BISC 111/113:Lab 11: Population Growth 2: Difference between revisions

'''Population Structure'''<br>

A population is a group of individuals of the same species in a given area with the potential to interbreed. Each population has a <b>structure</b> that includes features such as density, spacing, and movement of individuals over time and space.<br>

The study of '''population dynamics''' examines the ways that populations grow or shrink over time. Reproduction and immigration account for population increases, and death and emigration account for decreases. While some populations may reproduce continually, others experience discrete periods of reproductive growth. Because some populations (e.g. human) have no distinct reproductive season, the population grows more or less continuously. <br><br>

Mathematical models offer a way to describe and predict population growth over time and under a variety of conditions.  Generally, populations grow by multiplication, if all individuals have the potential to contribute equally to the population by reproducing.  It follows then that the amount of growth that occurs is proportional to population size.  As an example, consider the measurements of a population’s size below. How fast is this population growing?<br>

Why use <b>r</b> instead of <b>λ</b>? The geometric constant depends on the interval of time specified; <b>λ</b>= 1.6 over 1 yr, in the previous example, but 2.56 over 2 yr.  The exponential constant <b>r</b> is an instantaneous measure of relative population growth at every moment in time, and is hence more generally useful.  Exponential growth is like a compound interest savings account, where the interest is continually added to the principal.  Geometric growth is akin to simple interest, where the account balance is updated once a year. Exponential growth is especially applicable to continuously reproducing populations, such as the human population.   

'''Logistic Growth.''' <br>

Exponential growth, if unchecked, could lead to unimaginable numbers of everything from bacteria to elephants. After all, the exponential rate of population increase is proportional to the population size; the bigger the population gets, the faster it grows! Of course, most natural populations never achieve their potential for unlimited size; Darwin was keenly aware of this fact.  A third model, the '''logistic population growth model''', tends to be more realistic because it takes into account “environmental resistance” ('''K''') or carrying capacity. '''K''' is the maximum, or equilibrium, population size that can be sustained theoretically by the environment. When '''K''' is reached the population growth rate is zero due to a balance of births and deaths. '''K''' is influenced by resource availability, waste accumulation, and other density-dependent factors (see below).  

 

'''Population growth in nature'''<br>

The models we have presented are more often representative of laboratory populations growing under controlled conditions, rather than the patterns seen in natural populations.  In the logistic model, as long as the population size (N) is less than the carrying capacity (K) the population will increase, and the rate of increase slows as N approaches K. However, even this model is often too simple to capture the dynamics of natural populations. If you read any of the original articles by Park about ''Tribolium'' beetles, you see that the growth curves are complex and not usually predictable. It is important to understand that K in the logistic equation is fixed, but that in reality K will continually change as environmental characteristics (e.g., availability of food & space) change. <br><br> 

 

Models of natural populations must account for the complexity of multiple interacting environmental factors.  For example, in many populations, there are distinct breeding seasons and periods of growth so it becomes important to measure the population at the same time each year to take into account when the majority of births and deaths occur.  The resources supporting populations are dynamic quantities, as are habitat characteristics, interspecific competitors, predators, and pathogens. And now, natural populations are facing the challenges of rapid local and global climate change. <br><br>

'''Density-independent''' factors, in particular, environmental factors such as temperature, precipitation, and disturbances (e.g., fire, floods, earthquakes, tsunamis) can also alter the rate of population growth. These factors, however, are density independent because they affect a certain proportion of the population independently of population size (and largely independent of individual fitness).<br><br>

Density-dependence is difficult to demonstrate in nature, in part because of frequent changes in environmental conditions. As a result, some ecologists refute the concept of “equilibrium” entirely and are currently interested in models based on chaos theory.  Chaotic systems behave in unpredictable ways, even though the factors influencing them may be quite deterministic.  As the number of such interacting factors increases, the ultimate “trajectory” a system takes, such as how a population grows, depends strongly on the starting conditions, and can be highly unpredictable. Chaos typifies many such “complex systems”.