Environmental Systems, Dynamics, and Modeling: A Primer
1. Environmental Systems
Our environment is a product of many different plants and animals, shaped by the past, the climate, the physical landscape and, of course, human activity. As species adapt to circumstances, they also influence their habitats and reshape the environments in which they live. Ecosystems (and our planet) are also subject to random shocks that can radically change the course of life. Indeed, the universal constant of life is change. The mass deaths that led to the extinction of the dinosaurs almost certainly contributed to mammal speciation and an increase in mammal size. Thus, if the Alvarez hypothesis is correct, and if a meteor had not hit the Earth 65 million years ago at the end of the Cretaceous period, it is extremely unlikely that modern humans would exist and that you would be reading this book!
One of the most important processes by which life changes over time is natural selection. This simply means that those members of a species whom are fortunate enough to reproduce will bequeath their genetic material to the next generation. Members of a species that by chance, or physical characteristics, or behavior are less successful at reproducing, will be less favored in the gene pool in the subsequent generation. In this manner, life evolves over time. The process of evolution involves many different paths and interactions with predators and prey, and with parasites and hosts coevolving. For example, slower deer are more likely to be caught by, say, wolves. As a result, slower deer are less likely to be successful in reproducing and thus, over time, they are eliminated and the species becomes faster at running. Similarly, wolves that are less able to cooperate in their hunting may be less successful at catching game and, thus, over time wolves that cooperate (assuming that cooperation is an inherited characteristic) reproduce more and dominate their species gene pool. Co-evolution can also be in the form of symbiosis or mutualism, such as with flowering plants that provide food (in the form of nectar) for insects that, in turn, increase the reproductive success of the plants that attract such insects.
The greater the period of time, all other things equal, the greater will be the effect of evolution on life. Nevertheless, even in very short time periods (on a geological timescale), species can evolve rapidly. For example, the widespread use (or rather misuse) of antibiotics, particularly in the livestock industry where animals are given low doses of antibiotics to increase weight gain, has, in a short period of time, led to antibiotic-resistant bacteria. Rapid changes p. liimay also occur in multicellular species. A classic example is the peppered moth found in the United Kingdom that, prior to the Industrial Revolution, had light-colored wings and rested on lichen which helped camouflage them from predators, such as birds. Increased air pollution killed off much of the lichen on which they rested and the lighter-colored moths became conspicuous to birds, reducing their breeding success. In turn, in a few decades, the species, as a whole, evolved to have much darker colored wings that were less noticeable to predators in the black background of industrial Britain.
If the golden rule of ecosystems is change then evolution’s maxim is biological diversity – the genetic variation that exists both across species and among individuals within species. Life on Earth started at least 3.5 billion years ago and began with bacteria that still remain, in terms of their total biomass weight, the most successful life forms on our planet. By contrast, modern humans are the latest gatecrashers to a party that has been going on for almost 4 billion years! Beginning in the Cambrian period, some 570 million years ago, the first multicellular organisms appeared, ultimately leading to the plants and animals we see today. Almost all the life on Earth (bacteria deep in the Earth’s surface may be an exception) directly or indirectly survive from the energy that reaches us from the sun. Indeed, organisms that can photosynthesize (or take energy from sunlight) that first evolved some 2 billion years ago, represent a fundamental turning point of life on Earth. As important is the sun to the evolution of life, so has been the spin of the Earth and its tilt (that gives us seasons) and the interaction of our moon that collectively help generate the energy, mixing and turbulence in the atmosphere and oceans that help sustain life.
Along the many paths of evolution, species evolved into other species such that their archaic forms passed away. In addition, many species became extinct in the sense that they left no descendants. Indeed, the ratio of extinct to living species is likely to be at least 1000 to 1. In other words, if the Earth has between 10∼100 million species alive today, between 10 thousand million and 100 thousand million species that previously existed are now extinct. Given the genetic variation that exists within individual members of a species, the diversity of life on our planet since it first began is truly staggering.
If the species alive today are just 0.1 percent of all the species that have ever lived it begs the question, what strategies can individuals and species use to ensure their survival? The most obvious mechanism for survival is to produce many offspring. Indeed, the larger the number of individuals, all other things equal, the greater is the chance a species has of surviving into the future. Animals that use this approach are called r-strategists and include most species. An alternative strategy is to focus less on the number of offspring and instead to increase the probability of offspring successfully reproducing. Species that follow this approach, like humans, are p. liiicalled k-strategists. These strategies, however necessary, are insufficient to ensure the long-term survival of species. This is because any environment is subject to perturbations and shocks that can lead to mass deaths. For example, life on an island could be destroyed by a volcanic eruption, or many of the species on an entire continent could be obliterated by a meteor, or the Earth’s climate could suddenly become much colder leading to mass deaths (events that have all happened more than once on our planet). Unless members of a species can acclimatize and adapt quickly, or the species can evolve to adjust to the changed circumstances, the species will become extinct. Thus, to ensure resilience to local or regional shocks or events, species need to have meta-populations or to be widely distributed spatially. In other words, species (no matter how numerous) that are only found in geographically limited locales are at particular risk of extinction.
Resilience is a term that can be applied equally well to ecosystems as to species. Interestingly, some studies suggest that increased diversity of species (at least to a certain point) can result in a greater biomass from ecosystems and may foster stability in the sense that plant and animal communities can “bounce back” from shocks and perturbations. Resilience is, in part, determined by population dynamics. To a greater or lesser extent, species are regulated by their population density. Ultimately, since no population can increase indefinitely, the total population growth rate must eventually decline with population density. However, at low densities, increases in density may actually increase the rate of population growth. For example, at low densities some species are highly vulnerable to predation because to survive they need to aggregate, or school or herd together for protection (such as with schools of sardines or herds of zebra). Moreover, the rate of growth of populations is likely to depend on the density of other species, such as zebras and lions or deer and wolves, in what are called predator–prey relationships. These linkages across species, and with abiotic or non-biological factors, can lead to non-linearities in both growth and population numbers. For example, below a critical point in terms of numbers, a population may simply be unsustainable. Similarly, a change in the environment beyond a threshold or critical point (such as a decline in the pH level of a lake) can lead to mass deaths. The system dynamics of populations and their environments is extremely complicated and requires an understanding at the cellular level (such as genetics) and systems level (such as ecology). It also requires a comprehension of the many cycles and feedbacks on Earth that help maintain our ecosystems, such as the water cycle that refreshes and recirculates water on our planet. The feedbacks in cycles are illustrated with the carbon cycle (shown below) that represents the interaction between organisms that helps determine the concentration of carbon dioxide in the atmosphere.p. liv
At the ecosystem level, an understanding of the food web is required to appreciate the feedbacks and links across species and to understand how perturbations or shocks can travel throughout an ecosystem or environment. These links can be highly complex and may even be chaotic such that there exists neither an equilibrium nor periodicity in how populations change over time, and the future population numbers may be highly sensitive to past values.
How life interconnects is a subject of much debate. Some writers have gone so far as to view the world as one giant interconnected organism, as in the so-called Gaia hypothesis. By contrast, others view ecosystems as merely overlapping habitats of different species. Whatever the interpretation, there is no question that how species interconnect plays an important role in their survival and their ability to adjust to shocks. An important step to understanding these interactions is to model the relationships and linkages among the many factors that constitute our environment.
2. Modeling and Dynamics
Modeling is a process by which an abstract or simplification of the world around us, or events, is developed. Models can simply be “mental maps” or rules we develop about how the world operates. Unfortunately, the insights from models that exist in someone’s head can be very difficult to impart to others. Moreover, although we are very good at expressing mental models in terms of cause and effect (I jump out of a window, I fall to the ground), we are often unable to develop mental models that reflect the feedbacks and interconnectedness that exist in even the simplest systems. Thus, to model an ecosystem or economic system, we need tools to help us visualize p. lvrelationships and to quantify how the parts of the system affect each other. These tools include, but are not restricted to, mathematics, to help us be as explicit and as clear as possible about the nature of the system, and computers to help us make the many calculations required to quantify how a system changes over time.
Models are used for two principal purposes: optimization and simulation. Optimization models include an objective function that needs to be optimized (such as social welfare or species diversity) subject to a set of constraints (such as the resources available) using a set of control or choice variables (factors that can be changed, such as tax rate or the area of land in conservation areas). Optimization models are prescriptive and are thus part of normative analysis and help answer the questions of what should happen. Simulation models are used to represent a system or systems and, to be useful, must adequately reflect the relationships among the variables within the system(s). Such models are often used for predictive purposes and help answer what if questions. For example, general circulation models in climate modeling help us answer the question what will be the Earth’s climate in 50 years should we continue to emit greenhouse gases in a business-as-usual scenario?
Models are often criticized as not being an adequate representation of reality. No matter how complex the model, it must (inevitably) be a simplification of the system being modeled. The art and science of modeling, however, is not to include every possible variable or relationship (which is impossible) but to include those variables and links that are important or significant within the system. In this sense, what is “important” or “significant” will depend on the purpose of the model and availability of data. For instance, a general circulation model used for predicting surface temperatures a century hence must include the atmospheric concentrations of greenhouse gases in the atmosphere. By contrast, a model used for predicting whether it will rain in a particular region in the next three days can ignore the interactions between atmospheric greenhouse gas concentrations and the local weather. Choosing what should and what should not be included in a model (variables and feedbacks), and whether variables should be treated as exogenous (determined outside the model) or endogenous (determined within the model), are questions that all modelers face. Good models are able to represent the system parsimoniously, or in as simple a way as possible, while still being able to effectively answer the questions for which the model was built.
Given that the environment, the economy, and human activity are always changing, models need to be dynamic or inter-temporal in order to adequately reflect these systems. In other words, variables within the model should change over time. All dynamic models include stocks and flows. p. lviStocks are state variables and may be called reservoirs, levels or inventories, depending on what system is being modeled. They characterize “the state of the world” such as the biomass of fish in a fishery model, the volume of standing trees in a forestry model, or the surface temperature in a climate model. The value or level of a stock depends on the initial conditions or past values, and can change over time depending upon additions and subtractions from flow variables. For instance, recruitment represents a flow into a fishery as it increases the stock of fish, while harvesting of fish is a flow out of the fishery as it reduces the stock, as shown below.
Flows represent rates of change in a system and could be the birth rate or death rate in a population model, or the water used and discharged by a pulp and paper mill in a model of water use. Although stocks are changed by inflows and outflows, stocks may also influence the flow variables through feedbacks. For instance, the death rate (flow) of a population is likely to be influenced by the total size of the population (stock) such that there is a feedback in the model.
Stocks that are uniquely determined in the model by flows and feedbacks are state variables of a system. A model may also include auxiliary variables that are functions of both stocks and flows. For instance, the recruitment into a fishery is itself influenced by a birth rate that is a function of both the total population (state-determined stock) and environmental factors (such as ocean temperature) that may be treated as exogenous to the model, as shown below.
Modeling requires tests of the robustness and the effect of changes in a model, and its assumptions, in terms of results. These tests should include running or simulating the model under a variety of scenarios such as different initial conditions, parameter values or constants. Further, a model’s predictions can sometimes (where the data is available) be compared to past values and used as a possible indicator of performance for predictions or forecasts. However, just as correlation between variables does not imply cause and effect, neither does past performance of a model ensure accurate predictions. In addition, a model should be tested to explore the p. lviieffect of changes in the feedbacks and interrelationships of the system. By performing such tests and sensitivity analysis, researchers are better able to understand the limitations of their models and, thus, to comprehend better what questions the models can help answer and what questions they cannot resolve.
An understanding of our environment, and how to model it, is the basis of scientific research. Clearly, neither this primer nor this dictionary can do justice to the myriad of topics that encompass the many disciplines needed to understand the world around us. Readers interested in understanding more about the environment and environmental economics should, as a first step, use the references, words and appendices in this dictionary as tools in their journey of learning.