Growth in a Finite World

Knowing a set of concepts (e.g., logistic growth) in an abstract way is a starting point to understanding, but application, as suggested by folks like Dewey ( and Bloom (, is a better training ground for thinking.


Food and water scarcity =>

Urbanization and biodiversity =>

Regional population growth =>

Global population growth =>

Peak oil =>

Social injustice =>

Local climate change =>

Global climate change =>

How do you currently understand the connection between evolution and ecology?


5 Responses to “Growth in a Finite World”

  1. Tamar Bouchard says:

    Peak oil is defined by Wikipedia as “the point in time when the maximum rate of global petroleum extraction is reached, after which the rate of production enters terminal decline.” This definition reminds me of the ball analogy talked about in the Limits to Growth information – The concept of carrying capacity seems to best fit into this definition, as our oil dependent human population is very effected by the availability of oil for the continued technological assistance necessary to handle the increased population we see at this time. The natural environment would be hard pressed to support the current population, especially in huge metropolitan areas, without the aid of petroleum dependent technology at this point in time.

    Evolution and ecology seem to be directly linked to each other. Ecology as the study of the natural world was shaped in its infancy by the study of evolution and that shaping continues to this day. When ecologists are talking about population density and carrying capacity that very much feeds into the theories of evolution and what effects changes over time in a population. Ecology is also the study of evolution.

    I had a hard time with the exponential and logistical equations, not just because I am not a huge fan of math and statistics, but also because you can prove anything you want to if you set a formula up correctly. The exponential growth rate equation is dN/dt = rN and the logistical growth rate equation is dN/dt = rN((K – N)/(K)). I do understand a bit about how these work, but I have to admit that I would need a lot more time than we have in this class to play with it to truly use it as a working tool, it had me stopped for a while. The exponential growth rate states that populations will increase unhindered until they reach the carrying capacity of the environment in a graphically represented “j” curve pattern. The logistical rate of growth is represented in more of an “s” curve pattern, showing a more gradual increase and then a slowed to leveling off rate of increase as carrying capacity is neared and then reached.

  2. Michelle Audas says:

    The concept of carrying capacity, as it applies to population growth, provides insight into understanding how we make decisions around the utilization and allocation of resources. The starting point is to identify a definition of carrying capacity that relates to population growth. The definition that I want to apply to thinking about this is, ““Carrying capacity refers to the number of individuals who can be supported in a given area within natural resource limits, and without degrading the natural social, cultural and economic environment for present and future generations”

    If we are thinking globally about population growth, then we have to look at natural resources limits globally as well. Based on these parameters and this definition, I think there is strong evidence to support that the current global population has surpassed its carrying capacity. There is sufficient evidence through research in the areas of climate change and oil supply to confirm that we have caused degradation to the natural world for the current generation and future generations. If we go a step further and look at issues of social and cultural degradation, ongoing wars like those in Afghanistan and Iraq are evidence of social and cultural degradation in our current society, and we don’t yet know the degree to which we have negatively impacted future generations.

    This challenges the application of the more common theory of carrying capacity that suggests that when a population reaches its carrying capacity, the competition for resources will increase death rates and decrease birth rates to allow the population to sustain itself. The challenge with accepting this model and applying it to human populations is that we have to accept the risks associated with applying this kind of pressure to both human and natural systems, and the degree to which we intervene with natural lifecylcles through technology. I wonder what kind of measures humans would take as their survival becomes more threatened by the existence of their neighbors? Is war an example of humans trying to adapt to changing constraints in their habitat?

    I think exploring the concept of carrying capacity allows us to think more deeply about how consumption patterns vary across different human populations. It should guide our thinking about how we create a model of accountability to our neighbors for our choices. It also causes us to consider how we allocate economic resources for the intervention of natural epidemics which would impact population growth.

    If evolution is about change in biological systems, and ecology is the study of the relationship between organisms and their environment, or the system of biological subsystems, then evolutionary theory may be considered the foundation for understanding ecological processes. It provides us with guiding principals to ask ecological questions, and explore our findings.

    As far as applying exponential and logistic equations quantitatively, after reading both Monica Ian’s responses, I figured I could just change the variables and plug them in. Here is my attempt, which you will see I quickly get lost in…..

    If the same community starts out with 25 people, and they were to have 12 births and 2 deaths in a year, the growth rate would be:

    N= 25

    b= 12

    d= 2

    Yr 1= ((12-2)/25)(25)=10

    YR2= .4(35)=14

    YR3= .4(49)=19.6

    I feel like I am starting to get lost…..I guess I can see how many people are being added to the population, but I am not sure if I can state what the growth rate. I could a little more explanation on applying the equations with real variables.

  3. Matt says:

    To start with I’d like to introduce the concept of scale. Scale is defined by ecological economists as the physical size of the economic subsystem relative to the ecosystem that contains and sustains it. Ecological economists argue that to achieve sustainability we must move beyond the micro issues of efficient allocation and work at the macro level to determine the appropriate scale for our economy and the specific activities that are impacting our local/global ecosystem(s). This is directly related to carrying capacity, becuase we must first understand the carrying capacity for our containing ecosystem. This analysis must be done at multiple-scales from local to global, but ecology shows us how difficult achieving this understanding might be. Looking at food for example, one might try to understand the carrying capacity for a specific farm. If you analyze the land available one might see that as the limiting factor, but going further one might look at soil quality and come to understand that as the true limiting factor. But, then there’s climate. Farms growing plants need rain and sun. But, what about replacability – can’t we replace degraded soil with fertilizer and rain with irrigation? Heck, we can even replace sunlight with artificial lights. But, what about oxygen and CO2? I guess we could probably find a way to capture C02 and deliver it directly to plants. OK, so then is the supply of fertilizer, water, energy, etc. the limiting factor? Well, those come from the larger, containing ecosystem, so I guess we need to undertand the global carrying capacity to understand this farm’s specific carrying capacity right? Maybe, but then there’s economic/financial factors that make some of the ideas above infeasible.

    Due to these factors one might determoine that a farm with 100 acres has a specific carrying capacity and is therefore only capable of producing a specific maximum amount which might be seen as the farm’s net primary productivity. According to “Net primary production is the rate at which all the plants in an ecosystem produce net useful chemical energy…. Some net primary production goes toward growth and reproduction of primary producers, while some is consumed by herbivores.” I’m trying to point out the connection between carrying capacity, net primary productivity, and scale to explain that we can only consume what we can produce and that all production is limited by carrying capacity.

    So, how do we calculate this? How many plants can a 100 acre farm support? There are so many factors. I don’t know how to start other than to say that we could assume a specific carrying capacity with healthy soil and appropriate amounts of other inputs like sun and rain, such as asumming a 100 acre farm can produce 10,000 plants per year. Using the formula below would Carrying Capacity of “K”=10,000, Population Size or “N”=100 (because each acre represents a person that could produce offspring), and time or “t”=1year? If so, we would get the following results, but this doesn’t seem right.


    dN/dt = 10,000(10,000-100)/10,000)

    dN/dt = 9,900

    I guess I’m stuck.

  4. Ian Raphael says:

    It is pretty clear to see the relationship between population growth and fossil fuel use. Access to abundant energy resources leads to more people ,which leads to further energy consumption. Below is a graph of population growth and oil production. As you can population growth boomed during the industrial revolution. The invention of the steam engine changed every aspect of how humans operate in this world. Productivity dramatically increased, leading to huge population growth. This graph also shows that not only has population increases oil production but the ratio of per capita consumption is also rising.

    This phenomenon can easily be seen in developing countries where increased economic production has increased populations size. The problem is that the increased population also has increasing consumption demands. Examples of this are the amount of vehicles being bought in china, televisions and other appliances etc.

    This problem in how do you maintain this productivity in the midst of peak oil concerns? What will happen to population growth? As our reading referenced, there are definite signs that there are limits to population growth due to the carrying capacity of the earth and its resources. A great example that was used was deer. With the lack of enemies, deer can increase population size beyond carrying capacity causing over grazing and an unsustainably environment to further support the population. The human population could have the same fate if changes are not made in our use of fossils fuels, as well as our per capita consumption demands. This is no easy task. So far it is questionable whether increased energy efficiencies are having an effect in overall consumption. It could be argued that increased efficiencies allow more financial ability to consume more or just use that product more. A good example of this is the Prius. Research has shown that Prius owners drive more than they did before buying the hybrids. Are they reducing CO2 or fuel consumption?

    There are very high energy inputs to produce “clean energy”. Ethanol is a great example. The Energy Bulletin believes the ethanol production consumes six units of energy to produce just one unit of fuel. “Taking into account the energy required to grow the corn and convert it to ethanol, burning the biofuel as a gasoline additive result in a net energy loss of 65%.

    To make a long story short. Peak oil and population growth are undeniably linked. I’m not sure if we can dig ourselves out of this hole. We could see dramatic decreases in population as we begin to go down the other side of the peak oil curve.

    After looking through Monika’s calculations I am way more comfortable with my math, I think…

    N= 10,000

    b= 100

    d= 10

    Yr 1= ((100-10)/10,000)(10,000)= 90

    YR2= .009(10,090)=90.81

    YR3= .009(10,180.81)= 91.62

    YR4= .009(10,272.43)=92.45

  5. Monika Derrien says:

    An ecological concept such as carrying capacity and population growth is critical to understanding food and water scarcity. Improved agricultural knowledge and techniques, genetically modified foods, more sophisticated irrigation and water filtration systems, and other technologies that makes agricultural land more productive and water more accessible and easily purified, all make the planet able to increase its carrying capacity. But at some point, according to logistic growth model, there will not be enough resources, regardless of new technologies, to support infinite population growth. The population density will eventually reach the point where any further growth will not be able to be supported by the available resources.

    What will the world look like at carrying capacity? How much physical space does “as dense as sustainably possible” give each person? Are our “factories in the field,” that produce a nation’s food where nothing used to be able to grow, and GMO miracle foods to “cure” world starvation actually creating a new carrying capacity that can feed the human race (disregarding the rest of the organisms of the world) but not give it a chance to thrive and be culturally and socially productive? To what extent can human actions shape population possibilities in the future, and at what point do we disregard negative feedback in favor of the human “can do” attitude? What are the ill-effects of a highly human-engineered carrying capacity?

    Evolution is the result of ecological interactions over long periods of time, taking place within ecosystems. In fact, it is those systems that shape evolution. And then, in turn, evolution shapes ecology by changing the players in the system. Ecology would be rather static if not for evolution – only a set number of interactions would take place, with much less possible variability. The overlap between the fields of evolution and ecology is due to the fact they they are shaped by the same forces. Ecology, in a way, is the sum and manifestation of all of evolution.

    I haven’t done any calculus in two or three years, but for these equations you can just plug in the variables to get the growth rates.

    Very simply put, if a community starting out with 100 people were to have 10 births and 5 deaths every year, the growth rate, for that year, would be:


    The following year the growth rate would be:


    The following year, it would be:


    The following year, it would be: dN/dt=.05(115.7625)=5.788125.

    As you can see, the growth rate is increasing each year, by a little bit more than the year before. There is no limiting factor, and growth will grow exponentially.

    To show logistic growth, I’ll use the same example of a 100 person community, an rmax of 5/100, and a carrying capacity of 500:


    So the rate of population growth at this specific time, when the population is 100 people, will be four people per year.

    The following year,


    The following year,


    As soon the population gets to 500, it will stop:


    This is carrying capacity – there will be no growth or decline in population.

    If the population manages to go above 500, the rate will be negative until it returns to 500:

    dN/dt=(.05)(550)((500-560)/500)= -3.3

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