3.1. Population Density and Survival
Several population density expressions have been used: Per branch, per m
2, per 10 ft
2 or 10 m
2 or per kg of foliage are common in the literature. Insects per kg of branch reduces branch to branch variance, is easy to measure, and eliminates differences in SBW density between balsam fir, white spruce and black spruce [
18]. While counting growing shoots is more tedious, we have found it has the same virtues of variance reduction and homogenization between host plants. We believe that, because the number of shoots per unit foliage weight can vary in response to defoliation, and because it is shoots that are the main budworm food resource, whenever possible this is the ideal unit to use as denominator in density calculations. On balsam fir, the transformations between density expressions can be done with the following factors: 1052 shoots/m
2 and 722 shoots/kg, and 0.686 m
2/kg.
There was no significant difference in adult density estimated from the pupal samples or from pupal exuviae recovered in the eggs samples in 2014 (intercept −0.001 ± 0.003, not significantly different from 0: t = −0.46, p = 0.65; slope 1.065 ± 0.083, not significantly different from 1: t = 0.78, p = 0.45). Thus, estimating adult density using the exuviae recovered from the egg sample is an adequate cost-cutting strategy, provided that the egg sample is not delayed any longer than necessary once egg hatch is complete.
The most important result of this study is the density-dependent shape of the relationship between survival from early feeding larvae to adults
S, and larval density
N, well described with Equation (1) (
R2 = 0.71;
Table 1;
Figure 3), excluding the observation from plot LSL-24, an outlier where an unexpectedly high survival to adults was observed (see
Figure 3e). Two terms of this model were not significant (after stepwise reduction). In particular, there was no significant difference in survival between untreated populations in 2012 and 2013 (parameter
p1|2013 not significantly different from 0,
Table 1). Survival in the LSL as well as the SOPFIM untreated plots was significantly higher in 2014 than in 2012 (parameters
p1|2014 and
p1|SOPFIM both significantly higher than 0,
Table 1).
The relationship between larval and adult density (given by the product
A =
N ×
S with
S predicted by Equation (1)) is sigmoidal, with a rapidly increasing slope as larval density increases, and levelling off near 0.05 adults per shoot at larval densities exceeding 0.25–0.3 L
4/shoot, suggesting increased competition for food (
Figure 3a–c). Survival
S followed a non-monotonic pattern of rise and decline in each dataset (compare to
Figure 1, Theory 1 curve): Low survival at low density, high survival at medium density, and decreasing survival at still higher density (
Figure 3d–f).
These data confirm that even in rising outbreaks, low-density incipient populations face heavy mortality. Rising spruce budworm populations that are high compared to endemic populations, but still low compared to full outbreak are still facing growth challenges due to density-dependent mortality, consistent with double-equilibrium theory (
Figure 1, Theory 1) but not with oscillatory theory (
Figure 1, Theory 2).
The treatment parameter
p2|2012 for the effect of Btk in 2012 was not significantly different from zero (
Table 1), and there was no detectable mortality attributable to Btk in 2012 (
Figure 3a,d). Because deposit was not measured in 2012, there are no data to support the hypothesis that poor deposit was the cause for this poor product performance. Yet, because the application was done with a small Cessna aircraft with weak wake, it is possible that little product ended up on the target foliage. The tebufenozide applications in 2013 and the Btk applications in 2014 both generated very high mortality rates (parameters
p2|3013 and
p2|2014 both significantly lower than zero,
Table 1;
Figure 4). We estimated the mortality inflicted by the insecticide treatments
π from the observed survival in treated plots
S and the survival expected to occur in untreated populations at the same larval population density calculated with Equation (1),
S(
N):
The resulting estimates range from 70% to 100% mortality from insecticides (
Figure 4). It is interesting that mortality attributable to insecticides was higher in lower density populations both in 2013 and in 2014, despite the fact that two products with very different modes of action were used. This could very well be an indication of compensation (see [
5]): Some of the mortality due to competition was relaxed by the insecticide applications.
3.2. Defoliation
The relationship between defoliation and larval population density (at the L
4) varied by year and insecticide treatment (
Table 2;
Figure 5). From other sources, one would expect a saturating shape with a monotonically-declining slope [
22]. High natural mortality rates in lower density rising populations are probably responsible for the sigmoid shape of this relationship, depressing defoliation at lower densities. Among untreated populations, defoliation increased significantly from year to year at lower population densities, reflecting the increasing survival trend noted in the previous section. The Btk applications of 2012 had no effect on defoliation. The tebufenozide treatment in 2013 produced a significant but modest reduction in defoliation (dotted line in
Figure 5a). In 2014, the Btk applications had a very pronounced effect on defoliation (bold dotted line in
Figure 5a). We suspect that the limited impact of tebufenozide on defoliation in 2013 was caused by the late application (5th instar) compared to the 4th instar application of Btk in 2014.
There was a strong relationship between emerging adult density at the end of the season and the defoliation inflicted by the larval populations in untreated plots (
Figure 5b). This relationship suggests that adult density is limited by competition for food, and that this competition reduces survival once defoliation exceeds 40%, corresponding to larval populations of 0.2 L
4 per shoot.
3.4. Recruitment to the Egg Stage
There was a clear relationship between egg and surviving adult density in each year (or dataset) except 2013. This relationship was very well described by Equation (5), fitted by non-linear regression (
R2 = 0.92) (
Table 4;
Figure 7). The intercept parameter
I, representing the immigration rate (eggs/shoot), varied between 0.015 ± 0.006 in 2012 to 0.248 ± 0.072 eggs per shoot in 2014, and was always significantly different from zero implying that there was always detectable immigration in those sites. The realized fecundity parameter
F ranged from 1.61 ± 1.61 in 2013 (not significantly different from 0), and 45.7 ± 7.7 in 2015, a level of variation that indicates a wide range of emigration rates from year to year.
In 2012, when the developing outbreak in the LSL was just beginning and populations were generally low in the region, the immigration rate and the realized fecundity of resident moths (parameters
I and
F of Equation (5)) were low (
Figure 7a). As a result, the relationship between apparent fecundity and resident adult density had a slope near 0, an indication of limited migration activity (
Figure 7b) (see [
20] for a thorough discussion of this topic). The same was true in 2014 among SOPFIM sites (
Figure 7e,f). Although we suspect the resident adult density in the SOPFIM sites was overestimated in 2014 due to an early pupal sample (as evidenced by the high upper asymptote of adult density in
Figure 3c), these parameter values suggest net emigration of gravid females with little immigration, but may also have been the result of low mating success [
15]. The exact contribution of those factors to the low reproduction in 2012 and again in 2014 among SOPFIM sites is not clear, but we speculate that intensive emigration with little immigration is the most likely explanation. Those populations were located at the edge of the developing outbreak in the corresponding years. In both situations, spruce budworm populations were sparse in the study area and sources of regional immigrants would have been few or distant.
This is in sharp contrast with 2013, when there was no significant relationship between egg and resident adult density (
Figure 7c). In that year, the realized fecundity of moths (
F2013) was so low that it was not significantly different from zero, which suggests that many moths emigrated before laying eggs. While this is biologically unlikely, it does indicate that 2013 was a particularly intensive migration year (high immigration, low realized fecundity of resident moths). As a result, the slope of the relationship between apparent fecundity and resident moth density in 2013 was very near the extreme of −1 (
Figure 7d), which is a telltale sign of regionally random redistribution of eggs through extensive migration of ovipositing female moths (defined as panmixis and explained in detail in [
20]). In 2014, the immigration rate was highest among the LSL sites (
I2013 = 0.25 ± 0.07 eggs per shoot), and realized fecundity was high (
F2013 = 33.8 ± 9.4 eggs per moth) (
Figure 7e). In 2015, realized fecundity of resident moths was high (
F2015 = 45.7 ± 7.7 eggs per moth), and immigration rate was near average (
I2015 = 0.112 ± 0.05 eggs per shoot), suggesting a year with low migration activity (
Figure 7g). Because of the relatively high adult populations in the LSL in both 2014 and 2015, the slopes of the apparent fecundity relationships with resident adult density was closer to 0 than in 2013, which indicates that those were not years of extensive moth migration (
Figure 7f,h).
The relationship between apparent fecundity and current-year defoliation was highly significant (
Table 5) and was well described by Equation (7) (
Figure 8a). Its slope and intercept varied between years (datasets), but generally apparent fecundity dropped to its minimum at defoliation in the range of 20%–30%. This pattern supports the hypothesis that spruce budworm females tend to emigrate from defoliated stands, and that they can sense a fairly low amount of defoliation.
Additional support for this hypothesis comes from the significant reduction of egg mass size in populations with clear net immigration, as represented by Equation (8) (
Table 6,
Figure 8b). While egg mass size variability was very high (due in large part to small sample sizes), the relationship explained 47% of this variation. The mechanism for this relationship seems simple: Immigrant moths are often mostly “spent” (have few eggs left in their oviducts), and there is a strong correlation between egg mass size and remaining fecundity in spruce budworm [
21]. Thus, small egg masses indicate oviposition by immigrants, while large egg masses indicate oviposition by residents.
3.5. Annual Population Growth Rate
Population growth rates in 2012 were near the replacement line (
R = 1), and were not clearly affected by applications of Btk (
Figure 9a). In 2013, population growth rates were very high in low density populations, and well below replacement in higher density sites. Although the tebufenozide applications of 2013 were highly efficacious, they did not result in a clear reduction of population growth rates (
Figure 9b). Moth migration activity was extremely pronounced in 2013, blending populations over the entire study area. In 2014, among the 13 LSL sites, annual growth rates were very high in untreated populations, and at or below replacement in sites treated with Btk (
Figure 9c). Among the 10 SOPFIM sites in 2014, located at the western periphery of the expanding outbreak of the LSL, growth rates were close to replacement, and had a very similar density dependence to that observed in 2012 in the LSL (
Figure 9d). Clearly, insecticide applications can have a strong impact on population growth rates, but not in years when extensive moth dispersal occurs, such as in 2013 in the LSL region.