1. There is a clear correlation between the hare population and the lynx population across time. In particular, we see a correlation between the population sizes: An increase in the hare population is coupled with an increase in the lynx population, and vice versa. The time series population curves match one another in frequency but not in phase: The lynx population shows a slight lag compared to the hare population. The graph shows a cyclical fluctuation in the population. Finally, while perhaps a trivial observation, we see (and could have noted from the data table) that at no point in time is either the hare or lynx population zero. This is rather logical: As long as there are some members of a population alive, the population has the possibility of rebounding; if a population were to be completely extinguished (i.e., the population curve touches the horizonal axis), there would be such possibility, and we wouldn't see the sort of oscillation that we do.
2. A time series visualization of changes in two data sets allows one to track, analyze, and interpret relationships between the elements of the sets both individually and collectively. By graphing two sets of data on one graph, not only can one readily quantify the absolute differences between data from each set at a common point, but one can discern how the data change relative to each other across time. When the data sets are populations of predator and prey species, plotting both on a single time series graph allows one to quantify the populations of each at any given time as well as to compare the rate and magnitude of the changes in the absolute values of the each population within a common interval. Analyzing these parameters can help one discern any correlations between the population data, including (and perhaps most importantly) correlations that are characteristic of predator-prey relationships.
3. Lynx are specialist predators: Their primary prey is the hare. In other words, the lynx population subsists on the hare population. It's not surprising, then, that the number of lynx would be coupled with the number of hare. The greater the hare population, the greater the food supply for the lynx population. When hare are plentiful, the lynx can feed and reproduce: This results in a rise in the lynx population, which eventually results in a fall of hare population due to predation. In turn, the hare population is no longer sufficient to sustain the lynx population, so the lynx population then falls due to starvation. As the lynx population decreases, predation of the hare population also decreases; the lack of predation allows the hare population to reproduce and rise, which in turn replenishes the food supply for the lynx. This is a classic predator-prey population dynamic, and it bears out the correlation between the changes in the hare and lynx populations. Of course, in reality, there are many other factors that affect their population sizes; that's why there isn't a perfectly injective (one-to-one) correspondence in the oscillation between hare population decline and lynx population growth. But the predator-prey interaction here is significant enough to generate the sort of close coupling we see in the changes of their respective populations.
