses were completed as described above, with the exception that a mean matrix of the transition matrices from all sites was constructed and used as a reference matrix in which comparisons with each site was made (Caswell 2001).

RESULTS FOR SITE SUMMARY MATRICES

Table C1 presents the contributions of each transition to differences in λ between the site summary matrices. Transitions of size classes IV and V contributed the most to observed differences in λ between sites. Significantly greater λ for A(CR30) compared to A(CR15) was largely due to a large positive contribution from stasis of size class IV individuals at the 30 m Conch Reef site (Table C1). This is in agreement with the high elasticity value for this transition (Appendix J) and the higher frequency of this transition for A(CR30) compared to A(CR15).

TABLE C1. Contributions of transitions to differences in λ between sites. Contributions were calculated by comparing each site summary matrix to a reference matrix, which is a mean of all site summary matrices. Negative values indicate transitions that contributed to accelerated population decline and positive values indicate transitions that contributed to slowed population decline compared to the reference matrix. Contributions > ±0.01 are in bold.

Location and size class

Size class

15 m Conch

Base

I

II

III

IV

V

Base

0.0008

0

-0.0006

0.0018

0.0082

-0.0118

I

0.0017

-0.0012

-0.0001

0

0

0

II

-0.0033

0.0019

-0.0003

-0.0030

0

0

III

-0.0044

0.0001

-0.0003

0.0098

-0.0099

-0.0091

IV

0.0024

0

0

-0.0034

-0.0134

-0.0368

V

0.0012

0

0

-0.0004

0.0064

0.0077

20 m Conch

 

 

 

 

 

 

Base

0.0043

0

0.0005

0.0006

-0.0002

-0.0101

I

0.0008

0.0002

-0.0007

0

0

0

II

-0.0044

0

0.0005

0.0040

0

0

III

0.0013

0

0.0015

-0.0042

0.0016

-0.0065

IV

0.0015

0

0

-0.0009

-0.0227

-0.0150

V

-0.0004

0

0

-0.0004

0.0068

0.0370

30 m Conch

 

 

 

 

 

 

Base

-0.0029

0

0.0003

-0.0010

-0.0049

0.0081

I

-0.0014

0.0001

-0.0005

0

0

0

II

0.0062

-0.0005

-0.0007

0.0008

0

0

III

-0.0029

0

-0.0012

-0.0049

0.0207

-0.0033

IV

-0.0022

0

0

0.0035

0.0843

0.0336

V

-0.0004

0

0

-0.0006

-0.0383

-0.0305

15 m Pickles

 

 

 

 

 

 

Base

-0.0001

0

-0.0002

-0.0012

-0.0041

-0.0071

I

0.0002

0.0002

0.0007

0

0

0

II

-0.0004

0

0.0002

-0.0028

0

0

III

0.0022

0.0001

-0.0003

0.0001

-0.0037

0.0180

IV

-0.0010

0

0

0.0032

0.0143

-0.0100

V

-0.0002

0

0

0.0016

0.0045

0.0241

Reference matrix

 

 

 

 

 

 

Base

0.6568

0

0.0268

0.0215

0.0219

0.0147

I

0.0379

0.4618

0.0369

0

0

0

II

0.0535

0.2816

0.5244

0.0304

0

0

III

0.0349

0.0035

0.3326

0.5800

0.0340

0.0071

IV

0.0270

0

0

0.3160

0.7007

0.0420

V

0.0069

0

0

0.0081

0.1846

0.8153

LITERATURE CITED

Caswell, H. 1996. Analysis of life table response experiments. II. Alternative parameterizations for size- and stage-structured models. Ecological Modelling 88:73–82.

Caswell, H. 2001. Matrix population models. Sinauer, Sunderland, Massachusetts, USA.


[Back to E091-040]