What is the impact of management on tree mortality caused by insect pest? I am monitoring tree death caused by insects and potential impact of human treatment on yearly amount of tree mortality in areas with and without human intervention. My data are recorded by remote sensing, thus my results represents the area of trees killed per year. 
Please, is there a way how to evaluate the effect of human intervention? My data contain one observation per year per category intervention/non-intervention. Is this the case of dynamic regression? 
Dataset: two areas, differing by management or non-management approaches - one without chemical treatment (A), another with chemical treatment (B). Both contain the area of killed trees in yearly time step. 
How can I decide if these two types of management differs, or if one potentially leads to decreased tree mortality? Is there a way how can I include in my analysis the amount of treatment applied each year and its impact in subsequent year? The insects develop within a year, and the treatment is applied by aerial treatment, not on specific tree thus I don't observe the immediate effect on chemical on the insect individual, as the treatment can stay on leafs of bark.
Thank you a lot for your suggestions !

sample data:
library(ggplot2)
library(gridExtra)

set.seed(100)
df<-data.frame(year = c(2001:2010),
               A = floor(runif(10, min=0, max=200)),
               B = floor(runif(10, min=0, max=60)))

a<- ggplot(df, aes(factor(year), y = A)) + ggtitle("Non Management") +
geom_bar(stat = "identity") + ylim(0,200) + ylab("area in ha") +
theme_classic() + theme(axis.text.x = element_text(angle = 90))

b <- ggplot(df, aes(factor(year), y =B)) + ggtitle("Management") +
  geom_bar(stat = "identity") + ylim(0,200) + ylab("area in ha") +
  theme_classic() + theme(axis.text.x = element_text(angle = 90))

grid.arrange(a,b, ncol = 2)

 A: The short answer is your data is too small to capture any dynamic relationship.  From your example it appears you only have 20 observations which makes any type of statistical analysis difficult.  This is especially true for model that include lags since the inclusion of a lag in a model requires the first observation of data to be drop making your already small data set even smaller.
Can you obtain data at a more disaggregated level? For example, assume that the unit of observation in your data was a hectare in a given year.  For each hectare-year you have data containing the number of trees that have died and whether or not they received the treatment.  Given this data set you could use a auto-regressive distributed lag (ARDL) model.
$$Morality_{i,t} = \alpha + \gamma Morality_{i,t-1} + \beta_0 T_{i,t}  + \beta_1 T_{i,t-1} +  \epsilon_{i,t}$$
Where $T_{i,t}$ is an indicator variable that takes on a value of 1 if the $i^{th}$ hectare in year $t$ received the treatment.  You may want to consider interacting the treatment indicator with the auto-regressive terms as well.  This will further help you answer the question, how does treatment affect the dynamics of morality.
That all being said, you may be facing a much more fundamental problem.  Is the treatment randomly assigned to the trees?  If your answer is either no or I don't know then you're potentially in a bit of trouble.  For example, in your example, imagine that the park ranger first identifies those trees which are most vulnerable to insects and applies chemicals to those trees.  If this is the case, then comparing mortality rates between treated and untreated trees is fundamentally flawed.  As a result estimate of the any treatment effect will under estimate the true treatment effect. 
The good news is that there are work arounds for this problem.  A natural solution to your application would be a panel estimator which only utilizes the variation within treatment groups.  This approach is not with out flaws.  Specifically, this approach requires that the asymmetries between groups are time invariant, which may not be true in your case.
A: This would be pretty simple to do IF (and this is a big "if") you've got data for how many trees lived, too. The other assumption, which appears to not be the case here, is that your groups are assigned randomly, ie. this area of trees is randomly selected for treatment, leaving this other group to be non-treated.
Let's pretend that you do. Let's pretend that your data looks like this:
|  Area                |  TreeID     |  Died  |
|  Intervention        |  A1         |  FALSE |
|  Intervention        |  A2         |  FALSE |
|  Intervention        |  A3         |  TRUE  |
|  NonIntervention     |  B1         |  FALSE |
|  NonIntervention     |  B2         |  TRUE  |
|  NonIntervention     |  B3         |  TRUE  |
|  NonIntervention     |  B4         |  FALSE |

At that point, it's just:  
library(dplyr)
intervention     <- alldata %>% filter(Area == "Intervention")
nonintervention  <- alldata %>% filter(Area == "NonIntervention")

results          <- t.test(intervention$Died, nonintervention$Died)

And then take a look at the new results object and see if the means are significantly different than each other.
