Populations are incredibly complex as they are always changing - hence why we talk about population dynamics. The factors responsible for those changes are a mix of unpredictable (weather, floods, fish kills, etc.) and somewhat predictable (interactions among individuals - competition, predation, etc.). However, there are some simple ideas at the heart of all population changes and the first principles of population dynamics are pretty simple. Individuals in a population can be born or they can die. They can enter the population from another population (immigration) or they can leave the population and go elsewhere (emigration). This "BIDE" approach is at the heart of all models, no matter how simple or complex. Now, as I will talk about later, understanding why births, deaths, immigrants, and emigrants change over time is much more difficult.
I think in any conversation about how to understand models, three ideas need to be understood. First, a model is a simplification of reality, of something more complex. We use them, quite unknowingly, all the time to better understand our world. A globe, a map, the GPS on our phones - all models. Today's, tomorrow's, or next week's weather forecasts are models. Models are qualitative, quantitative, or a combination of the two. Second, to quote University of Wisconsin statistician George Box, "All models are wrong but some are useful". This is to say, models do not have to be 100% correct for them to be informative and useful. You do not care that the weatherperson misses tomorrow's temperature by a degree or two; that prediction still prepared you for the day. Useful simply means that the model helped us better understand and maybe predict a more complex phenomena. And lastly, models can be accurate, transferable, and/or simple but it is impossible to meet all three at once. There are tradeoffs.
You probably remember, maybe with a bit of coaxing, that populations grow exponentially ("J-curve") or logistically ("S-curve") and not linearly (straight lines). These are simple models that describe how populations change over time. You probably remember how when the actual populations are plotted, the exponential and logistic models are good approximations but they do not fix the data exactly. These models are simple and transferable but they are generally not very accurate. To improve the model's accuracy, to better represent changes to the population; we would need to know more about what causes births, immigrants, deaths, and emigrants to change and built that into our model. This makes our model more accurate but less transferable and not as simple.
As discussed in an earlier post, populations are regulated through factors that are, or are not, related to the populations density (density-dependent and density-independent). Density-dependent factors are often built into models because we have an understanding of how the density of a population, its prey, or its predators affect the BIDE components. Logistic models have density-dependence built in. As the population nears carrying capacity (K), births and immigrants tend to go down and deaths and emigrants go up so the rate at which the population grows is slowed.
Of course, population size is really only one of the measures of a population that we interested in. The size and age distribution of a population often tells us as much as the "N" (N = total population size). A stream full of small trout may tell us that it is a nursery area that is unable to provide resources for larger fish, that mortality is high and prevents fish from living long enough to grow larger, a density-independent event - a flood, for example - occurred recently, or something else is responsible for the young age population.
A Tale of Two Fishes
I will compare trout and Smallmouth Bass (Micropterus dolomieu) because they are probably the most sought-after species on the fly rod in Wisconsin and they offer a contrast in life history characteristics and thus population dynamics. Typically, Smallmouth Bass population densities are much lower than are trout densities. For one thing, they have different trophic statuses. Smallmouth Bass feed higher on the trophic pyramid whereas trout are largely invertivores until they become larger and feed higher on the tropic pyramid. As a reminder, primary producers (plants, algae) are the base of the trophic pyramid, primary consumers are herbivores, and then secondary, tertiary, and quaternary consumers are successively above the primary consumers.
From: By Swiggity.Swag.YOLO.Bro - Extracted from this Commons file, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=85276916
Smallmouth Bass feed higher on the trophic pyramid, tend to live longer, and be less fecund (have fewer eggs); these are all things that contribute to their lower densities. They also tend to live longer. We often talk about a continuum from r-selected species like bacteria that reproduce quickly but are very short-lived to K-selected species (K comes from carrying capacity in the logisitic, density-depending model) like elephants, Blue Whales, and humans that have low fecundity, enjoy long lives, and generally have parental care that lasts until maturity. A simpler way to state it are that r-selected species live fast and die young whereas K-selected species live slow and die old. On the r/K continuum, trout are a little further on the r-selected end and Smallmouth Bass more on the K-selected end.
As such, Smallmouth Bass populations - at least without harvest - tend to be more stable. We often think of carrying capacity (K) not so much as a single number but the actual carrying capacity occurs within a range. Additionally, this generally means that trout populations can withstand a significantly larger harvest than can Smallmouth Bass. Trout can also recover from density-independent disturbances - floods and manure spills - more quickly than can Smallmouth Bass.
Though they are imperfect, models are the way we understand the world. How population change is pretty simple - through births, deaths, immigrants, and emigrants. Why those changes happen are much more difficult to understand and predict. In fact, the density-independent changes to populations are by definition, unpredictable. Populations are regulated simultaneously by density-dependent and density-independent factors. Scientists can make these models more accurate by adding parameters but it comes at the expense of simplicity and transferability. Reducing simplicity by adding parameters means that we need to know more about what alters BIDE which generally means much more time, effort, and expense. This brings us to the transferability of models. As we add more parameters and make them more accurate to where they are developed, they are less likely to be applicable in other places, at least without significant "tweaking".
It is difficult to monitor and model populations on a single stream, let alone over a number of different counties and watersheds. Yet, having a good understanding of what factors affect populations and size structure are critical for effectively managing a population, to understand what effect harvest, flooding, manure spills, and land use changes are having on fish and their prey. This is why transferability is important. Biologist certainly can not sample often or as widely as they would like so they need to be able to sample "trend sites" and be able to apply those results to a wide range of streams in the area.
Models are tradeoffs between accuracy, transferability, and simplicity. They are wrong, yet they are useful. Lastly, they are an important tool for understanding out world. Knowing a little bit more about how populations change and how we understand these changes will make you a better bar stool biologist.