Lecture week 12 (11-7, 11-9) - Notes Population Ecology

Biol 114 Fall 2023

Lecture week 12 (11/7-11/9)

Population Ecology

1. Intro to population Ecology
   1. What is it?
      1. Population ecology is the study of how and why population size changes over time and the effects that population change has on the population. Population genetics answered how populations change genetically over time, and how new populations may get started. The two fields are often linked in discussions, but populations may get larger or smaller without genetic change, and genetic change may occur without population size changes.
   2. Why study it?
      1. Understanding how populations change, and what is causing those changes, provides us with important information. For example, knowing how populations of food plants grow, and are limited by density, helps us to better plan our farms, and knowing how insect populations grow and decline helps us to maintain local ecosystems that keep our water and air clean.
   3. How is it done?
      1. A typical problem for conservation biologists is to figure out how many individuals there are in a population and why the population is growing or declining.
      2. This central question is answered by monitoring the changes of specific elements of a population (e.g., numbers, ages, sex ratio, etc.) over time, keeping track of the factors that affect these elements, and making predictions about and studying outcomes of population changes.
      3. Example: Case Study of Caribou on Pribilof Islands.
2. Exponential Growth
   1. Elephants Galore!
   2. Imagine a population of organisms living in an unlimited environment, with unlimited resources, and unlimited space. Imagine that the organism divides into 2 every 24 hours. You could then chart its population growth:

Day Population Size

1. 1
2. 2
3. 4
4. 8
5. 16
6. 32

This is exponential growth

When these data are graphed, you get a curve that starts out with a relatively slow increase that quickly turns to a rapid increase in numbers with very little change in time.

• 1. Paper-folding Demo
  2. We can describe these patterns mathematically.
     1. Individuals have the probability of dividing/giving birth (b)
     2. Individuals have the probability of dying (d)
     3. Instantaneous rate of growth per individual (or per capita) is b-d, which is typically known as r. Rate of growth (r) = b - d (typically considered as a maximum r or r_max).
     4. If the population size = N, then the rate of population growth = rN
  3. Formally written as the Exponential Growth Equation:

(ΔN/Δt) = rN

Note: not only should you know this equation, but, more importantly, you should know what it means and how to describe it in terms other than the variables listed. For example, the above exponential growth equation can be translated as: the change in population size per change in time (rate of growth) equals the rate of population growth for the individual multiplied by the number of individuals in the population.

1. Logistic Growth
   1. Consider the sheep of South Australia.
   2. Logistic or Sigmoid growth involves three stages:
      1. Initial exponential growth.
      2. Decelerating growth rates.
      3. Fluctuations around some “average” population size, often called K or carrying capacity of the environment.
   3. Again, we can describe this pattern mathematically.
   4. The changing rate of growth of a population showing sigmoid growth can be modeled by the Logistic equation:

(ΔN/Δt) = rN((K-N)/K)

• 1. Where:
     1. N = current pop. size
     2. K = the highest value that N can take or the “carrying capacity” of the environment
     3. Watch out for r. Where r was r-max in the exponential equation, r here is relative (r_rel). How an individual can reproduce relative to the influence population size has on the individual.
     4. How can the equation be translated into ideas and descriptions from variables (as we did in IIe above)?
  2. Overall, the logistic model comes closer to predicting real populations than the exponential model does. The exponential model doesn’t take into account the limit that resources place on populations.
  3. Notes about Carrying Capacity (K).
     1. It can be defined as the point at which the population size is in equilibrium with resources
     2. Or the number of individuals of a species that the environment can support.
     3. Or the number of individuals that can survive in the environment.
     4. K is not constant! As environmental conditions change, so does K. That is, as time goes by, and the environment changes (food base changes, other resources change, etc.) the K for a given population in a given environment shifts.
     5. Note: the differences between i, ii, and iii above are based on point of view. One is the population and environment together (i), the environment (ii), and the population (iii).
  4. Using the logistic model
     1. If N > K:
     2. If N < K:
     3. If N = K:
  5. Example Case Study of Gray Wolf populations in Wisconsin

1. Problems with the models.
   1. What are some of the problems with these models?

THIS IS THE END OF LECTURE MATERIAL FOR TUESDAY 11/7. THE LECTURE NOTES BELOW WILL BE COVERED AS CLASS PREP FOR THURSDAY 11/9.

1. Demography
   1. Demography is the study of factors that determine the size and structure of a population over time.
      1. Demography involves the age classes, sex ratio, rates of immigration and emigration, survivorship, mortality, and fecundity of a population, in an effort to better understand how a population changes, and, maybe more importantly, to better predict how a population will change in the future.
      2. Population change is best understood by creating and analyzing Life tables.
   2. Life Tables
      1. Life tables summarize the probabilities that an individual age class will survive and reproduce in any given year over the individual’s lifetime. All the individuals that are born at the same time, and are thus represented by an age class, are called a cohort. Life tables are constructed by keeping track of a cohort over several years time, while keeping track of how many of the original cohort survive into each new age class (frequently 1 year’s time). (Note: you can also create a life table by collecting data on several age classes at once. This requires being able to distinguish the ages of your organism, but it is quicker to do than to follow one cohort for several years.).
      2. Life tables are based on survivorship (survivorship until reproduction, if you want to link this concept to nat. sel.) per age class. The typical life table has several variables listed in it (consider the life table of the gray squirrel):
         1. x is the year in consideration. It can also be considered an age class. The term “age class” is often used for those organisms that do not count their ages in years (e.g., bacteria), or have periods of many years where very little changes in the life history of the organism (e.g., Humans in industrial societies have periods throughout life where survival is not threatened. The resulting age classes may be considered as, infancy, childhood, early reproductive, late reproductive, and post-reproductive, depending on what data you are trying to convey.)
         2. n is the number of the cohort remaining in the population. n_x is the number remaining for a particular age class (x).
         3. l_x is survivorship. It represents the percentage of the original cohort to survive into a particular age class (x).
         4. d_x is mortality. It represents the percent of the original cohort that dies in each year (essentially, l_x – l_x+1 = d_x).

As said above, survivorship is key to understanding life tables, and, as a result, the changes in a population over time. For example, if individuals in a particular species have several thousand offspring, you would believe that the environment would be overrun in a short time, they would consume all the resources available to them, the population would crash, and maybe the community would suffer as well. However, if few of these offspring survived long enough to consume many resources, you would expect a dramatically different outcome.

Remember, survivorship is the proportion of offspring produced that survive to a particular age.

From survivorship data, scientists can make survivorship curves, by plotting the log of the number of survivors vs age. There are 3 general types of curves.

1. Type I survivorship curve: Typified by having a large percentage of survivors throughout much of the individual’s life time, which is followed by a rapid decline in individuals within the cohort. Examples include: humans, and some plants.
2. Type II survivorship curve: Typified by a relatively constant decline in survivorship throughout the life of the species. Examples include: independent birds (although your book just says “birds”), and many perennial plants.
3. Type III survivorship curve: Typified by having a low survivorship (high mortality) early in the life of the organism, followed by a fairly high survivorship throughout the remainder of the lifespan. Examples include: many annual plants, and most invertebrates.

Survivorship curves do several things for population biologists and conservationists. Survivorship curves pinpoint when in an organism’s life it is most susceptible to dying. As a result, steps can be taken to ensure population survival if necessary. Additionally, in conjunction with life tables, the curve helps us to pinpoint when, during a species lifetime, it is at its peak reproductive output, as demonstrated below.

• 1. Fecundity
     1. Fecundity is the number of offspring an individual can have in its lifetime. Fecundity and fitness are theoretically the same. However, fecundity represents an actual value, where fitness is typically referred to in relative terms, like those found in discussions about evolution. Also, fecundity typically refers only to the number of female offspring a female can have in her lifetime, since the females are the ones producing offspring and are considered the high-investment sex. Also for this reason, when producing life tables, researchers normally use only female data. Fecundity can be combined with life table data to get yet a better picture of the potential of population change.
     2. If you add age-specific fecundity (= average number of female offspring produced by a female at a certain age) to the survivorship information on a typical life table, you can calculate the growth rate of a population.
     3. Net reproductive rate of any one age-class is calculated by multiplying Survivorship x Fecundity. If these numbers are added together across all age-classes, you get a net reproductive rate for the entire population (Keep in mind, this ignores immigration and emigration.).
        1. If the sum is <1.0 the population is getting smaller,
        2. = 1 staying same,
        3. >1 the pop is growing.
        4. What’s happening with the population in the table provided?

1. Life History Traits
   1. Generally speaking, the cost of reproduction is higher mortality. That is, the more offspring you have, the shorter your life is. An organism spends its life growing, reproducing, and maintaining its body. However, not all of these things can typically be done at the same time. How an organism allocates energy and effort into these processes is referred to as its life history. The balancing act between living and growing and reproducing is referred to as a life history trade-off, because these functions cannot occur at the same time. See the example of the common lizard (Lacerta vivipara) in the text.
   2. All organisms are selected for maximizing fitness over their lifetimes (The alternative is a lower relative fitness, which results in fewer genes in the next generation.).
   3. Those individuals (populations and species too) with high fecundity, generally have low survivorship (example: mustard plant). Lower fecundity is associated with higher survivorship (example coconut palm).