Matrix Population Model construction and analysis v20
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The Matrix Population Models Workflow provides an environment to create stage-matrices with no density dependence and to perform several analyses on them:
- Eigen analysis;
- Age specific survival;
- Generation time (T);
- Net reproductive rate (Ro);
- Transient Dynamics;
- Bootstrap of observed census transitions (Confidence intervals of lambda);
- Survival curve;
- Keyfitz delta;
- Cohen's cumulative distance.
If multiple year transitions are selected, the results will be ordered by year.
This workflow requires an instance of Rserve on localhost
This workflow has been created by the Biodiversity Virtual e-Laboratory (BioVeL http://www.biovel.eu/) project. BioVeL is funded by the EU’s Seventh Framework Program, grant no. 283359.
This workflow uses R packages ‘popbio’ (Stubben & Milligan 2007; Stubben, Milligan & Nantel 2011) and 'popdemo' (Stott, Hodgson and Townley 2013).
References:
Caswell, H. 1986. Life cycle models for plants. Lectures on Mathematics in the Life Sciences 18: 171-233.
Caswell, H. 2001. Matrix population models: Construction, analysis and interpretation, 2nd Edition. Sinauer Associates, Sunderland, Massachusetts.
de Kroon, H. J., A. Plaiser, J. van Groenendael, and H. Caswell. 1986. Elasticity: The relative contribution of demographic parameters to population growth rate. Ecology 67: 1427-1431.
Horvitz, C., D.W. Schemske, and Hal Caswell. 1997. The relative "importance" of life-history stages to population growth: Prospective and retrospective analyses. In S. Tuljapurkar and H. Caswell. Structured population models in terrestrial and freshwater systems. Chapman and Hall, New York.
Jongejans E. & H. de Kroon. 2012. Matrix models. Chapter in Encyclopaedia of Theoretical Ecology (eds. Hastings A & Gross L) University of California, p415-423
Mesterton-Gibbons, M. 1993. Why demographic elasticities sum to one: A postscript to de Kroon et al. Ecology 74: 2467-2468.
Oostermeijer J.G.B., M.L. Brugman; E.R. de Boer; H.C.M. Den Nijs. 1996. Temporal and Spatial Variation in the Demography of Gentiana pneumonanthe, a Rare Perennial Herb. The Journal of Ecology, Vol. 84(2): 153-166.
Stott, I., S. Townley and D.J. Hodgson 2011. A framework for studying transient dynamics of population projection matrix models. Ecology Letters 14: 959–970
Stubben, C & B. Milligan. 2007. Estimating and Analysing Demographic Models Using the popbio Package in R. Journal of Statistical Software 22 (11): 1-23
Stubben, C., B. Milligan, P. Nantel. 2011. Package ‘popbio’. Construction and analysis of matrix population models. Version 2.3.1
van Groenendael, J., H. de Kroon, S. Kalisz, and S. Tuljapurkar. 1994. Loop analysis: Evaluating life history pathways in population projection matrices. Ecology 75: 2410-2415.
Data Inputs (1)
censusDataFile (text/plain)
Description:
The input data file must have the format of a table containing the demographic data on a series of individuals over several years. Each individual has a table row for each year and is identified by a number (plant column in example). For the year specified in the column 'year', each individual has a certain life stage ('stage'). The stage codes can be chosen by the user, but they cannot be longer than 8 characters.
For all individuals, the number of offspring is specified in a chosen way (in the example, 'reprstr' gives the number of flowers/fruits for each plant. In the example, it can be seen that only generative adults (stage=G) have flowers. Individuals without offspring must be indicated by filling in '0' in this column (i.e. the cannot have empty cells).
The column 'recruitment' specifies those individuals that are new in the second year census to the population by means of a code. In the example, 'RS' is a new seedling, and 'RJ' a new juvenile plant. As can be seen in the example, no code is needed in this column for individuals that were already present.
Example value:
plant year stage reprstr recruitment 2 1987 D 0 4 1987 J 0 5 1987 D 0 31 1987 V 0 36 1987 G 5 37 1987 J 0 41 1987 J 0 43 1987 S 0 46 1987 V 0 2 1988 V 0 4 1988 D 0 5 1988 V 0 9 1988 J 0 RJ 14 1988 J 0 RJ
Parameter Inputs (4)
iterations (text/plain)
Description:
Number of iterations for calculation of confidence interval
Example value:
10000
label (text/plain)
Description:
Descriptive title for labelling generated outputs.
Example value:
Gentiana pneumonanthe, Terschelling
longTermYears (text/plain)
Description:
This value contains the maximum number of iterations in the transient dynamic analysis, and hence the total number of years for the long term graphs.
The number of years will be used in two output graphs:
1) StageVectorPlotLongTermProportional: the proportion of individuals per stage in the long term.
2) StageVectorPlotLongTermLogarithmic: the number of individuals per stage in the long term.
Example value:
50
shortTermYears (text/plain)
Description:
This value will be use to plot a graph that shows a simulation of the number of individuals per stage a few years after the study. This value represents the years of axis X of the output graph: StageVectorPlotShortTerm.
Example value:
10
Result Outputs (24)
cohen_cumulative_distance (text/csv)
Description:
Cohen’s cumulative distance measures the difference between observed and expected vectors along the matrix path that the population would take to reach the expected population vector. It is a function of both the observed stage distribution (n0) and the structure of the matrix (A) (Williams et al 2011). Cohen’s cumulative distance will not work for reducible matrices and returns a warning for imprimitive matrices (although will not function for imprimitive matrices with nonzero imaginary components in the dominant eigenpair) (Caswell 2001).
confidence_interval_95pc_of_lambda (text/csv)
Description:
Calculate bootstrap distributions of population growth rates (lambda) by randomly sampling with replacement from a stage-fate data frame of observed transitions. Resampling transitions with equal probability.
damping_ratio (text/csv)
Description:
The ratio between the dominant eigenvalue and the second highest eigenvalue of a transition matrix is called the damping ratio, and it can be considered as a measure of the intrinsic resilience of the population, describing how quickly transient dynamics decay following disturbance or perturbation regardless of population structure, (the larger the damping ratio, the quicker the population converges). High damping ratios tell you that the dominant stable stage distribution is reached fairly soon.
Example value:
2.0901.
eigenanalysis (text/csv)
Description:
The Eigen analysis results are a set of demographic statistics:
Lambda or dominant eigenvalue: This value describes the population growth rate of a stage matrix. The population will be stable, grow or decrease at a rate given by lambda: e.g.: ? = 1 (population is stable), ? > 1 (population is growing) and finally ? < 1 (population is decreasing).
The stable stage distribution (w): It is the proportion of the number of individuals per stage. It is given analytically by the right eigenvector (another property of the transition matrix) that corresponds to the dominant eigenvalue
Elasticity and Sensitivity: Sensitivity and elasticity analyses are prospective analyses.
The sensitivity matrix: The sensitivity gives the effect on ? of changes in any entry of the matrix, including those that may, at a given context, be regarded as fixed at zero or some other value. The derivative tells what would happened to ? if aij was to change, not whether, or in what direction, or how much, aij actually change. The hypothetical results of such impossible perturbations may or may not be of interest, but they are not zero. It is up to you to decide whether they are useful (Caswell 2001).
When comparing the ?-sensitivity values for all matrix elements one can find out in what element a certain increase has the biggest impact on ?. However, a 0.01 increase in a survival matrix element is hard to compare to a 0.01 increase in a reproduction matrix element, because the latter is not bound between 0 and 1 and can sometimes take high values. Increasing matrix element a14 (number of S (seedlings) the next year produced by a G (Reproductive individuals)) with 0.01 from 7.666 to 7.676 does not have a noticeable effect on ?. For comparison between matrix elements it can therefore be more insightful to look at the impact of proportional changes in elements: by what percentage does ? change if a matrix element is changed by a certain percentage? This proportional sensitivity is termed elasticity (Description based on Oostermeijer data, based on Jongejans & de Kroon 2012).
The Elasticity matrix: The elasticities of ? with respect to the stage are often interpreted as the “contributions” of each of the stages to ?. This interpretation relies on the demonstration, by de Kroon et al (1986) that the elasticitis of the ? with respect to the stage, always sum to 1. For further information see: de Kroon, et al., 1986. and Caswell 2001.
Reproductive value (v): scaled so v[1]=1. To what extent will a plant or animal of a determinate category or stage , contribute to the ancestry of future generation.
The damping ratio: it can be considered as a measure of the intrinsic resilience of the population, describing how quickly transient dynamics decay following disturbance or perturbation regardless of population structure, the larger the p, the quicker the population converges.
Example value:
$lambda1 [1] 1,232338 $stable.stage S J V G D 0,14218794 0,16166957 0,65944861 0,02285525 0,01383863 $sensitivities S J V G D S 0 0 0 0,006042076 0 J 0,14255579 0,1620878 0 0,02291438 0 V 0,08206359 0,0933074 0,3806 0,01319088 0,00798695 G 0 2,7675986 11,28901 0,391255815 0,2369016 D 0 0,3325676 1,35654 0 0,02846721 $elasticities S J V G D S 0 0 0 0,037589187 0 J 0,006706037 0,001315287 0 0,15406651 0 V 0,03088315 0,062844075 0,27823767 0,003058271 0,005576792 G 0 0,089832455 0,08252831 0,196541848 0,022353201 D 0 0,008096016 0,01983398 0 0,000537213 $repro.value S J V G D 1 3,792468 2,18317 64,755197 7,781288 $damping.ratio [1] 2,0902
eigenanalysis_elasticity_matrix (image/png)
Description:
The elasticity matrix, displayed with coloured squares to highlight the magnitude of the values.
eigenanalysis_sensitivity_matrix_1 (image/png)
Description:
A sensitivity matrix showing the sensitivities of the actual transitions (i.e. the sensitivity values of non-zero elements), displayed with coloured squares to highlight the magnitude of the values.
eigenanalysis_sensitivity_matrix_2 (image/png)
Description:
A sensitivity matrix showing the sensitivities of all possible transitions (i.e. the sensitivity values of zero and non-zero elements), displayed with coloured squares to highlight the magnitude of the values.
elasticity_matrix (text/csv)
Description:
See Eigen analysis
elasticity_plot (image/png)
Description:
An Elasticity matrix plot showing the elasticities values per stage.
fundamental_matrix (text/csv)
Description:
Age specific survival
The fundamental matrix workflow gives the basic information on age-specific survival, this includes the mean, variance and coefficient of variation (cv) of the time spent in each stage class and the mean and variance of the time to death.
Fundamental matrix (N): is the mean of the time spent in each stage class. e.g.: For our Gentiana example means a J plants will spends, on average, about 1 year as a Juvenile, 11 as vegetative plant, less than a year a reproductive and dormant plant.
Variance (var): is the variance in the amount of time spent in each stage class.
Coefficient of variation (cv): is the coefficient of variation of the time spent in each class (sd/mean- the ratio of the standard deviation to the mean).
Meaneta: is the mean of time to death, of life expectancy of each stage. e.g. The mean age at death is the life expectancy; the life expectancy of a new individual seedling is 8 years.
Vareta: is the variance of time to death.
Example value:
$N
S J V G D
S 1.00000000 0.0000000 0.0000000 0.0000000 0.0000000
J 0.05855658 1.0101010 0.0000000 0.0000000 0.0000000
V 6.89055876 11.9968091 13.3581662 10.0186246 12.9606017
G 0.20844800 0.4667882 0.3911175 2.9183381 0.6919771
D 0.12890879 0.2523299 0.2464183 0.1848138 1.2628940
$var
S J V G D
S 0.00000000 0.00000000 0.0000000 0.0000000 0.0000000
J 0.05631067 0.01020304 0.0000000 0.0000000 0.0000000
V 129.72009930 164.59050165 165.0824377 157.2694415 165.3219447
G 0.96474493 2.03981226 1.7387357 5.5983592 2.8680368
D 0.18007000 0.32133154 0.3152601 0.2478305 0.3320072
$cv
S J V G D
S 0.000000 NaN NaN NaN NaN
J 4.052468 0.100000 NaN NaN NaN
V 1.652910 1.069391 0.9618417 1.2517398 0.9920649
G 4.712035 3.059674 3.3713944 0.8107646 2.4473757
D 3.291836 2.246508 2.2785654 2.6936618 0.4562542
$meaneta
S J V G D
8.286472 13.726028 13.995702 13.121777 14.915473
$vareta
S J V G D
143.4207 181.1844 181.6537 177.2333 181.2319
generation_time (text/csv)
Description:
Generation time:
The time T required for the population to increase by a factor of Ro (net reproductive rate).
e.g. for Generation time T and Net reproductive rate Ro:
If T = 8.13 and Ro = 5.46 then the average individual in the study year replaced itself with about five new plants and took approximately 8 years to do so.
Example value:
8.1302
histogram_ci_95pc_of_lambda (image/png)
Description:
Histogram generated from the analysis of the confidence interval of lambda.
keyfitz_delta (text/csv)
Description:
A distance measure between probability vectors of n (Observed Stage Distribution, abundances per stage) and w (Stable Stage Distribution). Its maximum value is 1 and its minimum is 0 when the vectors are identical.
long_term_logarithmic_stage_vector_plot (image/png)
Description:
The number of individuals per stage in the long term
long_term_proportional_stage_vector_plot (image/png)
Description:
Stage vector plot long term proportional:
Is the proportion of individuals per stage in the long term (e.g.: 50 years)
net_reproductive_rate (text/csv)
Description:
The net reproductive rate is the mean number of offspring by which a new-born individual will be replaced by the end of its life, and thus the rate by which the population increases from one generation to the next.
Example value:
5.4657
population_projection (text/csv)
Description:
Population projection:
Lambda or dominant eigenvalue: The population will be stable, grow or decrease at a rate given by lambda: e.g.: ? = 1 (population is stable), ? > 1 (population is growing) and finally ? < 1 (population is decreasing). e.g. The projected population growth rate (?) is 1.237, meaning that the population is projected to increase with 23% per year if these model parameters remain unchanged.
The stable stage distribution (stable.stage): It is the proportion of the number of individuals per stage and it is given by (w).
Stage vector (stage.vectors): it is the projection of the number of individuals per category per year in the long term, the long term was stipulated in the input port (long term years) (e.g. 50 years).
Population sizes (pop.sizes): it is the total population size per year in the long-term (e.g. 50 years).
Population change (pop.changes): are the lambda values per year in the long-term (e.g. 50 years).
Example value:
$lambda
[1] 1.232338
$stable.stage
S J V G D
0.14218794 0.16166957 0.65944861 0.02285525 0.01383863
$stage.vectors
0 1 2 3 4 5 6 7
S 69 161 176.33333 187.22072 219.09046 261.92397 318.22637 389.44517
J 100 179 201.69476 214.57709 249.78014 298.27181 362.08839 442.95984
V 111 258 467.40332 685.98643 903.75302 1149.34660 1437.18683 1783.39662
G 21 23 24.42009 28.57702 34.16400 41.50779 50.79720 62.39105
D 43 6 10.15818 14.70876 19.13949 24.22235 30.22041 37.46071
8 9 10 11 12 13 14
S 478.33138 588.52367 724.70467 892.75361 1099.9811 1355.4346 1670.2865
J 543.96054 669.21317 824.03064 1015.09148 1250.7042 1541.1537 1899.1418
V 2204.99218 2721.56781 3356.41003 4137.71650 5099.9406 6285.3667 7746.0003
G 76.76396 94.52670 116.44612 143.47580 176.7958 217.8635 268.4762
D 46.29325 57.12499 70.44214 86.83496 107.0256 131.9009 162.5519
15 16 17 18 19 20 21
S 2058.3178 2536.5199 3125.836 3852.0783 4747.0575 5849.9764 7209.1464
J 2340.3370 2884.0582 3554.118 4379.8647 5397.4679 6651.5012 8196.8954
V 9545.8697 11763.8434 14497.093 17865.3551 22016.1771 27131.3836 33435.0416
G 330.8504 407.7177 502.445 619.1814 763.0404 940.3234 1158.7961
D 200.3221 246.8664 304.224 374.9074 462.0130 569.3564 701.6396
22 23 24 25 26 27 28
S 8884.1038 10948.218 13491.904 16626.585 20489.572 25250.078 31116.629
J 10101.3442 12448.269 15340.474 18904.649 23296.916 28709.674 35380.022
V 41203.2756 50776.363 62573.642 77111.875 95027.892 117106.479 144314.761
G 1428.0284 1759.814 2168.685 2672.553 3293.488 4058.691 5001.679
D 864.6572 1065.550 1313.118 1618.205 1994.175 2457.498 3028.468
29 30 31 32 33 34 35
S 38346.204 47255.483 58234.725 71764.863 88438.565 108986.20 134307.83
J 43600.144 53730.113 66213.658 81597.604 100555.825 123918.76 152709.79
V 177844.559 219164.602 270084.859 332835.826 410166.224 505463.41 622901.75
G 6163.759 7595.834 9360.634 11535.465 14215.591 17518.41 21588.61
D 3732.096 4599.204 5667.773 6984.612 8607.403 10607.23 13071.69
36 37 38 39 40 41 42
S 165512.64 203967.51 251356.91 309756.66 381724.90 470414.08 579709.13
J 188190.08 231913.78 285796.15 352197.45 434026.28 534867.07 659136.99
V 767625.48 945974.02 1165759.69 1436609.93 1770388.96 2181717.52 2688613.33
G 26604.46 32785.68 40403.04 49790.20 61358.36 75614.23 93182.29
D 16108.74 19851.41 24463.65 30147.49 37151.89 45783.69 56420.97
43 44 45 46 47 48 49
S 714397.57 880379.2 1084924.8 1336994.0 1647628.4 2030435.1 2502182.2
J 812279.54 1001002.9 1233573.9 1520179.9 1873375.5 2308631.7 2845014.5
V 3313280.28 4083081.1 5031735.8 6200799.1 7641480.1 9416886.1 11604786.2
G 114832.08 141511.9 174390.5 214908.1 264839.4 326371.6 402200.1
D 69529.71 85684.1 105591.8 130124.7 160357.7 197614.8 243528.3
$pop.sizes
[1] 3.440000e+02 6.270000e+02 8.800097e+02 1.131070e+03 1.425927e+03
[6] 1.775273e+03 2.198519e+03 2.715653e+03 3.350341e+03 4.130956e+03
[11] 5.092034e+03 6.275872e+03 7.734447e+03 9.531719e+03 1.174646e+04
[16] 1.447570e+04 1.783901e+04 2.198372e+04 2.709139e+04 3.338576e+04
[21] 4.114254e+04 5.070152e+04 6.248141e+04 7.699821e+04 9.488782e+04
[26] 1.169339e+05 1.441020e+05 1.775824e+05 2.188416e+05 2.696868e+05
[31] 3.323452e+05 4.095616e+05 5.047184e+05 6.219836e+05 7.664940e+05
[36] 9.445797e+05 1.164041e+06 1.434492e+06 1.767779e+06 2.178502e+06
[41] 2.684650e+06 3.308397e+06 4.077063e+06 5.024319e+06 6.191659e+06
[46] 7.630217e+06 9.403006e+06 1.158768e+07 1.427994e+07 1.759771e+07
$pop.changes
[1] 1.822674 1.403524 1.285293 1.260689 1.244995 1.238412 1.235219 1.233715
[9] 1.232996 1.232652 1.232488 1.232410 1.232372 1.232354 1.232346 1.232342
[17] 1.232340 1.232339 1.232338 1.232338 1.232338 1.232338 1.232338 1.232338
[25] 1.232338 1.232338 1.232338 1.232338 1.232338 1.232338 1.232338 1.232338
[33] 1.232338 1.232338 1.232338 1.232338 1.232338 1.232338 1.232338 1.232338
[41] 1.232338 1.232338 1.232338 1.232338 1.232338 1.232338 1.232338 1.232338
[49] 1.232338
projection_matrix (image/png)
Description:
The stage matrix, displayed with coloured squares to highlight the magnitude of the values.
sensitivity_matrix (text/csv)
Description:
See Eigen analysis
sensitivity_plot (image/png)
Description:
A sensitivity matrix plot showing the sensitivities values of the actual transitions (i.e. the sensitivity values of non-zero elements) per stage.
short_term_stage_vector_plot (image/png)
Description:
A plot that charts the number of individuals per stage vs. years in the short-term (e.g. 5 or 10 years). The number of years is related to the short-term years input value.
stable_stage_distribution (image/png)
Description:
A bar plot which shows the stable stage distribution (w) of the analysed matrix. In other words, the proportion of individuals per stage.
stage_matrix (text/csv)
Description:
A stage matrix contains transitions probabilities from each stage to the next. In the example, the selected species, Gentiana pneumonanthe, has a matrix of 5 x 5 stages (Oostermeijer et al., 1996).
Example value:
S J V G D S 0.0000 0.0000 0.0000 7.6660 0.0000 J 0.0579 0.0100 0.0000 8.5238 0.0000 V 0.4637 0.8300 0.9009 0.2857 0.8604 G 0.0000 0.0400 0.0090 0.6190 0.1162 D 0.0000 0.0300 0.0180 0.0000 0.0232
survival_curve_plot (image/png)
Description:
A plot of survival curves is produced, one point for each stage.
Error/Log Outputs (0)
None
Abundance_InteractionDescription: Abundance iteraction: Initial abundance: In this dialogue authomatically appears the fields to fill out the initial abundance per stage observed in the field (see data below). After fill out the abundances, the user confirms the numbers. As a example Gentiana pneumonanthe has 5 stages with its respective abundance: stage abundance 1) S (seedlings) 69 2) J (Juveniles) 100 3) V (vegetative) 111 4) G (reproductive individuals) 21 5) D (dormant plants) 43 Inputs: stages, abundances, initialYear Outputs: abundances |
CategoriseStages_InteractionDescription: With this dialogue automatically appears the names of the stages or categories of the census data file. When the dialogue appears, the stages are in disorder, so the user drags and organizes the stages according to the order in the life cycle. Then, the author chooses if the stage belongs to the recruited, reproductive category or it should be excluded. Recruited means that new individuals can be recruited to this (these) stage(s). Reproductive stages are those that reproduce (produce offspring) (in this example the stage G). In the census data file Dt1.txt, x is use to denote when a plant has died in the second year, so the user must selected in the excluded column. Then the user clicks in confirm and you will read stages submitted. In the following example, the life cycle of Gentiana pneumonanthe has 5 stages or categories: 1) Seedlings S 2) Juveniles J 3) Vegetative V 4) Reproductive individuals G 5) Dormant plants D Inputs: unsortedStages Outputs: sortedStages, recruitedStages, reproductiveStages |
SelectYears_InteractionDescription: In this dialogue automatically comes the years of the census data file, the user selects the first census year. In this example the census was 1987 -1988, therefore the user selects 1987. After this step, the user should confirm the selection. Inputs: years Outputs: years |
CensusData_ReadFromFileDescription: Inputs: census_data_file Outputs: census_data Script: |
CalculateDefaultAbundanceDescription: Inputs: stages, year, data Outputs: abundances Script: |
PrettyPrintRDescription: Inputs: input Outputs: output Script: |
NetReproductiveRateAnalysisDescription: Inputs: stage_matrix, rows, columns Outputs: result Script: |
CalculateKeyfitzDeltaDescription: Inputs: stage_matrix, abundances Outputs: keyfitz_delta Script: |
GenerationTimeAnalysisDescription: Inputs: stage_matrix, rows, columns Outputs: result Script: |
PrepareDescription: Inputs: census_data, stages, recruited_stages, start_year Outputs: trans1, trans, log Script: |
AnalysisDescription: Inputs: trans1, stages Outputs: projection_matrix Script: |
PlotHistogramDescription: Inputs: a, ci, plot_title Outputs: ci, histogram Script: |
ConfidenceIntervalDescription: Inputs: trans1, bootstrap_iterations Outputs: a, ci Script: |
DisplayTrans1Description: Inputs: input Outputs: output Script: |
ParseStagesDescription: Inputs: census_data, stage_column_header Outputs: all_stages Script: |
SensitivityPlotDescription: Inputs: stage_matrix, identifier Outputs: sensitivity_matrix, sensitivity_plot Script: |
ElasticityPlotDescription: Inputs: stage_matrix, identifier Outputs: elasticity_matrix, elasticity_plot Script: |
StageMatrix_FromCensusDataDescription: Inputs: census_data, start_year, stages, recruited_stages Outputs: stage_matrix, report Script: |
ProjectionMatrixDescription: Inputs: plot_title, stage_matrix, plot_size Outputs: plot_image Script: |
EigenanalysisNonZeroElementsDescription: Inputs: stage_matrix Outputs: eigenanalysis Script: |
EigenanalysisAllElementsDescription: Inputs: stage_matrix Outputs: eigenanalysis Script: |
BarPlotDescription: Inputs: bar_plot_title, eigenanalysis Outputs: bar_plot_image Script: |
ElasticityMatrixDescription: Inputs: plot_title, eigenanalysis, plot_size Outputs: plot_image Script: |
SensitivityMatrixDescription: Inputs: plot_title, eigenanalysis, plot_size Outputs: plot_image Script: |
SensitivityMatrix_2Description: Inputs: plot_title, eigenanalysis, plot_size Outputs: plot_image Script: |
CalculatePlotSizeDescription: Inputs: stage_matrix Outputs: plot_size Script: |
fundamental_matrixDescription: Inputs: stage_matrix, rows, columns Outputs: a Script: |
SurvivalCurvePlotDescription: Inputs: survival_curve, plot_title Outputs: survival_curve_plot Script: |
SurvivalCurveAnalysisDescription: Inputs: stage_matrix, fecundity_rows, fecundity_cols Outputs: survival_curve Script: |
FecundityRows_FromRecruitedStagesDescription: Inputs: some_values, all_values Outputs: indices Script: |
FecundityCols_FromReproductiveStagesDescription: Inputs: some_values, all_values Outputs: indices Script: |
ParseYearsDescription: Inputs: census_data, year_column_name Outputs: census_years Script: |
CalculateCohenCumulativeDistanceDescription: Inputs: stage_matrix, abundances Outputs: cohen_cumulative Script: |
StageVectorPlot_ShortTermDescription: Inputs: populationProjection, plotTitle, iterations Outputs: stageVectorPlot Script: |
PopulationProjectionDescription: Inputs: stageMatrix, abundances, years Outputs: populationProjection Script: |
DisplayRExpressionDescription: Inputs: input Outputs: output Script: |
StageVectorPlot_LongTermProportionalDescription: Inputs: populationProjection, plotTitle, iterations Outputs: stageVectorPlot Script: |
DampingRatioDescription: Inputs: stageMatrix Outputs: dampingRatio Script: |
StageVectorPlot_LongTermLogarithmicDescription: Inputs: populationProjection, plotTitle, iterations Outputs: stageVectorPlot Script: |
Filename: matrix_population_models_construction_and_analyses-v20.t2flow
Category: Population Modelling
Author: Maria Paula Balcázar-Vargas, Jonathan Giddy and Gerard Oostermeijer
Uploader: Maria Balcazar-Vargas
Uploaded at: 14 Aug 2014 18:23:11 UTC
