R语言中plot(y=hare, x=zlag(hare))绘图的解读咨询

Let's break this down clearly—this is a super useful plot for spotting time series patterns, especially in ecological data like your hare population example!

First, let's confirm what zlag(hare) does:
This function shifts the hare time series 1 period forward (right). So if your hare data is a sequence like [t1, t2, t3, t4, ..., tn] (where each t is the hare count in a given time period), zlag(hare) becomes [NA, t1, t2, t3, ..., tn-1]. The first value is NA because there's no "previous period" before the first observation, and R will automatically ignore this missing value when plotting.

Now, what does the plot itself show?
plot(y=hare, x=zlag(hare)) creates a scatter plot where:

• The x-axis is the hare count from the previous time period
• The y-axis is the hare count from the current time period

Each point on the plot represents a pair: (hare value at t-1, hare value at t).

How to interpret this plot: #

• If you see a clear upward trend (points clustering from bottom-left to top-right): This means higher hare counts in one period are linked to higher counts in the next—this is positive autocorrelation. For hare populations, this makes sense: more hares mean more breeding, leading to higher numbers in the next cycle.
• If you see a downward trend (points clustering from top-left to bottom-right): That's negative autocorrelation. This might happen if overcrowding in one period leads to food scarcity, causing the next period's population to drop.
• If points are scattered randomly with no clear trend: There's no strong linear relationship between the previous period's hare count and the current one—population changes might be driven by other factors (like predator numbers, weather, etc.) instead of past population size.

As a quick concrete example: If your hare data is [10, 15, 20, 18, 22], zlag(hare) is [NA, 10, 15, 20, 18]. The plot will show 4 points: (10,15), (15,20), (20,18), (18,22). You can easily see how each current value relates to the one before it!

内容的提问来源于stack exchange，提问作者Nikola