Predation, competition, herbivory and disease are all species interactions which can influence what?



For a specific generation type, we say that each female has a life span of 1 year and 1 viable breeding season and that they produce R_{0} female offspring that survive to breed the following year. What is this generation subtype called?




N_{t+1} (the net reproductive rate, or number of female offspring produced per female per generation, times the population size of females at a generation t when mutliplied give the population size of females at generation t+1)


What is important about R_{0} being greater than or less than 1?


If R_{0} is less than one, the population will decrease in size and will eventually go extinct


What is so important to note about the equilibrium point, where R_{0}=1.0?


The birth rate equals the death rate (the population is perfectly stable)


The deviation from the equilibrium plot can be expressed as z=NN_{eq}. What do these values mean?


z: deviation from equilibrium density
N: observed population size
N_{eq}: equilibrium population size


1Bz_{t} (where B equals the slope of the deviation line and z equals the deviation from equilibrium density at a given time t) is another way to express what?



This value (obtained from multiplying B and N_{eq}) tells us what type of population growth we can expect with discrete generations and certain values of B and N_{eq}


L
If 0<L<1, the population approaches equilibrium without oscillations
If 1<L<2, the population undergoes oscillations of decreasing amplitude to the equilibrium point
If 2<L<2.57, the population exhibits stalbe limit cycles (predictable but irregular oscillations) that continue indenfinity
If L<2.57, the population fluctuates chaotically with random changes depending on starting conditions


What is the instantaneous rate of population growth?


r=bd where r = percapita rate of population growth


What does the equation rN=(bd)N express and what are its components?


It is the curve of geometric increase.
N: population size
r: percapita rate of population growth
b: instantaneous birth rate
d: instantaneous death rate


Because the presence of other organisms can limit the fertility and longevity of others, what do we often see in population growth graphs?


We often see a sigmoid (Sshaped) or logistic curve


What does the equation dN/dt=rN((KN)/K) calculate and what do its terms mean?


It produces a logistic curve and takes into account the carrying capacity, K, of the organism


What is the key distinction between geometric and logistic growth?


There is no resource limitation in the case of geometric growth


What did Gause show with his Paramecium studies with respect to the logistical growth model?


He showed that under a stable environment, the paramecium species follow a generally good logistical growth pattern


What was a key issue in Pearl’s (1927) argument that logistic growth is a law? (Hint: he studied Drosophilia which were fed by yeast)


Sang (1950) criticized his use of yeast since yeast is itself a growing and changing organism so the food source for the flies was not kept constant. He also only counted grown adults whereas both adults and larvae feed on yeast


What interesting theory did Pearl and Reed generate in 1920 regarding the US population?


It would reach a carrying capacity of about 197 million people around 2060


What is the theta logistic model and how does it theoretically operate?


It relaxes the assumption that population growth rate decreases linearly as density increases; rN((KN)/K) becomes r(1(N/K)^{theta})


Under the theta logistic model, 78% of population growth curve had a theta value less than 1. What does this mean?


When populations are below K, their growth rate is low and is also low relative to that predicted by normal logistic curves


What do timelag models say about animals and their population growth models?


R_{0} at a generation t may not depend on density in that generation but in the generation before that (t = 1)


In the timelag model, how is the equation N_{t+1}=R_{0}N_{t} impacted?


This equation now becomes N_{t+1}=(1Bz_{t1})N_{t}


How do the L values change for timelag models of population growth?


 If 0;L;0.25, there is stable equilibrium with no oscillation
 If 0.25;L;1.0, there is convergent oscillation
 If L;1.0, the stable limit cycles or there is divergent oscillation to the point of extinction


What interesting facet has been discovered from experiments on the zooplankton Daphnia with regards to time delay models?


Daphnia raised at high temperatures showed continuous over and undershooting of its equilibrium density

