Pine Beetle Infestation in the Black Hills. Grant Foster

Transcription

1 Pine Beetle Infestation in the Black Hills Grant Foster March 1, 2012

2 Pine Beetle Infestation in the Black Hills Grant Foster 1. Introduction At the request of Friends of the Norbeck, I have investigated the relationship between the number of trees killed each year by mountain pine beetles (MPB) and a variety of environmental factors. The factors are: drought severity index (PDSI), which measures longterm drought conditions; and third, the Palmer Z- index, which is a more short-term drought measure. To a large degree, these three measures indicate similar conditions, so all were included in order to determine which correlated most strongly with MPB outbreaks. Monthly mean temperature ( C). Freeze index, defined as the monthly minimum of 7-day exponentially smoothed overnight low temperature ( F). Average daily precipitation for each month (inches). Palmer drought severity index (PDSI). Palmer Z-index. Number of large wildfires per year. Acres burned by wildfire per year. Timber harvest (million board feet). Temperate data were included because temperature is known to be a major factor in controlling the life cycle of pine beetles throughout the year. In fact pine beetles appear to synchronize their life cycle to the seasons primarily through temperature control, by a process referred to as adaptive seasonality. Freeze index was computed because hard freeze can kill growing beetles within a tree, and is known to be a limiting factor in many instances. One should note that lower numbers indicate more severe cold. Hydrological conditions were represented by three separate measures: first, the average daily precipitation for a given month; second, the Palmer Finally, wildfire and timber harvest directly affect both the number of trees in the forest, and their hardiness (and therefore resistance to infestation), so it can be expected that these factors too might influence MPB infestation. 2. Data Data for annual tree kill due to mountain pine beetles, and for annual timber harvest, were taken from Black Hills National Forest Monitoring Reports, issued by the U.S. Department of Agriculture and the Forest Service. Data on wildfires in the Black Hills National Forest were compiled by the Wildland Fire Suppression divison of the South Dakota Department of Agriculture. 1 The data are for individual fires, recording the year of occurrence and acres burned of each fire for which historical evidence has been found. Data cover the time span from 1910 to These data constitute a reconstruction based on historical records and are certainly incomplete, with lesser reliability further back in time. Climatological temperature estimates were taken from monthly station data of the Global Historical Climate Network version 3 for the three stations nearest to the Black Hills National Forest: Rapid 1 1

3 City SD, Hot Springs SD, and Newcastle WY. 2 These data include the time-of-observation bias correction which makes them more suitable for longterm climatological study than uncorrected daily station data. To estimate the occurrence of extended hard freeze, uncorrected daily data for low temperature were acquired for those same three stations from the U.S. Historical Climate Newtork. 3 Exponential smoothing was applied with a 7-day time scale in order to characterize sustained rather than intermittent cold conditions. The lowest smoothed overnight low temperature was taken as the freeze index of a given month. 3. Time Series of MPB Tree Kill The very early (19 th century) numbers for MPB tree kill are vastly larger than those from the 20 th and 21 st centuries. We considered these early data suspect, since they are so different from later figures and are based on scant evidence. Therefore we studied the time series of MPB tree kill from 1909 through The estimated number of trees killed by MPB (in thousands) is shown in figure 1. It is evident that MPB infestation occurs as multi-year outbreaks, which explains the very strong autocorrelation of the MPB tree kill data (figure 2). In fact the autocorrelation function (ACF) of MPB tree kill is consistent with an AR(1) process, i.e., a 1 st -order autoregressive process. For such a process, the value y t of annual MPB tree kill for a given year t is a constant µ, plus a multiple φ of the previous year s value, plus a random fluctuation ε t y t = µ + φy t 1 + ε t. (1) The closeness of the MPB tree kill time series to such an AR(1) process is further indicated by the partial autocorrelation function (PACF), shown in figure 3. The only statistically significant value is at lag 1 year, which is characteristic of an AR(1) process. We further tested the general class of autoregressive integrated moving-average (ARIMA) models for AR orders p, I orders d, and MA order q from 0 to 5, in order to select the best model by the Akaike Information Criterion (AIC). 4 Using this much more thorough and rigorous approach also indicated that the best model for MPB tree kill which did not utilize environmental factors, was the simple AR(1) model. In fact, even in models which did include environmental factors, the AR(1) influence dominated the model. Therefore we began by fitting an AR(1) model to the MPB tree kill data values, then computed residuals as the difference between the observed values and the values which would have occurred if the data followed this model exactly. The model, compared to the observed data, is shown in figure 4, while the residuals from this model are shown in figure 5. The AR(1) model shown in figure 4 seems to lag the actual data by about 1 year. This is because other factors strongly influence MPB outbreak, and their impact is not included in the AR(1) model. These influences only affect the AR(1) model indirectly, through the fact that their impact is persistent, and it is this persistence which is captured by the AR(1) model. Hence in spite of the strong explanatory power of the AR(1) model, the apparent lag between this model and the data is indicative of the strength of other influences which are at work. The residuals from the AR(1) model show the departure of MPB tree kill from a simple model which excludes environmental factors, i.e., it shows the likely changes which are actually due to those environmental factors. The most extreme departures from zero indicate those years in which environmental factors are likely to have had the strongest impact. A number of such values are indicated with The Akaike Information Criterion, or AIC, is a measure of the quality of a statistical model which accounts for both how well the model fits the data, and how many parameters are required to define the model. 2

4 Figure 1: Annual MPB tree kill in the Black Hills National Forest. Figure 2: Autocorrelation function (ACF) of MPB tree kill. 3

5 Figure 3: Partial autocorrelation function (PACF) of MPB tree kill. Figure 4: AR(1) model (red) of annual MPB tree kill (data in black). 4

6 Figure 5: Residuals from AR(1) model of annual MPB tree kill. their years, including 1974 (and to a lesser degree 1977 and 1970), 2001, and most recently 2010 and Therefore, to gain clues about which environmental factors may be at work, we next examined the cross-correlation function 5 of these residuals with all the factors included in this study. A typical example is shown in figure 6, which shows significant correlation with August temperature at lag 1 year. This indicates that warm August temperatures enhance pine beetle survival and reproduction, which causes greater infestation of trees and leads to increased tree kill in the following year. This is not really a surprise, since August is the month during which most adult pine beetles leave their trees to locate a new host in which to lay eggs for the next generation. It is important to be aware that not all the possible predictor variables are independent. For example, the cross-correlations with June precipitation (figure 7), June PDSI (figure 8), and June Palmer Z-index (figure 9) all show significant correlation at lag 2 years. All three variables indicate similar conditions (with some differences), namely, water availability during June. In order to resolve which of the indicators of June water availability best represents the environmental influence on pine beetle spread, all three were tested and only the variable which produced the best model was retained. Then, the residuals from that model could be analyzed to discover whether either of the other two still had a significant influence. The routine for incorporating environmental factors into the model was as follows: the crosscorrelation functions of residuals with environmental variables identified candidate variables which may (or may not) influence pine beetle tree kill significantly. The candidate variables were tried, and the one which produced the best model (as measured by AIC) was retained. Then the residuals from that model were used to compute cross-correlations with environmental variables in order to identify a second set of candidate variables. These were added to the model one at a time, and again the variable 5 The cross-correlation function computes the correlation between two factors, allowing for a time lag in the influence of one upon the other. 5

7 Figure 6: Cross-correlation between residuals from the AR(1) model of annual MPB tree kill, and August mean temperature. Figure 7: Cross-correlation between residuals from the AR(1) model of annual MPB tree kill, and June precipitation. 6

8 Figure 8: Cross-correlation between residuals from the AR(1) model of annual MPB tree kill, and June PDSI. Figure 9: Cross-correlation between residuals from the AR(1) model of annual MPB tree kill, and June Palmer Z-index. 7

9 which produced the best model was retained. This process was repeated until the addition of more variables no longer produced significant improvement in the model. This is essentially the process known as stepwise regression. The result was a final model which included the effect of seven environmental variables: lag-1 acres burned by wildfire, lag-1 August mean temperature, lag-1 October mean temperature, January freeze index, May freeze index, lag-1 April precipitation, and lag-2 June precipitation. 4. Full Model The final model has the form y = 441 (111) (53) x (53) x (42) x (31) x (86) x 5 (2) +4.1 (17) x (170) x (134) x 8 where y = the current year s MPB tree kill (thousands of trees), x 1 = lag-1 MPB kill, x 2 = lag-1 acres burned by wildfires, x 3 = lag-1 August mean temperature, x 4 = lag-1 October mean temperature, x 5 = January freeze index, x 6 = May freeze index, x 7 = lag-1 April mean daily precipitation, and x 8 = lag-2 June mean daily precipitation. Numbers in parentheses as subscripts to the coefficients are the standard errors of the final significant digits of the coefficients. The full model, compared to the data, is shown in figure 10. The residuals from this model are shown in figure Interpetation of the Model The strongest influence on pine beetle tree kill was the previous year s tree kill, almost certaintly because strong infestation produces many beetles in the following season, which again leads to greater tree loss. This emphasizes that pine beetle outbreaks are multi-year events, and that it take many years (on the order of a decade) for an outbreak to run its course and for the forest to return to conditions of minimal pine beetle infestation. The next strongest factor was lag-1 August temperature, with warm August conditions leading to greater tree kill the following season. As mentioned before, August is the peak time of beetles spreading to new hosts; apparently warm conditions enhance the success of this spread and lead to increased infestation the following year. Another strong influence was June precipitation, with wet conditions increasing tree kill. It is interesting that this is the only variable whose influence was felt, not during the current or the following year, but two years later. It is possible that a wet June affects tree growth in a way which favors the spread of pine beetles, but that the change in tree growth impacts the following season s beetle survival, which in turn impacts tree kill in the season after that. Wet conditions in April also favor MPB tree kill, but do so in the following season rather than two seasons later. Wet Aprils may influence tree growth during the given season, or may facilitate the survival or spread of the beetles themselves during the year of occurrence. It is noteworthy that the coefficient of the January freeze index is negative, indicating that stronger freeze increases tree kill. This is contrary to expectation, since it has often been speculated that reduced wintertime freeze means reduce kill of the mountain pine beetle, allowing their increase which would threaten pine trees. However, it is also notable that the lowest value of the January freeze index is 12.1 F, which is not nearly cold enough to threaten pine beetle survival during mid-winter. Research indicates that sustained temperatures colder than 30 F are required to kill beetles during this time period. Pine beetles are more susceptible to freezekill earlier in the season, before they have accumulated significant amounts of cryoprotective chemical (primarily glycerol). Even the colder temperatures at higher altitude are therefore not cold enough during January, since the black hills are of only modest altitude (the highest peak is at altitude only 2.2 km). As for the reason for this counterintuitive coefficient, there are several possibilities. Extreme cold during January might inhibit the pine beetle s natural predators, or it might reduce the trees ability to resist infestation. I emphasize that these are only speculations. 8

10 Figure 10: Full model (red) of annual MPB tree kill, depending on lag-1 autocorrelation, lag-1 wildfire acres burned, lag-1 August temperature, lag-1 October temperature, January freeze index, May freeze index, lag-1 April precipitation, and lag-2 June precipitation (data in black). Figure 11: Residuals from the full model of annual MPB tree kill. 9

11 During May, however, more intense nighttime cold decreases pine beetle tree kill. It is possible that the beetles are less well defended against cold at this time, and are therefore more susceptible to being killed by hard freeze conditions, or that intense cold during May simply slows their natural development (which is regulated by temperature) and therefore retards their flourishing. The model fit (shown in figure 10) is quite good, but some notable differences still exist (as illustrated by the residuals shown in figure 11). The present model still does not explain most of the strong increase of pine beetles in 1974 (although it does account for some), nor the high levels of infestation in 2008 and Clearly there are other factors at work which influence the spread of pine beetles in the Black Hills National Forest, but they are probably factors which were simply not included in this study. It is also possible that some of the important interactions are strongly nonlinear; the search for nonlinear influences is beyond the scope of this study. 7. Conclusion The number of trees killed by mountain pine beetles during any given year seems to be affected by many factors. The most important influence is the previous year s tree kill, which is almost certainly due to the large number of beetles inhabiting the forest. Other factors which enhance tree kill strongly include warm August temperature and wet June conditions. Weaker but still significant influences are warm October temperature, stronger January overnight cold, milder overnight cold during May, wetter conditions during April, and greater acreage burned by wildfires. It should be emphasized that in any study involving so many variables there is always the possibility that some purported influences may be only accidental. Increasing the number of included variables creates more opportunities for random fluctuations to create spurious correlations. Hence not all the factors identified in this study may be properly causal. In particular, the influence of acreage burned by wildfire may be too strongly influenced by the single extreme wildfire season of 2000, when more than twice as much acreage was burned as during any other season, and which was followed by a large increase pine beetle tree kill during The strength of the influence of August temperature and June precipitation creates confidence in the reality of their influence. It is interesting that the amount of timber harvest seems to have had no effect on pine beetle infestation. This calls into question attempts to control pine beetles by timber harvest, although historically, timber harvest seems not to have been targeted, i.e., aimed at removing infected trees or creating forest conditions which favor reduction of pine beetles. Therefore it is not possible to conclude that timber harvest, if so targeted, is ineffective at helping control the spread of pine beetles. But the fact remains that timber harvesting in general seems not to reduce (or increase) the spread of pine beetles. Perhaps the most unfortunate missing data for this study is the amount (and type) of effort expended by humans to control the spread of pine beetles. These data were simply not available, so it was not possible to evaluate their effectiveness. Nonetheless, given the detrimental aesthetic effect of pine beetle tree kill and the severity of the most recent outbreak, one hopes that efforts to limit pine beetles in the Black Hills National Forest will be successful. 10