Introduction

This report looks at whether the nonmasting red maple exhibits muted dynamics when compared to the the sugar maple. To figure this out, we’ll analyze data like growth rates, reproduction, and sap production. The main goal is to see if red maples have less growth overall compared to sugar maples, even when multiple factors are considered. We will also try to see what factors affect the masting of the sugar maples to see if it can be predicted.

We’ll start by comparing how many seeds are produced by the masting sugar maples. After that, we’ll look at how other factors involving the sap might indicate certain differences. We will also take a look at the flowering intensity to see if it predicts the masting of the sugar maples. By the end, we’ll have some conclusions about the masting of the sugar maples and the health of the red maples in comparison.

To analyze some of the data, we will use linear models that use three main statistics. First, the coefficient shows how much populations differ while considering specific factors. Second, the p-value tells us if those differences matter—if it’s below 0.05, it’s significant. Finally, the R-squared value shows how strong the relationship is between variables. A value close to 100% means a stronger connection. The data is retrieved from an online study named Maple Reproduction and Sap Flow at Harvard Forest since 2011.

The tidyverse library will be used for visualizations throughout the report.

library(tidyverse)

Analysis of Sugar Maple Seed Production

First, we will look at the seed production of the sugar maples over the years. Because the sugar maples are masting it is likely we will see large variation in the years. Masting is when a tree produces a large amount of seeds at the same time.

X09_maple_seed_count_csv <- X09_maple_seed_count_csv %>%
  mutate(year = as.numeric(format(as.Date(date, format = "%Y-%m-%d"), "%Y")))

yearly_data <- X09_maple_seed_count_csv %>%
  group_by(year) %>%
  summarize(average_count = mean(total.count, na.rm = TRUE))

ggplot(yearly_data, aes(x = year, y = average_count)) +
  geom_line() +
  geom_point() +
  labs(
    title = "Trend of Seed Production in Sugar Maples",
    x = "Year",
    y = "Average Seed Count")

Here we can see a large influx in certain years of seed production and then a major drop off on other years. This proves the hypothesis that the sugar maples are masting and therefore have large fluctuations in their seed production. One takeaway from this is that it seems as though masting one year leads to an increased chance of it not happening the next year and vice-versa. This is most clearly in the jumps from 2011 to 2013. However this is not entirely accurate either as there are similar counts between the years of 2014 to 2016. This data only includes the counts for the sugar maples, which makes it difficult to prove anything about the possibility of muted dynamics in comparison to the red maples. This dataset does not have counts for the red maples seeds therefore we cannot compare them.

Analysis of Average Sap Weight

Now, we’ll look at the sap production of red maples and sugar maples over the years. Since sugar maples are known for masting, we might expect to see variations in sap production as well. The goal here is to see if there are any noticeable trends in sap production for either of these species across the years.

hf285_02_maple_sap$sap.wt <- as.numeric(hf285_02_maple_sap$sap.wt)
hf285_02_maple_sap$date <- as.Date(hf285_02_maple_sap$date)
hf285_02_maple_sap$year <- format(hf285_02_maple_sap$date, "%Y")

sap_summary <- hf285_02_maple_sap %>%
  filter(!is.na(sap.wt)) %>%
  mutate(species = recode(species, ACRU = "Red Maple", ACSA = "Sugar Maple")) %>%
  group_by(year, species) %>%
  summarize(average_sap = mean(sap.wt, na.rm = TRUE), .groups = "drop")
ggplot(sap_summary, aes(x = year, y = average_sap, fill = species)) +
  geom_bar(stat = "identity", position = "dodge") +
  labs(
    title = "Average Sap Production Comparison by Year",
    x = "Year",
    y = "Average Sap Weight",
    fill = "Species")

From the graph, it’s clear that sugar maples have a higher sap production overall, with some years showing much more sap than others. On the other hand, red maples have much lower sap production and don’t seem to have the same kind of big spikes. If we take the previous graph to show the years of masting, then the sap production for the sugar maples is the highest in 2018, which had some of the lowest seed production. This could mean that sap weight is not a predictor of masting in sugar maples. However, 2013 has both high seed and sap production. Without as much data for the red maples it is hard to say if this is an exhibit of muted dynamics. They produce less sap, but that could just be a difference between the two species of maple. It would also help if there was data for each year for the red maple to help to see more patterns. Overall, sugar maples seem to experience more variation but greater sap production year after year.

Analysis of Average Sugar Concentration

We also have the sugar concentration provided by the same dataset. Likely we will see a increase in sugar concentration during the non masting years for sugar maples due to the production being higher during those years as well. For red maples we will likely see a consistant increase over the years from 2015 to 2018 in concentration if it follows the production.

hf285_02_maple_sap$sugar <- as.numeric(hf285_02_maple_sap$sugar)
hf285_02_maple_sap$date <- as.Date(hf285_02_maple_sap$date)
hf285_02_maple_sap$year <- format(hf285_02_maple_sap$date, "%Y")

sugar_summary <- hf285_02_maple_sap %>%
  filter(!is.na(sugar)) %>%
  mutate(species = recode(species, ACRU = "Red Maple", ACSA = "Sugar Maple")) %>%
  group_by(year, species) %>%
  summarize(avg_sugar = mean(sugar, na.rm = TRUE), .groups = "drop")

ggplot(sugar_summary, aes(x = year, y = avg_sugar, fill = species)) +
  geom_bar(stat = "identity", position = "dodge") +
  labs(
    title = "Average Sugar Concentration Comparison by Year",
    x = "Year",
    y = "Average Sugar Concentration",
    fill = "Species")

Sugar maples demonstrate a clear trend of higher overall sugar concentration with varying peaks in certain years, such as 2015, which coincides with minimal seed production. However, There is not enough data and it is not consistent enough to prove that sugar concentration has any relationship with masting for sugar maples. In contrast, red maples show steadier sugar production, though more data would be needed for a more definitive comparison across all years. Overall the concentration seems to be much more consistent and equal between the two maples regardless of masting for the sugar maple. Sugar concentration is also not a clear sign of muted dynamics if it is low which makes it difficult to make any conclusions from this graph.

Linear Model using Sugar Concentration to Predict Masting

Now we will try to see if we can predict the masting of the sugar maples using sugar concentration. To do this we will have to modify the data to set a masting value for the sugar maples. After looking at the data, the masting is set to yes if the total seeds produced is greater than 25 and no if it is lower. This is problematic because it bases the masting off of a single variable, but it is the best definition based on the data given.

X09_maple_seed_count_csv <- X09_maple_seed_count_csv %>%
  group_by(date, tree) %>%
  summarise(total.count = sum(total.count, na.rm = TRUE)) %>%
  ungroup() %>%
  mutate(masting = ifelse(total.count >= 25, 1, 0))
combined_data <- X09_maple_seed_count_csv %>%
  mutate(year = as.character(format(date, "%Y"))) %>%
  inner_join(hf285_02_maple_sap %>% mutate(year = as.character(year)), by = "year")

masting_model <- lm(masting ~ sugar, data = combined_data)

summary(masting_model)
## 
## Call:
## lm(formula = masting ~ sugar, data = combined_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.6807 -0.2574 -0.2464  0.7075  0.7843 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.198180   0.004341   45.65   <2e-16 ***
## sugar       0.021933   0.001689   12.99   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4343 on 150918 degrees of freedom
##   (18640 observations deleted due to missingness)
## Multiple R-squared:  0.001117,   Adjusted R-squared:  0.00111 
## F-statistic: 168.7 on 1 and 150918 DF,  p-value: < 2.2e-16

The linear model using sugar concentration to predict masting shows a positive relationship between sugar levels and masting events. The model is statistically significant with a p-value of 2e-16. However, the R-squared value is low at 0.0011, meaning that sugar concentration only explains a small portion of the variation in masting. This suggests that while sugar concentration may play a role in masting, other factors likely influence this process as well. Additionally, the model has a residual standard error of 0.4343, indicating some variability in the data that sugar concentration alone can’t fully explain. There could also be problems with this model based on the arbitrary set point of 25 seeds for the masting baseline.

Linear Model using Sugar Concentration to Predict Sap Weight

Now we will try to see if we can predict the sap weight using sugar concentration. This could show a positive relationship between the two that means the tree is healthier based on both increasing.

sap_model <- lm(sap.wt ~ sugar, data = hf285_02_maple_sap)

summary(sap_model)
## 
## Call:
## lm(formula = sap.wt ~ sugar, data = hf285_02_maple_sap)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -4.255 -2.396 -0.714  1.678 19.770 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  4.35298    0.14626  29.762   <2e-16 ***
## sugar       -0.05207    0.05747  -0.906    0.365    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.094 on 7573 degrees of freedom
##   (1447 observations deleted due to missingness)
## Multiple R-squared:  0.0001084,  Adjusted R-squared:  -2.364e-05 
## F-statistic: 0.821 on 1 and 7573 DF,  p-value: 0.3649

The results show a weak relationship between sugar concentration and sap weight. The coefficient for sugar is negative, meaning that as sugar content increases, sap weight slightly decreases. However, this relationship is not statistically significant, with a p-value of 0.365, much higher than common thresholds. The very low R-squared value of 0.0001084 suggests that the model explains only a tiny portion of the variance in sap weight. The high residual standard error of 3.094 indicates that the model doesn’t fit the data well. Overall, these findings suggest that sugar content has a minimal impact on sap weight, and other factors likely play a larger role. It is possible the health of the tree is not tied to these variables as they are not positively related to each other. However that is under the assumption that greater sap production or sugar concentration leads to a healthier tree.

Analysis of Flowering Intensity by Year

Moving to a different table within the data allows us to take a look at flowering intensity per year. This will be able to relate to the masting years that are indicated by the first graph above. Flowering should have a direct relationship to seed production as one leads to the other.

flowering_summary <- X03_maple_flower_qual %>%
  group_by(year, flowering.intensity) %>%
  summarize(flowering.intensity_count = n(), .groups = "drop")

ggplot(flowering_summary, aes(x = as.factor(year), y = flowering.intensity_count, fill = flowering.intensity)) +
  geom_bar(stat = "identity", position = "stack") +  
  labs(
    title = "Flowering Intensity by Year",
    x = "Year",
    y = "Count of Observations",
    fill = "Flowering Intensity")

From the graph, we can see that flowering intensity varies each year, with most years showing “none” or “low” flowering, and only a few years with “medium” or “high” flowering. However, there doesn’t seem to be a clear connection between flowering intensity and seed production. For example, in 2015, which had higher flowering intensity, seed production wasn’t very high, suggesting that flowering intensity might not be a good predictor of masting. On the other hand, in 2018 it was almost entirely “none” for flowering intensity and there was minimal seed production that year as well. Overall, the data doesn’t show a strong relationship between flowering intensity and masting.This data also does not include any of the red maples and only includes the data for the sugar maples. This makes it difficult to draw any conclusions from, but does allow us to see how the sugar maple relates to itself and its masting.

Conclusion

In conclusion, this analysis of sugar and red maples shows that sugar maples have large changes in seed production from year to year, which is typical of masting. However, there isn’t a clear connection between masting and sap production or sugar concentration. While sugar maples produce more sap, this doesn’t seem to match up with masting years, and sugar levels don’t strongly affect sap weight or seed production. The flowering intensity data also doesn’t show a strong link to masting. Overall, masting in sugar maples is noticeable, but it’s not easy to predict using factors like sap, sugar content, or flowering intensity. For red maples, it is too difficult with the lack of data pertaining to them to make any conclusions. The shared data to compare between the two species is small in the data provided, and difficult to compare as the expected values for certain indicators is not included. This means that whether or not the nonmasting red maple exhibits muted dynamics when compared to the sugar maple is not answerable using this dataset.