Table of Contents
BigUrchin is a population model. This model was developed to allow accurate examination of the effects of spatial management of an invertebrate fishery, in addition to the effects of conventional management by size limit and fishing effort. It consists of 24 size structured subpopulations, linked by larval dispersal. The size structure is described by von Bertalanffy growth with variation in L¥ among individuals. Larval dispersal is described by a dispersal matrix. Post-dispersal density-dependence is a Beverton-Holt relationship.
The program was originally designed to model the population of the red sea urchin (Strongylocentrotus franciscanus) along the northern California coast. It has been modified to be more generic. While being more generic, the model still has implicit assumptions about the life cycle of the organism that should be considered before using it to model other species.
The model assumes that the population disperses only during the larval phase and adult movement is within each subpopulation's range only. The population has synchronous spawning and a coherent settlement cycle. The current version has explicit assumptions about the size of the organisms but this can be adjusted by scaling the inputs. The growth, mortality and settlement functions are fixed, though parameter values may be varied as described in the Model section.
The model currently has default values corresponding to the northern California red sea urchin fishery. Parameter values of the size structured subpopulation models were estimated from size distribution and growth increment data. The 24 locations correspond to deep and shallow areas in each of the 12 CDF&G sectors which are 10' of latitude. These are likely management areas.
The model can be run in either a batch mode or an interactive mode through a graphical interface.
BigUrchin is an X based application that is designed to run on a workstation running Unix. Currently the program is compiled for Solaris 2.3 (or later), Linux and Irix. As it is a graphical program, the X11 libraries and server should be present. You must be using a window manager to run the model. If the model is being run from a PC, the remote machine must have an X window server package installed (e.g. ExCeed's Hummingbird software).
To use the on-line help for BigUrchin, you must have access to Netscape on the computer that the program is located.
BigUrchin requires that each user have a configuration item set prior to executing the program. Each user must have an environment variable, URCHINHOME, set with the full directory path of the model's home directory. This can be placed in the .cshrc file or set manually with the setenv command prior to use of the model after each login. If you do not know how to set the environment variable, see your system administrator for assistance.
For the help feature to work properly, you must have the Netscape navigator in your path. If you are not sure if you do, in a terminal window, type netscape and if the program begins then you do, otherwise see your system administrator about configuring your account appropriately.
It is recommended that the user of the model have a familiarity with the Unix operating system, at least to the level of understanding the file system hierarchy and the basic commands for performing simple file manipulation tasks on the workstation.
The urchin model consists of 24 subpopulations linked by a dispersal matrix. One dimension of the dispersal matrix is the number of fertilized eggs that provide larvae for dispersal from each location, and the other dimension is the number of larvae that attempt to settle out of the plankton, at each of the 24 locations. The matrix entries reflect the fraction of the portion of larvae that originate at one location that settle at another location. The dispersal matrix is currently created outside the program, then input, but we plan to allow options for creating it within the program.
Each urchin subpopulation is a size structured population model with von Bertalanffy growth and L¥ varying among individuals. The model keeps track of size-at-age for values of L¥ out to +/- 3 standard deviations (10 values per standard deviation, for a total of 61 possible values of L¥ ) from the mean L¥ up to a maximum age of 30 years (360 months). Since there are 24 independent subpopulations in the model, and they can each have different growth and mortality parameters, there are 24 size-at-age matrices. The abundance of organisms of each age and L¥ combination are stored in 24 abundance matrices of the same dimension as the size matrices. The algorithm below describes the computations of size distribution, egg production, and post-larval settlement that occurs at each site.
The details of the above algorithm are outlined as follows:
The model can be started either with the complete size and abundance
matrices filled in and specified in a state file or by specifying the 0 age class abundance distribution.
If the state file is not supplied, (and the initial distribution file is)
then the size-at-age computations are performed for each of the 24
sites. The size of an individual at age a with a value of L¥ indexed by s is:
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(1) |
where mL is the mean value of L¥, sL is the standard deviation and ksite is the von Bertalanffy k. The initial abundance matrix, A, for each site is set to all zeros except for the month 0 age class which is filled in from the data found in the initial distribution file.
If the initial state data is provided, then the size and abundance matrices are loaded directly from this file.
The populations are aged by advancing the abundance values for each
month to the next older month:
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(2) |
After the populations are aged, the survival of the populations is computed
along with the catch (if the phase is final). The equations for these computations
are described below:
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(3) |
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(4) |
Where m is the site specific value of natural mortality rate as specified on the site window, Llimit is the lower size limit on the catch that is set on the control window, f is fishing mortality rate and can vary by site. It will be generated based on economic models in the future. C is the catch value, which is computed for each site. The constants w and b have been derived from the allometric relationship between sea urchin weight and length and are set from the control panel.
After survival is computed, the month of the simulation is checked.
If it is spawning month specified by the user, then egg production is computed.
The egg vector (24 elements, one for each site) is given by:
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(5) |
The egg production is limited to urchins who's test size is larger than a constant Lmaturity (this value is set on the control window).
During the months specified by user input, settlement of the larva is
computed. For each month, a fraction of the egg production of each
site is used to compute larva survival:
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(6) |
Where p is the percentage of eggs produced that survive to settlement and D is the dispersal matrix as specified by the user on the control panel.
The number that actually settle at each site is then computed from a
Beverton-Holt stock recruitment relationship:
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(7) |
Where c is the asymptotic value of post settlement abundance at high pre-settlement
abundance and a is the ratio of post settlement to pre-settlement at low
pre-settlement. Then the age zero element of the abundance matrix, A, for
each site is the number reaching post settlement distributed over size:
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(8) |
Where N is the normal distribution, m
is L¥ for the site, s
is s L and sout
is the element of 
for
the site specified.
BigUrchin can be run in two ways. First it can be run interactively through its graphical interface. This requires the user to be in front of a Unix terminal or X-window capable machine. The user can watch the output displayed graphically (figures 5 and 6) while the model updates it as it processes. In addition, the displayed output values are stored in ASCII files for later analysis. The second method of running BigUrchin is in a batch mode. Batch mode does not use any of the program's graphics and can be set up to run numerous simulations while the user does other things.
The model is structured so that the simulation can be run for a user specified number of months with no fishing pressure. This is the Initial Phase of the model. After the initial phase the model starts including the fishing pressure values in computing mortality.
The population can be started from an initial single month size distribution or from a complete abundance distribution for all ages at all sites.
The running of the model is done through the control window (Figure
2). It contains most of the inputs of the model. To make a run of the model,
the inputs need to be filled out correctly and then the Go button is clicked.
Each input field is documented in Table 1.
Figure 2. Control Form
The control window has a tool bar of icons that are used in controlling the flow of the model (Figure 3). The Go button starts the model. When the model is running the cursor changes to a watch and the Go button becomes the Stop Button. Pressing the Stop button while the model is running stops the model at the end of a year (as defined by the Output Month value). Once the model is stopped any input can be modified and the model restarted (by clicking on the Go button). Note that L inf, sigma and k are values that are used in the set-up equations and so changing them after the model has been running will have no effect on the model.
Figure 3. Tool bar
The buttons from left to right in the figure are: Go/Stop, Open, Clear,
Save, Exit, Help Show/Hide Graphs and Show/Hide Charts
The Clear button will clear the inputs from both the control window and the site window.
The Save button brings up a file selection box. The user can then enter a filename and an input file containing the values on the control and site windows is written out.
The Open button brings up a file selection box. The user can then select an input file and the values are loaded into the control and site windows.
The Exit button is used to end the program.
The Help button brings up this document.
The Show/Hide Graphs button toggles the display of the graphs window. The Show/Hide Charts button toggles the display of the size distribution window.
The model allows certain parameters to be specific per site. These parameters are found on the Site Window (Figure 4). On this window there are text fields for each parameter for each site.
Table 1: Input Data for the Model
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| Initial Duration | initial_duration | 0-10,000 months | Model run without fishing |
| Final Duration | model_duration | 0-10,000 months | Model run with fishing |
| Starting Month | start_month | jan-dec | Input file accepts month spelled out fully or three letter abbreviation |
| Output Month | print_month | jan-dec | Input file accepts month spelled out fully or three letter abbreviation |
| Initial Distribution File | init_dist_file | Unix file name | File contains 61 values. Initial abundance for 0 age class 3 sigma range of size. |
| Initial State File | init_state_file | Unix file name | File is generated from a prior run of BigUrchin |
| Lower Size Limit | lower_size_limit | 0-500 mm | Lowest size class that fishing operates on |
| Reproductive Maturity | l_mature | 0-500 mm | Abundances of size classes > that this size are used in egg production |
| Recruit Type | recruit_type | spawning or constant | To set this value in the file, use a 1 to set to spawning and a 2 to set to constant. If constant is selected, then Initial Distribution File must also be entered. |
| Spawning Month | spawn_month | jan-dec | Input file accepts month spelled out fully or three letter abbreviation |
| Settling Start Month | settle_month | jan-dec | Input file accepts month spelled out fully or three letter abbreviation |
| Settling Duration | settle_duration | 1-12 months | |
| Dispersal Filename | dispersal_file | Unix filename | File consists of 24 by 24 array of numbers. Each row is the dispersal pattern from a site. |
| Coherent Environment | coherent_environment | yes/no | File value should be either "yes" or "no". If yes the gaussian environmental noise is applied to all sites with the same value. If no, the noise is computed individually for each site. |
| Environmental Sigma | environmental_sd | Any real number | The environmental noise is gaussian with a mean of 0. This value is the standard deviation of the noise. If no noise is wanted set coherent environment to yes and this value to 0. |
| b | b_const | Constant value used in equation (4) | |
| c | post_dispersal_c | Constant value used in equation (7) | |
| w | weight_const | Constant value used in equation (4) | |
| Harvest Refugia | rotation_rate | 1,2,3,4,6 | Rotating harvest schedule. For constant harvesting at all sites use 1. A value of 2 means that every site will be harvested once every 2 years. |
| Size Data File | output_file | Unix filename | This file stores the size distribution per site per year (written out during the print_month {Output Month}) |
| Yearly Data Prefix | yearly_data_file | Unix filename | This value is the prefix to a set of files that store yearly values per site for settlement, successful settlement, egg production and catch. So, the user will see four files with the prefix followed by .eggs, .catch, .settle, .success_settle |
| Output State File | output_state_file | Unix filename | This file stores the abundance and size values (Size and A matrices from the equations section) for all 24 sites. It can then be used for Initial State File. |
| Output Initial Data | display_init_data | yes/no | Yes means that the size distributions for initial phase will be written to Size Data File |
| Last Output Only | single_output | yes/no | Yes means only the last year of initial phase and last year of final phase will be written to the Size Data File |
| Max Organism Size | max_organism_size | 0-500 mm | Used to scale the output bins for size classes |
| Num Size Class | num_size_class | 0-500 | Number of bins to be used in output of size distribution. This value should be a divisor of max organism size. |
| Measurement Error | use_mean_error | yes/no | Simulates sampling error in population |
| % Error | mean_error | Percent error used in simulating the error of sampling | |
| Sample Size | sample_size | 0-100,000 | Number of samples to be taken from each site to estimate distribution |
| f | f_values | 24 values in the input file or data on the site form. Used in equations (3) and (4) | |
| m | m_values | 24 values in the input file or data on the site form. Used in equation (3) | |
| L | l_infinity | 0.0-500.0 | 24 values in the input file or data on the site form. Used equation (1) |
| sigma | sigma_l_infinity | 0.0-500.0 | 24 values in the input file or data on the site form. Used in equation (1) |
| k | k_values | 24 values in the input file or data on the site form. Used in equation (1) | |
| a | a_values | 24 values in the input file or data on the site form. Used in equation (1) |
Batch mode is run without the graphical interface. It does not allow for the modification of parameters during the run, but does not require continuous work by the user. Batch mode is invoked by the following command: BigUrchin -b <input filename>. The input file used in executing batch mode is a simple text file. Each line of the file contains one paramter (for site specific data all 24 values are listed on the line). Each line starts with the Input File Name as found in Table 1. This value is followed by a colon and then the data is put on the line. The distribution of BigUrchin comes with a file called defaults.txt. Please refer to this file as a specific example of the input file. To make multiple runs, create a text file and on each line include the batch command as described above. Each run should have a different input filename. The text file should be set as an executable file (see a Unix manual or your system administrator to do this). Then the batch file can be executed and multiple runs will be produced.
Outputs
Once the model is begun, two output displays appear. These displays
are updated continuously throughout the run (during the user specified
output month).
The Graph Window (Figure 5) contains 12 graphs. On each one is two sites. The odd numbered site is displayed in black and the even numbered site is displayed in red. The graph window also contains a pull down menu that lets the user select which types of graphs to be displayed. The current types include egg production, catch, initial settlement and successful settlement (recruitment). The data that is displayed in these graphs is the data that is written out to the files generated with the Yearly Data Prefix.
The Charts Window (Figure 6) contains 24 bar charts. Each chart consists of a site's size distribution. The charts are all scaled uniformly (currently the graphics do not allow for a maximum y-axis value). The data in blue is below the lower size limit while data in red is fishable. When the model is in final phase and the rotating spatial harvest is in effect, the sites that are being fished have a white background and those that are refuges have gray backgrounds. The data that is displayed on this window is stored in text form in the Size Data File.
Figure 6: Size Distribution Display
Note: BigUrchin does not provide a method for printing the graphics data directly. The suggested technique is to use the product, xv to take a snapshot of the window and to use this for printing. Since all the data displayed on the graphs and charts appears in text files, the user can generate graphics offline by using these text files.