# pva_workbook_010803

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```					Population Viability Analysis for Structured Populations

Population parameters are projected based on Lefkovitch life-stage transition matrices (Burgman et al. 1993, Lefkovitch 1965).

Version date: 1/8/2003

Usage notes:

1) Access the PVAStage macro by loading the PVA.XLS workbook and enabling macros when prompted.

2) Load the workbook containing model specification data, and make the worksheet that contains the data the active worksheet.

3) From the active model specifications data worksheet, execute the PVAStage macro by selecting:
Tools --> Macro --> Macros --> PVAStage --> Run
(if the PVAStage macro is not present, select All Open Workbooks in macro location window at the bottom of the menu screen)

4) The macro will be prompt you to specify initial values of population life-stage parameters, one or more Lefkovitch matrices
of transition probabilities between life stages, and to choose how to select the Lefkovitch matrix at each time step. If
appropriate, maximum values (ceilings) can be specified for each life stage to limit population growth. Also, frequency of
estimates below a specified threshold can be monitored for the life stage for which lambda is computed.

5) Matrix selection choices are: 1) random with either equal or specified probabilities; 2) cyclical with specified cycle length; .
3) specified sequence.

6) Matrix elements can be considered constant or randomly selected from a Normal distribution to reflect uncertainty in element
values. If matrix elements can be considered Normally distributed, then the macro will prompt you to specify a matrix of standard
deviations for each Lefkovitch matrix, and the number of random iterations to perform at each time step. For each iteration,
a Normal pseudo-random deviate is generated for each matrix element, multiplied by the specified standard deviation for each
element, then added to the element. If these operations result in a negative value, the matrix element is set to zero for the iteration.

7) If 100 or more random sequences and/or Normal random iterations of Lefkovitch matrices are requested, extended results
can be requested for any estimated parameter. A percentile confidence interval can be estimated for a parameter
by the alpha/2-th percentile and the (1-alpha/2)-th percentile. For example, the 2.5-th and 97.5-th percentiles estimate an
alpha = 0.05 (or 95-percent) confidence interval (see columns F and N of the extended results).

8) Projected parameters can be plotted against time if desired.
9) Random selection among Lefkovitch matrices (see note 5) and selection of matrix elements from a Normal
distribution (see note 6) require seeding of random number generators. Choices for seeds are: a) fixed constant for
repeatable results; b) user specified; c) based on computer system clock.

10) Every effort is made to provide accurate and useful information. However, the U.S. Government,
U.S. Department of Agriculture, the USDA Forest Service and their employees and contractors assume
no legal liability for the accuracy, completeness, or usefulness of any information, apparatus, product,
or process disclosed herein. Neither the U.S. Government, U.S. Department of Agriculture, the
USDA Forest Service, nor their employees and contractors makes any warranty, express or implied,
including the warranties of merchantibility and fitness for a particular purpose with respect to documents
or information available in this workbook. All indirect, consequential, implied, punitive and special damages
are deemed waived if you use the information in this workbook in any manner. The sole remedy is the price
paid or, at the seller's choice, replacement or repair of the defective information.

Computation notes:

1) Estimation of population parameters and elasticities follows Chapter 4 of Burgman et al. (1993).

References:
Burgman, M. A.; Ferson, S.; Akcakaya, H. R. 1993. Risk Assessment in
Conservation Biology . Chapman and Hall, 314p. (Chapter 4)

Lefkovitch, L. P. 1965. The Study of Population Growth in Organisms Grouped by Stages.
Biometrics , Vol. 21, pp. 1-18.
Western Prairie Fringed Orchid Population Viability Model

Stage names            Initial population levels:    Ceiling values:
Seeds                    1000000
Seedlings                    2000
Vegetative plants              750
Dormant plants                 200
Flowering plants               250                                  8000

Lefkovitch matrices:
Number:                         3

Average: (1)           Seeds        Seedlings        Vegetative Plants     Dormant Plants    Flowering Plants
Seeds                         0.5                0                     0                 0              13749
Seedlings                 0.0015                 0                     0                 0                   0
Vegetative plants               0           0.0301                0.2806            0.0815             0.2106
Dormant plants                  0                0                0.5783            0.1015             0.6968
Flowering plants                0           0.0099                0.1411            0.0299             0.1025

Wet: (2)               Seeds        Seedlings        Vegetative Plants     Dormant Plants    Flowering Plants
Seeds                         0.5                0                     0                 0              13749
Seedlings                  0.002                 0                     0                 0                   0
Vegetative plants               0           0.0301                0.3294            0.0033                0.25
Dormant plants                  0                0                0.3198            0.0825             0.3973
Flowering plants                0           0.0099                0.3409            0.0792             0.3528

Dry: (3)               Seeds        Seedlings        Vegetative Plants     Dormant Plants    Flowering Plants
Seeds                         0.5                0                     0                 0               13749
Seedlings                  0.001                 0                     0                 0                   0
Vegetative plants               0           0.0301                0.1535            0.1813           0.002599
Dormant plants                  0                0                0.8465            0.1813              0.9963
Flowering plants                0           0.0099                     0                 0           0.001399
Western Prairie Fringed Orchid Population Viability Model: Elasticity

Stage names         Initial population levels: Ceiling values:
Seeds                 1000000
Seedlings                 2000
Vegetative plants           750
Dormant plants              200
Flowering plants            250                            8000

Average Matrix with seed viability reduced to zero
Seeds     Seedlings       Vegetative Plants Dormant Plants Flowering Plants
Seeds                     0               0                 0               0              13749
Seedlings            0.0015               0                 0               0                  0
Vegetative plants         0          0.0301            0.2806          0.0815             0.2106
Dormant plants            0               0            0.5783          0.1015             0.6968
Flowering plants          0          0.0099            0.1411          0.0299             0.1025

Average Matrix with seed viability reduced to zero, but with increased seed production
Seeds     Seedlings       Vegetative Plants Dormant Plants Flowering Plants
Seeds                     0               0                 0               0              25779
Seedlings            0.0015               0                 0               0                  0
Vegetative plants         0          0.0301            0.2806          0.0815             0.2106
Dormant plants            0               0            0.5783          0.1015             0.6968
Flowering plants          0          0.0099            0.1411          0.0299             0.1025

Wet Matrix with seed viability reduced to zero
Seeds       Seedlings     Vegetative Plants Dormant Plants Flowering Plants
Seeds                      0              0                 0               0              13749
Seedlings             0.002               0                 0               0                   0
Vegetative plants          0         0.0301            0.3294          0.0033                0.25
Dormant plants             0              0            0.3198          0.0825             0.3973
Flowering plants           0         0.0099            0.3409          0.0792             0.3528
Western Prairie Fringed Orchid Population Viability Model: Stochasticity

Stage names                              Ceiling values:
Initial population levels:
Seeds               1000000
Seedlings               2000
Vegetative plants         750
Dormant plants            200
Flowering plants          250                        8000

Lefkovitch matrices:
Number:                   3

Average: (1)      Seeds      Seedlings Vegetative Plants Dormant Plants Flowering Plants
Seeds                    0.5          0               0                0           13749
Seedlings            0.0015           0               0                0                0
Vegetative plants          0    0.0301           0.2806          0.0815           0.2106
Dormant plants             0          0          0.5783          0.1015           0.6968
Flowering plants           0    0.0099           0.1411          0.0299           0.1025

Wet: (2)          Seeds      Seedlings Vegetative Plants Dormant Plants Flowering Plants
Seeds                    0.5          0               0                0           13749
Seedlings             0.002           0               0                0                0
Vegetative plants          0    0.0301           0.3294          0.0033              0.25
Dormant plants             0          0          0.3198          0.0825           0.3973
Flowering plants           0    0.0099           0.3409          0.0792           0.3528

Dry: (3)          Seeds      Seedlings Vegetative Plants Dormant Plants Flowering Plants
Seeds                    0.5          0               0                0            13749
Seedlings             0.001           0               0                0                0
Vegetative plants          0    0.0301           0.1535          0.1813         0.002599
Dormant plants             0          0          0.8465          0.1813            0.9963
Flowering plants           0    0.0099                0                0        0.001399

Standard deviations where available (otherwise, zero)

Average: (1)      Seeds       Seedlings Vegetative Plants Dormant Plants Flowering Plants
Seeds                     0            0               0                0                0
Seedlings                 0            0               0                0                0
Vegetative plants         0            0          0.0297          0.0297           0.1287
Dormant plants            0            0          0.0297          0.0792           0.1287
Flowering plants          0            0          0.0297          0.0198           0.0297

Wet: (2)          Seeds       Seedlings Vegetative Plants Dormant Plants Flowering Plants
Seeds                     0            0               0                0                0
Seedlings                 0            0               0                0                0
Vegetative plants         0            0          0.0990          0.0013           0.0693
Dormant plants            0            0          0.0693          0.2970           0.1683
Flowering plants          0            0          0.1188          0.0693           0.1089

Dry: (3)         Seeds        Seedlings Vegetative Plants Dormant Plants Flowering Plants
Seeds                     0            0               0                0                0
Seedlings           0   0        0        0        0
Vegetative plants   0   0   0.0693   0.1089   0.0014
Dormant plants      0   0   0.0693   0.1089   0.0023
Flowering plants    0   0   0.0000   0.0000   0.0018
Western Prairie Fringed Orchid Population Viability Model: Conservation and Management

Stage names                              Ceiling values:
Initial population levels:
Seeds               1000000
Seedlings               2000
Vegetative plants         750
Dormant plants            200
Flowering plants          250                        8000

Lefkovitch matrices:
Number:                   3

Average: (1)      Seeds      Seedlings Vegetative Plants Dormant Plants Flowering Plants
Seeds                    0.5          0                 0             0     13749
Seedlings            0.0015           0                 0             0          0
Vegetative plants          0    0.0301            0.2806        0.0815     0.2106
Dormant plants             0          0           0.5783        0.1015     0.6968
Flowering plants           0    0.0099            0.1411        0.0299     0.1025

Wet: (2)          Seeds      Seedlings Vegetative Plants Dormant Plants Flowering Plants
Seeds                    0.5          0                 0             0     13749
Seedlings             0.002           0                 0             0          0
Vegetative plants          0    0.0301            0.3294        0.0033        0.25
Dormant plants             0          0           0.3198        0.0825     0.3973
Flowering plants           0    0.0099            0.3409        0.0792     0.3528

Dry: (3)          Seeds      Seedlings Vegetative Plants Dormant Plants Flowering Plants
Seeds                    0.5          0                 0             0     13749
Seedlings             0.001           0                 0             0          0
Vegetative plants          0    0.0301            0.1535        0.1813 0.002599
Dormant plants             0          0           0.8465        0.1813     0.9963
Flowering plants           0    0.0099                  0             0 0.001399
30% Ungrazed sites average
Seeds      ProtocormsVegetative plants Dormant plants Flowering Plants
Seeds                    0.5         0                 0               0    16636
Protocorms           0.0015          0                 0               0         0
Vegetative plants          0    0.0301           0.2944           0.116    0.2244
Dormant plants             0         0           0.5392           0.136    0.6232
Flowering plants           0    0.0099           0.1664          0.0276       0.16

30% Ungrazed: Wet
Seeds      ProtocormsVegetative plants Dormant plants Flowering Plants
Seeds                    0.5         0                 0               0    16636
Protocorms            0.002          0                 0               0         0
Vegetative plants          0    0.0301           0.3156          0.0792       0.25
Dormant plants             0         0           0.3228             0.14   0.3328
Flowering plants           0    0.0099           0.3616          0.0608    0.4172

30% Ungrazed: Dry
Seeds      ProtocormsVegetative plants Dormant plants Flowering Plants
Seeds                    0.5         0                 0               0     16636
Protocorms          0.00176          0                 0               0         0
Vegetative plants          0    0.0301             0.234         0.2112 0.060076
Dormant plants             0         0             0.766         0.2112     0.9088
Flowering plants           0    0.0099                 0               0 0.031276

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