Natural resource managers often use quantitative methods to characterize and manage ecosystems. A firm understanding of these methods, ranging from simple counts to complex models, is critical in conducting accurate population and community assessments. Students can gain an advantage in understanding these methods through early exposure and contextual examples. This fictional case study follows three American Fisheries Society club members who perform an ecological assessment of a landowner’s ponds. The club members use multiple sampling methods and analyses to answer the landowner’s questions. In this study, students are introduced to common assessment metrics, such as community patterns (richness, diversity, evenness, and similarity), abundance estimates (mark-recapture, depletion, swept-area, and line-transect), size structure (proportional stock density), and growth estimates (absolute, relative, and instantaneous growth rates; von Bertalanffy growth model). Students will also interpret results and identify physical or biological factors that may influence those results. After completing this case study, students will be able to describe the need for population and community assessments and apply these assessments to various scenarios.

## INTRODUCTION

Natural resource managers often use quantitative methods to characterize and manage ecosystems on both public and private lands. This work often requires managers to solve problems using data and information collected during ecological assessments using field sampling methods and analyses. Managers then identify both biotic and abiotic issues and pathways to restore a healthy ecosystem function.

In this case study, a local student chapter of the American Fisheries Society (AFS) is recruited to help a local landowner to evaluate and solve her problem of declining fish catch in one of her ponds. The AFS club members work with her to survey her fish community and then analyze the data using several commonly used analyses to determine the cause of her local fish decline. After completing this case study, students will be able to describe the need for population and community assessments and apply these assessments to various scenarios, while also gaining a better understanding of the scientific process used in natural resource management.

## CASE EXAMINATION

### Part I—What’s in My Pond?

Shawn, Juliette, and Gus are Fish and Wildlife majors and members of their university’s AFS club. They joined the club in the fall and now, as soon-to-be seniors, are hoping to gain some hands-on experience before applying for technician positions and graduate school. Fortunately, their club advisor, Dr. Spencer, has found them an opportunity. A local landowner recently reached out to Dr. Spencer and asked if the AFS club could perform an assessment of her ponds. Eager to do fieldwork and use their quantitative skills for a real-world problem, the AFS club members quickly accept the offer and agree to meet the landowner on Saturday morning.

Morning! You all must be the group of students Dr. Spencer said could help me out. My name is Karen. How are you?

Nice to meet you, Karen. That is correct, we are with the AFS club. We are doing well, thank you! I am Gus, and this is Shawn and Juliette [both wave].

Thank you for inviting us out here. What can we help you with today?

Well, I bought this property 3 years ago and have really enjoyed fishing in the ponds. I caught quite a few fish in both ponds the first 2 years but have had barely any luck in the small pond this past year. I shared this with my neighbor down the road who works at the university, and they mentioned that the AFS club does pond assessments. I am curious why I cannot catch as many fish, and I am hoping you all can help me answer that question.

Sure thing. We can perform an assessment of your ponds and try to figure out the differences between them—like, what fish species you have and how many may be in each pond. Then, we can brainstorm some ideas of what factors may be causing your decline in catching in the smaller pond.

For this project, the AFS club members are assessing *lentic* (standing water; e.g., lakes and ponds) rather than *lotic* (moving freshwater; e.g., streams and rivers) systems. Lentic systems are commonly described by layers or zones, which are defined by temperature, light availability, and productivity. Surface waters receiving warmth from the sunlight and mixing by winds are separated from cool, unmixed waters at the thermocline. The upper layer of water penetrated by light is known as the *euphotic zone* (i.e., where photosynthesis occurs), which is dependent on light availability and water clarity. The *profundal zone* below receives no light and contains no photosynthetic activity. Lentic systems are also described by the degree of primary productivity occurring, on a gradient from oligotrophic (very low nutrient contents) to *eutrophic* (very high nutrient contents). Lakes naturally become eutrophic over time as nutrients accumulate, but the eutrophication process can be drastically expedited by human activities, like agricultural and urban runoff. Nutrient concentrations ultimately affect the biotic composition of a lentic system. Increased nutrient concentrations lead to increase respiration and turbidity, which influence temperature and oxygen concentrations. The temperature and amount of dissolved oxygen in the water will dictate the survival of various fish assemblages. For example, trout species thrive in cold, oxygen-rich water, while bass and sunfish species persist in warmer, oxygen-depleted water. Additional abiotic factors that influence these zones or layers include a waterbody’s physical characteristics (depth, surface area, and latitude), wind-driven circulation, and pH [1].

### Part II—Community Patterns

The landowner walks the three club members over to her ponds. As they observe the ponds for the first time, they ask themselves questions such as “what species are in the ponds?” and “how many of each?”. Developing an idea of the fish community present would provide the landowner with valuable information on her ponds.

The first pond is over here on the left. It is the larger of the two. I have caught several bluegills in both ponds and a few yellow perch in this big pond. I am not sure if there are any other species in the ponds though.

Not a problem. We should have a pretty good idea after we sample the ponds. What we will do is set a few nets, then identify and count all the fishes that we collect in those nets. After that, we can say how many species there are and describe the diversity within each pond. We will check in with you in a couple of hours.

[2 hours later]

How did your sampling go? Did you find any other fish in the ponds?

Oh yeah! Here is a breakdown of what we found living in your ponds.

Describing community patterns through different metrics helps managers to characterize communities and compare them with other areas [1, 2]. The simplest metric used, *richness* (S), is the number of species present in a given area.

Attempts to combine richness and abundance have resulted in various indices of *diversity*. The two most common indices are Simpson’s diversity (*D*) and Shannon’s diversity (*H*′). Simpson’s diversity index is a measure of dominance because more weight, or importance, is given to common species (Equation 1). *D* is a measure of concentration (i.e., as *D* increases, diversity decreases), so diversity is represented as 1 − *D*. On the other hand, Shannon’s diversity index assumes that all species are represented in the sample and randomly sampled (Equation 2). Although most diversity indices have some degree of correlation, each is inherently biased to some degree. Of the two indices described here, *D* is sensitive to more abundant species and *H*′ is sensitive to abundant and rare species [2].

*p _{i}* is the proportion of individuals in species

*i.*

*p _{i}* is the proportion of individuals found in

*i*th species.

#### Example 1

##### Simpson’s diversity

- Step 1:
- Step 2:
Calculate the proportion of each species in the third column. This is achieved by dividing the abundance of one species by the sum of all species abundances. In cell C2, type =B2/$B$9 and hit Enter. Then, select cell C2 and drag the bottom right corner of the green box to C8 to complete the function for all species. The “$” locks the “total abundance” cell in the equation when dragging down.

- Step 3:
Square the proportion of each species in the fourth column. In cell D2, type =C2^2 and hit Enter. Select D2 and drag down to complete function for all species.

- Step 4:
Calculate Simpson’s diversity by subtracting the sum of the squared proportions from one. Type =1−SUM(D2:D8) and hit Enter.

Species . | Pond 1 . | Pond 2 . |
---|---|---|

Black crappie | 6 | 0 |

Bluegill | 61 | 28 |

Largemouth bass | 14 | 8 |

Pumpkinseed | 23 | 11 |

Redear sunfish | 38 | 14 |

Smallmouth bass | 8 | 1 |

Yellow perch | 32 | 18 |

Species . | Pond 1 . | Pond 2 . |
---|---|---|

Black crappie | 6 | 0 |

Bluegill | 61 | 28 |

Largemouth bass | 14 | 8 |

Pumpkinseed | 23 | 11 |

Redear sunfish | 38 | 14 |

Smallmouth bass | 8 | 1 |

Yellow perch | 32 | 18 |

##### Shannon’s diversity

- Step 1:
Create a table in Excel with five columns, or for simplicity, add two additional columns to the table above (Figure 1)—natural log of proportion (ln(

*p*)), proportion multiplied by the natural log of proportion (*p**ln(*p*)). - Step 2:
Take the natural log of the proportion of each species in the fifth column. In cell E2, type =LN(C2) and hit Enter. Select E2 and drag down to complete function for all species.

- Step 3:
Multiply the proportion column by the natural log of the proportion for each species. In cell F2, type =C2*E2 and hit Enter. Select F2 and drag down to complete function for all species.

- Step 4:
Calculate Shannon’s diversity by taking the negative sum of the products of the proportion times the natural log of the proportion. Type =−SUM(F2:F8) and hit Enter.

*Evenness* compares the actual diversity of a sample to the maximum possible diversity, or rather, how individuals are split among species. Evenness is derived from the previous diversity indices, with both Simpson’s (Equation 3) and Shannon’s (Equation 4) measures:

*S* is species richness.

Several indices measure the similarity between communities. *Jaccard’s coefficient* accounts for the presence or absence of species between two communities, with no weight given for abundance of species (Equation 5). However, *Percent similarity* accounts for the abundance of species by calculating the proportion of individuals of each species relative to the total number of individuals. The lesser of each proportion is then summed for comparison (Equation 6).

*p* is # species present in both and *m* is # species present in one but not the other.

*j*, *k* is an assemblage and *i* is species.

#### Example 2

##### Percent similarity

- Step 1:
Create a table with six columns—species, abundance Pond 1, abundance Pond 2, the proportion of Pond 1 (

*p*1), the proportion of Pond 2 (*p*2), and the minimum proportion (Min*p*). Fill in the first three columns with the data provided (Figure 2). - Step 2:
Calculate the proportion of each species in the fourth and fifth columns. This is achieved by dividing the abundance of one species by the sum of all species abundances. For Pond 1, type = B2/$B$9 in cell D2 and hit Enter. For Pond 2, type =C2/$C$9 in cell E2 and hit Enter. Select cells D2 and E2, then drag down to complete the function for all species.

- Step 3:
Determine the minimum proportion between the ponds for each species. In cell F2, type =MIN(D2:E2) and hit Enter. Select F2 and drag down to complete the function for all species.

- Step 4:
Calculate percent similarity by taking the sum of the minimum proportions. Type =SUM(F2:F8) and hit Enter.

### Part III—Estimating Abundance

The AFS club was happy to gain a sense of the fish community and shared it with the landowner. Sensing her excitement from the information, they want to learn more about the ponds. A logical next step would be to develop an accurate estimate of abundance for each species.

You have some pretty popular species in your ponds. And in both, bluegill seems to be more abundant than every other species we found.

How neat! Happy to hear you found bluegill in there because I love to catch them. Any idea of how many bluegills are in each pond?

Yes, we do. We collected fishes with a couple of different methods to estimate their abundance.

Abundance estimates are used to estimate the number of individuals, cohorts, or populations in a given area. In most cases, it is difficult or impossible to count all wildlife in the environment, so abundances are commonly extrapolated from a sample. There are many abundance techniques used in fisheries and wildlife research and management, each with its own advantages and disadvantages [3, 4].

*Mark-recapture* involves initial capture of animals and then tagging all of these individuals with a unique individual marker (e.g., collar, passive integrated transponder (PIT) tag, dye, and fin clip). The marked animals during the first capture event (*M*) are then released back to their environment. After a specified amount of time, another sampling effort is performed in the same location with the same sampling techniques. Animals are identified as captures from the second effort (marked or unmarked *C*) or recaptured (*R*). These three categories are used to estimate the abundance of the population with Equation 7. For the mark-recapture method to provide a reasonable estimate, sampling should occur in a relatively closed population (e.g., an isolated reef or bay) [3].

The *depletion* method is based on the idea that if you can capture all of the individuals in a population, you will know the abundance. Because it is often impossible to capture all individuals, the method must extrapolate the abundance estimate. The estimate is obtained by performing a standard amount of effort to capture animals and removing them from the population. Then the same amount of effort is performed for a second time, again removing individuals from the population. This process is repeated until capture numbers with each sampling effort (also known as catch per unit effort (CPUE)) become very low (Figure 3). The linear relationship between cumulative catch (*k*; the sum of individuals caught and removed from the population) and CPUE is used to estimate the abundance with Equation 8. To acquire an accurate estimate through depletion, sampling a closed population is ideal [3].

intercept and slope of CPUE and cumulative catch (*k*).

#### Example 3

##### Depletion

- Step 1:
Create a table with five columns—pond, catch, effort, cumulative catch (

*k*), and CPUE. Fill in the second and third columns with the data provided (Figure 4). - Step 2:
Calculate the cumulative catch in the fourth column. The initial catch is zero, and each subsequent step adds the catch from the previous pass.

- Step 3:
Calculate CPUE in the fifth column. This is achieved by dividing the catch by the effort for each pass. In cell E2, type =B2/C2 and hit Enter. Select E2 and drag down to complete the function for each pass.

- Step 4:
Calculate the slope of the linear relationship between cumulative catch and CPUE. In cell H2, type =SLOPE(E2:E4,D2:D4) and hit Enter. The known

*x*’s are cumulative catch and known*y*’s are CPUE. - Step 5:
Calculate the intercept of the linear relationship between cumulative catch and CPUE. In cell H3, type =INTERCEPT(E2:E4,D2:D4) and hit Enter.

- Step 6:
Calculate the abundance by taking the negative quotient of the intercept and slope. In cell H4, type =−H3/H2 and hit Enter.

The *swept-area* method estimates the abundance of a large area (*A*) by measuring abundance (*n*) of a sub-area (*a*). This is typically done by visually counting the abundance of the sub-area. The following equation is used to estimate the abundance:

In areas where it is difficult to set traps or nets due to physical structure, the *line-transect* method can be used. This method assumes that there is great visibility and the probability of seeing the animal of interest is constant. Like the swept-area method, the line-transect method measures the abundance of a smaller area and then extrapolates the abundance to the total area. Abundance is estimated with the following equation:

*W* × *L* is the entire area, density is the catch/sample area, and *P* is the probability of seeing fishes.

### Part IV—Determining Size Structure

Now that the landowner knows what species are in her ponds and roughly how many, she begins to think about her favorite species to catch: bluegill. She has caught bluegill in both ponds but never gave much thought to their size. She wonders if she was catching small or large bluegill.

You three are awesome. It is so nice to know how many bluegills are in there. Do you have any idea how big they are?

As a matter of fact, we do!

In addition to counting the number of individuals caught for each species, the AFS club members measured the total length and weighed every individual. The collected length data are given in Question 1 of this section (Part IV).

Size structure provides managers with information on population dynamics including recruitment, growth, and mortality. One metric, proportional stock density (PSD), is a ratio of lengths that characterizes the size distribution of a population [6]. Managers often compare the stocking size of a fish to a length desired by anglers (Table 2). PSD is calculated with the following equation:

Species . | Stock . | Quality . | Preferred . | Memorable . | Trophy . |
---|---|---|---|---|---|

Black crappie | 5 | 8 | 10 | 12 | 15 |

Bluegill | 3 | 6 | 8 | 10 | 12 |

Largemouth bass | 8 | 12 | 15 | 20 | 25 |

Smallmouth bass | 7 | 11 | 14 | 17 | 20 |

Yellow perch | 5 | 8 | 10 | 12 | 15 |

Species . | Stock . | Quality . | Preferred . | Memorable . | Trophy . |
---|---|---|---|---|---|

Black crappie | 5 | 8 | 10 | 12 | 15 |

Bluegill | 3 | 6 | 8 | 10 | 12 |

Largemouth bass | 8 | 12 | 15 | 20 | 25 |

Smallmouth bass | 7 | 11 | 14 | 17 | 20 |

Yellow perch | 5 | 8 | 10 | 12 | 15 |

Table adapted from Gabelhouse Jr. DW [7].

*NQL* is # quality length and *NSL* is # stock length.

### Part V—Measuring Growth

The club members were enjoying the field work and thrilled the landowner wanted to know so much about her ponds. Recognizing they had collected quite a bit of data, they want to see if they can answer any other questions before leaving.

Sounds like there are some pretty good size fish in my ponds.

Yeah, a high PSD is something anglers really appreciate. Is there anything else you would like to know about the ponds?

Well actually I have been thinking about how big the fishes are. How much do you think they will grow this year? Is there any way we can track that?

Certainly! We can come back a few times and measure specific fish to track their growth.

That would be terrific. Thank you!

Over the next year, the AFS club members returned to the ponds to measure the fish length (averages for each year class presented in Table 3). They marked the fish so they could identify individuals.

Pond 1 . | Pond 2 . | ||
---|---|---|---|

. | |||

Age . | Length (mm) . | Age . | Length (mm) . |

1 | 47 | 1 | 44 |

2 | 75 | 2 | 69 |

3 | 90 | 3 | 83 |

4 | 99 | 4 | 89 |

5 | 109 | 5 | 95 |

6 | 120 | 6 | 104 |

Pond 1 . | Pond 2 . | ||
---|---|---|---|

. | |||

Age . | Length (mm) . | Age . | Length (mm) . |

1 | 47 | 1 | 44 |

2 | 75 | 2 | 69 |

3 | 90 | 3 | 83 |

4 | 99 | 4 | 89 |

5 | 109 | 5 | 95 |

6 | 120 | 6 | 104 |

The growth of individuals is measured to characterize the size or age of a population. Appropriate management, such as take or bag limits, can be designed around a population’s growth patterns. Growth can be presented in different ways, with each method accounting for different factors [8].

*Absolute growth* is the quickest and simplest measure of growth. In its simplest form, absolute growth has no relation to time (Equation 12). This measure is often seen as insufficient but can account for time with Equation 13.

*w _{t}* is final weight,

*w*is initial weight, and

_{i}*t*is time.

*Relative growth* rate expresses the absolute increase in weight relative to the initial weight. This is reported as a % increase using Equation 14. Much like the absolute growth rate above, an equation that accounts for time will provide a more accurate answer (Equation 15).

The *instantaneous growth* rate also relies on the absolute growth rate, but calculates values with the natural logarithm (ln):

The *von Bertalanffy* growth function is the most commonly used growth model in fisheries biology. This long-term measure of growth does not necessarily fit for an animal’s entire lifespan because pre-adult stages may grow differently than adults. Therefore, growth curves are fitted with data from adults and extrapolated back to a theoretical age (*t _{0}*) in which length is zero (Figure 5). Parameters (

*L*is the theoretical maximum length and

_{∞}*k*is the growth coefficient that measures the rate at which maximum size is reached) can be estimated through linear regression (e.g., Ford-Walford plot) or non-linear least squares [3]. The von Bertalanffy equation is:

*L _{t}* is the length at age

*t*.

#### Example 4

##### von Bertalanffy growth model (Ford-Walford)

- Step 1:
- Step 2:
Calculate the slope of the linear relationship between length and length at time

*t*+1. In cell F2, type =SLOPE(C2:C6,B2:B6) and hit Enter. The known*x*’s is the length and known*y*’s is the length at time*t*+1. - Step 3:
Calculate the intercept of the linear relationship between length and length at time

*t*+1. In cell F3, type =INTERCEPT(C2:C6,B2:B6) and hit Enter. The known*x*’s is the length and known*y*’s is the length at time*t*+1. - Step 4:
Calculate

*L*by dividing the intercept by one minus the slope. Type =F3/(1−F2) and hit Enter._{∞} - Step 5:
Calculate

*k*by taking the negative natural log of the slope. Type =−LN(F2) and hit Enter.

#### Example 5

##### von Bertalanffy growth model (non-linear method)

- Step 1:
Create a table with five columns—age, length, length from von Bertalanffy growth function (von B), residual differences between length and von Bertalanffy estimated length (residuals), and residuals squared (

*r*^{2}). Fill in the first two columns with the data provided (Figure 7). - Step 2:
Type parameter values

*L*,_{∞}*k*, and*t*at time 0 in cells H4–H6, respectively. Values for*L*and_{∞}*k*can be taken from the Fold-Walford estimates (Example 4).*t*at time 0 can be estimated—select a small, non-zero number. These cells will be referenced for the von Bertalanffy growth function. - Step 3:
Estimate length with the von Bertalanffy growth function. In cell C2, type =$H$4*(1−EXP(−$H$5*(A2−$H$6))) and hit Enter. Select C2 and drag down to complete the function for each age.

- Step 4:
Calculate the residual difference between length and von Bertalanffy estimated length. In cell D2, type =B2−C2 and hit Enter. Select D2 and drag down to complete the function for each age.

- Step 5:
Calculate the squared residuals. In cell E2, type =D2^2 and hit Enter. Select E2 and drag down to complete the function for each age.

- Step 6:
Calculate the sum of squared residuals. In cell H2, type =SUM(E2:E7) and hit Enter.

- Step 7:
Estimate parameter values with the non-linear method (i.e., Solver). Select sum of squared residuals cell (H2) and open Solver in “Data” tab of Excel (If Solver is not in the “Data” tab, you must install Solver with the “Get Add-ins” function under the File or Insert tabs.). Under “To”, select “Min” because the goal is to minimize the sum of squared residuals. “By Changing Variable Cells” refers to the parameter values (

*L*,_{∞}*k*, and*t*), so select those three cells. Finally, make sure to check the box “Make Unconstrained Variable Non-Negative”. When “Solve” is clicked, a prompt will ask if you wish to “Keep Solver Solution” or “Restore Original Values”. Ensure the parameters are realistic values; if so, select “Keep Solver Solution” and click “OK”._{0}

### Part VI—What Happened to the Fish?

At the end of the school year, the AFS club members met in Dr. Spencer’s office to share their findings and experiences. After hearing their account, Dr. Spencer congratulates the students on a job well done and assigns them one final task: a technical report.

Thanks for coming in. How do you feel this project turned out? Do you feel like you learned a thing or two?

I think we are all proud of the work we did. [Shawn and Gus nod in agreement] We were able to use most of the sampling techniques we learned in class.

Yeah, and now I feel so much more confident with data analysis. Having a real-world experience makes the math more tangible, you know?

I certainly do! Glad to hear it went well for you. Now I have one last task for you. I want the three of you to write a technical report. This will summarize the entirety of your field sampling and data analysis. I have some examples I can provide, too.

Got it, thanks. I think we can manage one more group paper before graduation.

A bit of advice when writing your report, keep in mind the initial question: what caused the decline in fish caught by the landowner? All this data you have collected is great but only helps the landowner if you keep the big picture in mind. Make sense?

[The students nod]

Finally, you are about to graduate. You have taken the courses. And now, you have some field experience. Put your management caps on and think about this: as a natural resource manager, what management actions would you recommend to the landowner? Thinking about these things will not only produce an excellent report but give you an advantage in your next job or degree. Best of luck!

More often than not, any type of ecological assessment or data collection effort will be accompanied by a written report. A technical report summarizes the work performed and data collected, and usually justifies the necessity of the project—or more likely, the justification for current and future funding. While the structure may vary, the report will typically have some form of introduction, methods, results, and discussion. The introduction will describe the purpose of the project and outline any objectives. The methods include detailed sampling techniques and data analyses. The results are a report of what was collected and can reference tables or figures. The discussion interprets the results and ties them back to the purpose of the project. This is not a restatement of the results but rather discusses the reasoning behind those results, identifies connections between this assessment and previously published information to support the results, and provides management suggestions.

## CONCLUSION

This case study introduced common assessment metrics used by natural resource managers, such as community patterns, abundance estimates, size structure, and growth estimates. The results provided by these quantitative methods help managers to identify physical or biological factors that may influence natural populations or communities. Thus, managers can implement effective management strategies based on empirical data. After completing this case study, students will be able to describe the need for population and community assessments and apply these assessments to various scenarios and also gaining a better understanding of the scientific process used in natural resource management. Although this case study is based on an assessment of a fish community, the questions can be easily adapted for other wildlife species and biological topics.

## CASE STUDY QUESTIONS

### Part I

What data should the AFS club members collect to perform an ecological assessment of the ponds? Be sure to consider environmental, habitat, food web, and fish community factors.

Why would this assessment information be beneficial in answering the landowner’s questions about the changes in her pond?

### Part II

Using the data the club members collected during their sampling (Table 1), what is the species richness of each pond?

Calculate both the Simpson’s and Shannon diversities and evenness of each pond. Which pond is more diverse? Which pond is more even?

To gauge similarity between the two ponds, calculate the Jaccard coefficient and percent similarity. How similar are the ponds based on these calculations?

### Part III

Identify two methods that would have been appropriate for sampling the ponds. Briefly describe how the AFS club members would perform each sampling method.

Assume the AFS club members used the mark-recapture method. In their initial sampling effort in Pond 1, they collect 20 fishes. A portion of each fish’s pelvic fin is clipped and the fishes are released back into the pond. In the second sampling effort, the club members collect 32 fishes, 10 of which have clipped fins. In Pond 2, the initial sampling effort yields 10 fishes. After clipping each fish’s pelvic fin, the fishes are released. The club collects 18 fishes in the second sampling effort, 6 of which have clipped fins.

Estimate the abundance of bluegill in each pond.

What are the assumptions for this method?

Now assume the AFS club members used the depletion method. Use data from the table below to answer the following:

Pass # . Pond 1 . Pond 2 .

.. Catch . Effort . Catch . Effort . 1 30 18 17 15 2 16 20 7 19 3 9 24 3 22 Pass # . Pond 1 . Pond 2 .

.. Catch . Effort . Catch . Effort . 1 30 18 17 15 2 16 20 7 19 3 9 24 3 22 Estimate the abundance of bluegill in each pond.

What are the assumptions for this method?

Are the abundance estimates different between methods? If the AFS club members only had time to use one method to estimate abundance, which one would you recommend and why?

### Part IV

Calculate the PSD of bluegill for each pond (use Table 2 to determine stock and quality categories). Which pond has a more desirable PSD?

Pond 1 . 3 3 4 4 3 4 4 5 4 5 5 5 5 3 4 4 4 4 4 3 4 3 3 3 4 5 5 3 5 3 5 5 4 4 3 4 5 6 7 6 6 6 6 6 7 6 6 6 7 7 7 7 6 7 7 7 6 7 7 6

**Pond 2**

5 5 4 5 5 5 4 4 5 5 4 5 5 4 5 5 5 4 3 3 5 4 4 6 6 6 7 6 7 6 7 Pond 1 . 3 3 4 4 3 4 4 5 4 5 5 5 5 3 4 4 4 4 4 3 4 3 3 3 4 5 5 3 5 3 5 5 4 4 3 4 5 6 7 6 6 6 6 6 7 6 6 6 7 7 7 7 6 7 7 7 6 7 7 6

**Pond 2**

5 5 4 5 5 5 4 4 5 5 4 5 5 4 5 5 5 4 3 3 5 4 4 6 6 6 7 6 7 6 7 How would you explain the PSD values to Karen?

### Part V

Assume an individual bluegill grows from 38 to 71 g over 92 days. Calculate growth using the following:

Absolute

Relative

Instantaneous

Use the von Bertalanffy growth model and data from Table 3, to calculate

*L*,_{∞}*k*, and*t*with:_{0}The Ford-Walford plot

A non-linear method (i.e., Solver in Excel)

Based on the results from Question 2, which pond has a higher growth rate?

### Part VI

Describe, in detail, a scenario in which the fish community would decline. Consider the following:

Physical factors

Pond productivity

Species composition and abundance

Using the same scenario, describe management actions that Karen, the landowner, could take to help the fish community recover.

Bonus: Draft a technical report summarizing the work performed by the AFS club members. Be sure to include the following:

Introduction: purpose and description of the study area

Methods: sampling and analysis techniques

Results: community patterns, abundance estimates, size structure, and growth

Discussion: potential reasons for differences in ponds, proposed management action

## AUTHOR CONTRIBUTIONS

TS developed questions, created the data set, and wrote the manuscript. EF provided guidance and wrote the manuscript.

The authors would like to thank Dr. Tomas Höök for the analysis and literature recommendations and Dr. Mitchell Zischke for the inspiration behind the case study narrative.

## FUNDING

The authors have declared no funding source.

## COMPETING INTERESTS

The authors have declared that no competing interests exist.

## SUPPORTING INFORMATION

Teaching Notes: Description of how the case study can be used, including teaching activities and discussion prompts; DOC format.

## ANSWER KEY

Answers and in-depth steps to solving case study questions; DOC format—this file can be requested by contacting the corresponding author at tsenegal13@gmail.com.