Revision as of 04:54, 17 October 2014

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Purpose

The fish model allows users to see the effects of different concentrations of estrogen on a freshwater ecosystem containing algae, fish, and birds. The model attempts to capture the long-term effects of estrogen on male fish, and demonstrates how sensitive a freshwater ecosystem can be to various concentrations of estrogen. model is and it complex A stochastic model employs probability to determine the behavior of its components, thus it is the best type of model to capture the randomness of an ecosystem. The model was also demonstrated to local public school teachers so that they could help their students visualize interactions between different organisms and organisms and their environment. The current lake we are simulating is fictional, however, the code has been developed in such a way that one could substitute the parameters in our model with parameters they have received from a particular lake they wish to test.

Outline

The fish model follows a simple tropic pyramid structure. The algae is the food source of the fish, which in turn are the food source for the birds. If no estrogen is introduced into the environment, the ecosystem is stable and the model simulates what is essentially the predator-prey interaction. Initially there is a relatively high amount of fish, and relatively low amounts of birds and algae. This puts a strain on the fish population, while simultaneously making it easy for the birds to find prey due to the combination of a large food source and low competition for that food source. Thus this leads to a dip in the fish population and a peak in the bird population. The dip in the fish population also leads to a peak in the algae population, as the algae can grow without being consumed as fast due to the lack of fish. This scenario puts a strain on the bird population as there is now too much competition for a smaller food source, while simultaneously making it easy for the fish to find food due to the combination of a large food source and low competition for that food source. Thus the population is back to the initial starting conditions, and the model continues to cycle through these scenarios ad infinitum. The user can tamper with the ecosystem by adding varying concentrations of estrogen. The estrogen leads to the feminization of male fish, with higher concentrations of estrogen corresponding to an increased likely hood of feminization. Feminized male fish cannot reproduce, which leads to more frequent dips in the fish population and can throw the entire ecosystem out of the equilibrium that was described above. To run the model simply go to the interface tab, hit setup, and then run. Each fish in the model represents a school of 100 fishes.

The Parameters

The parameters do not entirely reflect reality. For example both the max age of the fish and birds are the same in the model, even though in actuality birds typically live much longer than fish. However, the parameters are organized in such a way that the math for the model works out in a manner which is easy to program. Essentially the most important thing for the model to do is capture the effects of estrogenic on a freshwater ecosystem, which is what the default parameters do.

Parameter	Value (if applicable)	Reasoning (if applicable)
water-color	blue	Aesthetic purposes. Static value.
male-fish-color	cyan	Aesthetic purposes. Static value.
female-fish-color	pink	Aesthetic purposes. Static value.
feminized-fish-color	yellow	Aesthetic purposes. Static value.
bird-color	orange	Aesthetic purposes. Static value.
algae-color	green-scale	Aesthetic purposes. Static value. Darker green squares correspond to more algae.
fish-stride	0.8	The distance traveled each tick. Static value.
bird-stride	0.5	The distance traveled each tick. Static value. Birds should be a little slower than the fish so that the fish are not decimated.
fish-size	0.8	Relative size of the fish. Static value.
bird-size	1.2	Relative size of the birds. Static value. Birds should be bigger than their prey.
fish-reproduction-age	20	The age at which a fish is mature enough to reproduce. Static value.
bird-reproduction-age	20	The age at which a bird is mature enough to reproduce. Static value.
fish-max-age	100	The age at which a fish will die of old age. Static value.
bird-max-age	100	The age at which a bird will die of old age. Static value.
max-fish-offspring	2	Maximum number of offspring a female fish can produce each time she successfully reproduces. Static value. DO NOT CHANGE as the value must always be greater than the max number of offspring a bird can produce but almost all computers cannot handle a value of > 2.
max-bird-offspring	1	Maximum number of offspring a female bird can produce each time she successfully reproduces. Static value. DO NOT CHANGE as the value must always be less than the max number of offspring a fish can produce but almost all computers cannot handle a value of > 1.
male?	true/false	Assigned when an agent is born. Static at birth. 50% chance of being true.
energy	≤ 100	Initialized to 100 when an agent is born. If it is less than or equal to 0, then the agent dies. Increases as the agent consumes food, up to a max value of 100. Decreases by a fixed amount each tick.
current-age	0-100	The age of an agent. Initialized to 0 when an agent is born. Incremented by one each tick.
estrogen-concentration	≥ 0	Initialized to 0. Represents the current concentration of estrogen (ppt) in the water. Decreases over time and as fish are feminized. Can be increased by the user.
estrogen-resistance	200	The ability of a male fish to resist feminization. Static value. Higher number corresponds to higher base resistance (different types of fish resist estrogen to various extents so the model can be used to simulate different freshwater sources).
estrogen-accumulated-max	0.1	Essentially captures how much estrogen can be accumulated in the fat tissue of a male fish over time. Static value.
estrogen accumulated	≤ estrogen-stored-max	The current amount of estrogen accumulated in a male fish due to exposure to estrogen from environment. As this number increases the chance a male fish is feminized also increases.
algae-energy	0-100	The amount of algae present in a square. If it equals 0, then there is no algae present in the square and the square is blue.
algae-growth-rate	10	The amount of energy an algae tile gains each time it reproduces. Static value.
algae-growth-delay	15	The amount of time the algae needs to wait before it can reproduce. Static value.
algae-max-energy	100	The maximum amount of algae that can be located in a tile. Static value.
fish-survival	0.30	Probability that a fish makes it out of infancy. Static value.
bird-survival	0.15	Probability that a bird makes it out of infancy. Static value.
fish-find-egg	10	The more male fish there are the greater the chance is that an egg is fertilized. Increasing this number increases the number of male fish needed to fertilize eggs (a large body of water will have a greater value for this parameter).
bird-egg	1	The more male birds there are the greater the chance is that an egg is fertilized. Increasing this number increases the number of male birds needed to fertilize eggs (a large body ecosystem will have a greater value for this parameter).

Insight

In the following section we explain the reasoning behind the two stochastic processes employed in the model: • Feminization of the male fish • Reproduction of the birds/fish. All male fish accumulate estrogen in their bodies when exposed to high levels of estrogen in their environment. Juvenile males will be more affected by exposure to estrogen, thus they will store it at a faster rate than sexually matured males. The rate of estrogen storage for a juvenile male fish is captured by the formula below: Estrogen stored = min (estrogen-stored + estrogen concentration * 0.001, estrogen stored max) Mature male fish store estrogen at a slower rate. A male fish is defined as mature when its age is greater than or equal to the age it is old enough to reproduce. The rate of estrogen storage for a mature male fish is captured by the formula below: Estrogen stored = min (estrogen-stored + estrogen concentration * 0.0005, estrogen stored max) The model updates the state of each agent each tick. A tick is essentially representative of all the life functions an agent needs to carry out. In a tick each organism will consume food, increment its age, move, reproduce, and determine whether or not it needs to die. Each tick, the model of a male fish will call a function that uses a random number generator (RNG) to determine whether or not they are feminized. The chance for a male fish to be feminized is captured by the formula below: Feminization chance = (estrogen concentration in lake/estrogen resistance of species of fish) + estrogen stored in the particular fish’s body The RNG then generates a floating point number between 0 and 1.0. If said number is less than the feminization chance of a particular male fish, then that particular male fish will become feminized. Thus fish with high amounts of estrogen accumulated in their body (representing a prolonged exposure to estrogen) and placed in a very estrogenic environment will have a high chance of becoming feminized. The reproduction function for both the fish and birds follow the same exact principles (they differ in only the parameters they use). The fish reproduction function will be explained below, and the reasoning will be the exact same for the bird reproduction function. Essentially each female fish that is above the reproduction age will call a reproduction function that uses RNG to determine whether or not it successfully creates offspring. The chance that a female reproduces is based on the following formula below: Reproduction chance = chance newborn fish survive infancy * (fertile males) / (males + constant that males find Thus the chance any female can successfully reproduced varies as a function of the number of fertile males of reproduction age. If there are only a few males in the lake relative to the size of the lake, adding more males will greatly increase the chance that the eggs of a female are fertilized. Conversely if there are a large number of males in the lake additional males will not really affect the rate at which eggs are fertilized. The constant fish- find-egg represents the number of males after which additional males will not greatly affect the rate at which eggs are fertilized. female to reproduce with)

Results

The most important thing to take away from the model is how fickle the organisms at the top of the food chain are to changes in the chemical composition of the water. Even though the estrogen directly affects the fish by feminizing them, the birds are the species which are more prone to dying out first if the estrogen level is too high as they are highly responsive to even slight dips in the population of their food source, due to the fact that they are a trophic level higher than the fish.

INSERT GRAPHS

References:
Novak, M. and Wilensky, U. (2011). NetLogo Bug Hunt Predators and Invasive Species model. http://ccl.northwestern.edu/netlogo/models/BugHuntPredatorsandInvasiveSpecies. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

@@ Line 99: / Line 99: @@
 <h1><center>Purpose</center> </h1>
-<p> <center> The stochastic fish model was written in NetLogo, an agent-based modeling language which allows users
+<p> <center> The fish model allows users to see the effects of different concentrations of estrogen on a freshwater ecosystem
-to view and analyze interactions between agents and their environment in an attempt to model complex
+containing algae, fish, and birds. The model attempts to capture the long-term effects of estrogen on male fish,
-interactions. The fish model allows users to see the effects of different concentrations of estrogen on a
+and demonstrates how sensitive a freshwater ecosystem can be to various concentrations of estrogen. model is
-freshwater ecosystem containing algae, fish, and birds. The model attempts to capture the long term effects of
+and it complex A stochastic model employs probability to determine the behavior of its components, thus it is
-estrogen on male fish, and demonstrates how sensitive a freshwater ecosystem can be to various concentrations
+the best type of model to capture the randomness of an ecosystem. The model was also demonstrated to local
-of estrogen. The model was also employed in local public schools in the area to help students visualize
+public school teachers so that they could help their students visualize interactions between different organisms
-interactions between different organisms and organisms and their environment. The current lake I am
+and organisms and their environment. The current lake we are simulating is fictional, however, the code has
-simulating is fictional, however, the code has been developed in such a way that one could in theory substitute
+been developed in such a way that one could substitute the parameters in our model with parameters they have
-my parameters with parameters they have received from a particular lake they wish to test. <center></p>
+received from a particular lake they wish to test. <center></p>
 <hr>
 <h2> <center>Outline</center></h2>
-<p> <center> The fish model follows a simple food pyramid structure. The algae is the food source of the fish, which in
+<p> <center> The fish model follows a simple tropic pyramid structure. The algae is the food source of the fish, which
-turn are the food source for the birds. If no estrogen is introduced into the environment, the ecosystem is
+in turn are the food source for the birds. If no estrogen is introduced into the environment, the ecosystem is
 stable and the model simulates what is essentially the predator-prey interaction. Initially there is a relatively
@@ Line 148: / Line 148: @@
 fish population and can throw the entire ecosystem out of the equilibrium that was described above.
-To run the model simply go to the interface tab, hit setup, and then run. <center></p>
+To run the model simply go to the interface tab, hit setup, and then run.
+Each fish in the model represents a school of 100 fishes. <center></p>
 <hr>
 <h2> <center>The Parameters</center></h2>
+<p>The parameters do not entirely reflect reality. For example both the max age of the fish and birds are the same
+in the model, even though in actuality birds typically live much longer than fish. However, the parameters
+are organized in such a way that the math for the model works out in a manner which is easy to program.
+Essentially the most important thing for the model to do is capture the effects of estrogenic on a freshwater
+ecosystem, which is what the default parameters do.</p>
 <table border="1" cellspacing="0" cellpadding="0">
      <tbody>
@@ Line 164: / Line 176: @@
                  </p>
              </td>
-             <td width="224" valign="top">
+             <td width="156" valign="top">
                  <p align="center">
                      <strong>Reasoning (if applicable)</strong>
@@ Line 181: / Line 193: @@
                  </p>
              </td>
-             <td width="224" valign="top">
+             <td width="156" valign="top">
                  <p align="center">
                      Aesthetic purposes. Static value.
@@ Line 198: / Line 210: @@
                  </p>
              </td>
-             <td width="224" valign="top">
+             <td width="156" valign="top">
                  <p align="center">
                      Aesthetic purposes. Static value.
@@ Line 215: / Line 227: @@
                  </p>
              </td>
-             <td width="224" valign="top">
+             <td width="156" valign="top">
                  <p align="center">
                      Aesthetic purposes. Static value.
@@ Line 232: / Line 244: @@
                  </p>
              </td>
-             <td width="224" valign="top">
+             <td width="156" valign="top">
                  <p align="center">
                      Aesthetic purposes. Static value.
@@ Line 249: / Line 261: @@
                  </p>
              </td>
-             <td width="224" valign="top">
+             <td width="156" valign="top">
                  <p align="center">
                      Aesthetic purposes. Static value.
@@ Line 266: / Line 278: @@
                  </p>
              </td>
-             <td width="224" valign="top">
+             <td width="156" valign="top">
                  <p align="center">
                      Aesthetic purposes. Static value. Darker green squares correspond to more algae.
@@ Line 283: / Line 295: @@
                  </p>
              </td>
-             <td width="224" valign="top">
+             <td width="156" valign="top">
                  <p align="center">
                      The distance traveled each tick. Static value.
@@ Line 300: / Line 312: @@
                  </p>
              </td>
-             <td width="224" valign="top">
+             <td width="156" valign="top">
                  <p align="center">
                      The distance traveled each tick. Static value. Birds should be a little slower than the fish so that the fish are not decimated.
@@ Line 317: / Line 329: @@
                  </p>
              </td>
-             <td width="224" valign="top">
+             <td width="156" valign="top">
                  <p align="center">
                      Relative size of the fish. Static value.
@@ Line 334: / Line 346: @@
                  </p>
              </td>
-             <td width="224" valign="top">
+             <td width="156" valign="top">
                  <p align="center">
                      Relative size of the birds. Static value. Birds should be bigger than their prey.
@@ Line 351: / Line 363: @@
                  </p>
              </td>
-             <td width="224" valign="top">
+             <td width="156" valign="top">
                  <p align="center">
                      The age at which a fish is mature enough to reproduce. Static value.
@@ Line 368: / Line 380: @@
                  </p>
              </td>
-             <td width="224" valign="top">
+             <td width="156" valign="top">
                  <p align="center">
                      The age at which a bird is mature enough to reproduce. Static value.
@@ Line 385: / Line 397: @@
                  </p>
              </td>
-             <td width="224" valign="top">
+             <td width="156" valign="top">
                  <p align="center">
                      The age at which a fish will die of old age. Static value.
@@ Line 402: / Line 414: @@
                  </p>
              </td>
-             <td width="224" valign="top">
+             <td width="156" valign="top">
                  <p align="center">
                      The age at which a bird will die of old age. Static value.
@@ Line 419: / Line 431: @@
                  </p>
              </td>
-             <td width="224" valign="top">
+             <td width="156" valign="top">
                  <p align="center">
                      Maximum number of offspring a female fish can produce each time she successfully reproduces. Static value. DO NOT CHANGE as the value must
@@ Line 437: / Line 449: @@
                  </p>
              </td>
-             <td width="224" valign="top">
+             <td width="156" valign="top">
                  <p align="center">
                      Maximum number of offspring a female bird can produce each time she successfully reproduces. Static value. DO NOT CHANGE as the value must
@@ Line 455: / Line 467: @@
                  </p>
              </td>
-             <td width="224" valign="top">
+             <td width="156" valign="top">
                  <p align="center">
                      Assigned when an agent is born. Static at birth. 50% chance of being true.
@@ Line 469: / Line 481: @@
              <td width="156" valign="top">
                  <p align="center">
-                     &lt;= 100
+                     ≤ 100
                  </p>
              </td>
-             <td width="224" valign="top">
+             <td width="156" valign="top">
                  <p align="center">
                      Initialized to 100 when an agent is born. If it is less than or equal to 0, then the agent dies. Increases as the agent consumes food, up
@@ Line 490: / Line 502: @@
                  </p>
              </td>
-             <td width="224" valign="top">
+             <td width="156" valign="top">
                  <p align="center">
                      The age of an agent. Initialized to 0 when an agent is born. Incremented by one each tick.
@@ Line 504: / Line 516: @@
              <td width="156" valign="top">
                  <p align="center">
-                     &gt;= 0
+                     ≥ 0
                  </p>
              </td>
-             <td width="224" valign="top">
+             <td width="156" valign="top">
                  <p align="center">
                      Initialized to 0. Represents the current concentration of estrogen (ppt) in the water. Decreases over time and as fish are feminized. Can
@@ Line 525: / Line 537: @@
                  </p>
              </td>
-             <td width="224" valign="top">
+             <td width="156" valign="top">
                  <p align="center">
                      The ability of a male fish to resist feminization. Static value. Higher number corresponds to higher base resistance (different types of
@@ Line 535: / Line 547: @@
              <td width="156" valign="top">
                  <p align="center">
-                     estrogen-stored-max
+                     estrogen-accumulated-max
                  </p>
              </td>
@@ Line 543: / Line 555: @@
                  </p>
              </td>
-             <td width="224" valign="top">
+             <td width="156" valign="top">
                  <p align="center">
-                     Essentially captures how much estrogen can be stored in a male fish over time. Static value.
+                     Essentially captures how much estrogen can be accumulated in the fat tissue of a male fish over time. Static value.
                  </p>
              </td>
@@ Line 552: / Line 564: @@
              <td width="156" valign="top">
                  <p align="center">
-                     estrogen stored
+                     estrogen accumulated
                  </p>
              </td>
              <td width="156" valign="top">
                  <p align="center">
-                     &lt;= estrogen-stored-max
+                     ≤ estrogen-stored-max
                  </p>
              </td>
-             <td width="224" valign="top">
+             <td width="156" valign="top">
                  <p align="center">
-                     The current amount of estrogen stored in a male fish due to exposure to estrogen from environment. As this number increases the chance a
+                     The current amount of estrogen accumulated in a male fish due to exposure to estrogen from environment. As this number increases the chance
-                     male fish is feminized also increases.
+                     a male fish is feminized also increases.
                  </p>
              </td>
@@ Line 578: / Line 590: @@
                  </p>
              </td>
-             <td width="224" valign="top">
+             <td width="156" valign="top">
                  <p align="center">
                      The amount of algae present in a square. If it equals 0, then there is no algae present in the square and the square is blue.
@@ Line 595: / Line 607: @@
                  </p>
              </td>
-             <td width="224" valign="top">
+             <td width="156" valign="top">
                  <p align="center">
                      The amount of energy an algae tile gains each time it reproduces. Static value.
@@ Line 612: / Line 624: @@
                  </p>
              </td>
-             <td width="224" valign="top">
+             <td width="156" valign="top">
                  <p align="center">
                      The amount of time the algae needs to wait before it can reproduce. Static value.
@@ Line 629: / Line 641: @@
                  </p>
              </td>
-             <td width="224" valign="top">
+             <td width="156" valign="top">
                  <p align="center">
                      The maximum amount of algae that can be located in a tile. Static value.
@@ Line 646: / Line 658: @@
                  </p>
              </td>
-             <td width="224" valign="top">
+             <td width="156" valign="top">
                  <p align="center">
                      Probability that a fish makes it out of infancy. Static value.
@@ Line 663: / Line 675: @@
                  </p>
              </td>
-             <td width="224" valign="top">
+             <td width="156" valign="top">
                  <p align="center">
                      Probability that a bird makes it out of infancy. Static value.
@@ Line 680: / Line 692: @@
                  </p>
              </td>
-             <td width="224" valign="top">
+             <td width="156" valign="top">
                  <p align="center">
                      The more male fish there are the greater the chance is that an egg is fertilized. Increasing this number increases the number of male fish
@@ Line 698: / Line 710: @@
                  </p>
              </td>
-             <td width="224" valign="top">
+             <td width="156" valign="top">
                  <p align="center">
                      The more male birds there are the greater the chance is that an egg is fertilized. Increasing this number increases the number of male
@@ Line 709: / Line 721: @@
 <h2> <center>Insight</center></h2>
-<p> <center> In the following section will explain the reasoning behind the two stochastic processes employed in the model: the feminization of the male fish and the reproduction of the birds/fish.
+<p> <center> In the following section we explain the reasoning behind the two stochastic processes employed in the model:
+• Feminization of the male fish
+• Reproduction of the birds/fish.
+All male fish accumulate estrogen in their bodies when exposed to high levels of estrogen in their environment.
+Juvenile males will be more affected by exposure to estrogen, thus they will store it at a faster rate than sexually
+matured males. The rate of estrogen storage for a juvenile male fish is captured by the formula below:
+Estrogen stored = min (estrogen-stored + estrogen concentration * 0.001, estrogen stored max)
+Mature male fish store estrogen at a slower rate. A male fish is defined as mature when its age is greater than or
+equal to the age it is old enough to reproduce. The rate of estrogen storage for a mature male fish is captured by
+the formula below:
+Estrogen stored = min (estrogen-stored + estrogen concentration * 0.0005, estrogen stored max)
+The model updates the state of each agent each tick. A tick is essentially representative of all the life functions
+an agent needs to carry out. In a tick each organism will consume food, increment its age, move, reproduce, and
+determine whether or not it needs to die.
+Each tick, the model of a male fish will call a function that uses a random number generator (RNG) to
+determine whether or not they are feminized. The chance for a male fish to be feminized is captured by the
+formula below:
+Feminization chance = (estrogen concentration in lake/estrogen resistance of species of fish) + estrogen stored
+in the particular fish’s body
+The RNG then generates a floating point number between 0 and 1.0. If said number is less than the feminization
+chance of a particular male fish, then that particular male fish will become feminized. Thus fish with high
+amounts of estrogen accumulated in their body (representing a prolonged exposure to estrogen) and placed in a
+very estrogenic environment will have a high chance of becoming feminized.
+The reproduction function for both the fish and birds follow the same exact principles (they differ in only the
+parameters they use). The fish reproduction function will be explained below, and the reasoning will be the
+exact same for the bird reproduction function.
+Essentially each female fish that is above the reproduction age will call a reproduction function that uses RNG
+to determine whether or not it successfully creates offspring. The chance that a female reproduces is based on
-All male fish are capable of storing estrogen in their bodies when exposed to high levels of estrogen in their environment. Juvenile males will be more affected by exposure to estrogen, thus they will store it at a faster rate than sexually matured males.
+the following formula below:
-Each tick, the males will call a function that uses a RNG to determine whether or not they are feminized. The chance a male fish has of being feminized is captured by the formula below:</br></br>
+Reproduction chance = chance newborn fish survive infancy * (fertile males) / (males + constant that males find
-Feminization chance = (estrogen concentration in lake/estrogen resistance of species of fish) + estrogen stored in the particular fish’s body</br></br>
+Thus the chance any female can successfully reproduced varies as a function of the number of fertile males of
-The RNG then generates a floating point number between 0 and 1.0. If said number is less than the feminization chance of a particular male fish, then that particular male fish will become feminized. Thus fish with high amounts of estrogen stored in their body (representing a prolonged exposure to estrogen) and placed in a very estrogenic environment will have a high chance of becoming feminized.
+reproduction age. If there are only a few males in the lake relative to the size of the lake, adding more males
-The reproduction function for both the fish and birds follow the same exact principles (they differ in only the parameters they use). The fish reproduction function will be explained below, and the reasoning will be the exact same for the bird reproduction function.
+will greatly increase the chance that the eggs of a female are fertilized. Conversely if there are a large number of
-Essentially each female fish that is above the reproduction age will call a reproduction function that uses RNG to determine whether or not it successfully creates offspring. The chance that a female reproduces is based on the following formula below:</br></br>
+males in the lake additional males will not really affect the rate at which eggs are fertilized. The constant fish-
+find-egg represents the number of males after which additional males will not greatly affect the rate at which
-Reproduction chance = chance newborn fish survive infancy * (fertile males) / (males + constant that males find female to reproduce with)</br></br>
+eggs are fertilized.
-Thus the chance any female can successfully reproduced varies as a function of the number of fertile males of reproduction age. If there are only a few males in the lake relative to the size of the lake, adding more males will greatly increase the chance that the eggs of a female are fertilized. Conversely if there are a large number of males in the lake additional males will not really affect the rate at which eggs are fertilized. The constant fish-find-egg represents the number of males after which additional males will not greatly affect the rate at which eggs are fertilized.
+female to reproduce with)
 <center></p>

Team:Carnegie Mellon/Fish

From 2014.igem.org