Ecological Archives E087-161-A1

Joseph S. Elkinton, Dylan Parry, and George H. Boettner. 2006. Implicating an introduced generalist parasitoid in the invasive browntail moth's enigmatic demise. Ecology 87:2664–2672.

Appendix A. Calculation of mortality.

We used standard techniques ( Varley et al. 1973, Royama 1981, Elkinton et al. 1992) to correct for the obscuring effect of other contemporaneous causes of death on our measures of mortality from each cause. The goal of these techniques is to estimate mortalities or marginal attack rates ( Royama 1981) from each cause of death such that the product of the corresponding proportions surviving from each cause (1- mortality, expressed as a proportion) is equal to the total survival from all causes in the interval or life stage. The techniques begin with the Varley et al. (1973) method of assuming, where appropriate, that mortalities act sequentially. For example, our collections of late instar BTM contained immature parasitoids of three tachinid species: Compsilura concinnata, Carcelia laxifrons, and Townsendiellomyia nidicola. In the last week before BTM pupation, both C. concinnata and C. laxifrons emerge from BTM larvae and form puparia outside of the host. In contrast, T. nidicola pupate within the BTM pre-pupa that are not killed by prior emergence of the other two tachinids. In the absence of experiments revealing the result of competitive interactions between these parasitoids when two or more of them attack the same host individual, the most reasonable assumption is that the species that emerges first ‘wins’ and kills the later-emerging species along with the host. Based on this assumption, the proportion of hosts attacked by T. nidicola would be the number of BTM larvae containing T. nidicola pupae divided by the number of surviving larvae following the emergence of both C. concinnata and C. laxifrons. This provides a more accurate estimate of the proportion of hosts attacked by T. nidicola than would result from dividing the number of BTM larvae containing T. nidicola pupae by the number of BTM larvae collected. When parasitoid emergence is truly contemporaneous and no sequential assumption could be made, we used the method of proportional hazards (Elkinton et al. 1992) to estimate the proportion of hosts attacked by each species:


where mj is the estimated marginal attack rate, dj is the observed proportion dying from the jth cause, and d is the proportion dying from all causes combined during the interval or host life stage. This method is appropriate when attacks by two or more parasitoid species occur simultaneously over the same interval and when, for any larva attacked by both, the first parasitoid to attack ‘wins’ and kills the other species along with the host. Again, we do not know if this condition applies to C. concinnata and C. laxifrons, but it is the most reasonable assumption to make in the absence of experimental data on what happens when both parasitoid species attack the same host individual.

We applied these calculations to the proportion of hosts yielding emerged parasitoids in the two-week interval following each collection. This approach has been termed death rate analysis (Bellows et al. 1992). We computed the cumulative BTM larval mortality (c) attributable to each mortality agent across all intervals as follows: c = 1-(1-m1)(1-m2)…(1-mi) where mi is the estimated proportion of larvae attacked or infected by that cause (marginal attack rate) that died during the two-week interval between collection (i) and (i+1), or at any time after the last collection. The estimates of survival (1 – mi) during each two-week interval multiply across causes to equal the total survival of BTM during the interval, and across intervals to equal the total survival of BTM during the time between emergence from the winter web and pupation. These calculations are fundamentally equivalent to the Varley et al. (1973) technique of expressing mortality as k-values (k = -log10 (survival)) which sum to the total K for the life stage or generation.

We illustrate the use of these techniques by applying them (Table A1) to the historical data on percent parasitism by these tachinid species collected by Burgess and Crossman (1929; Table 1). In Table A1, we present both the original percent parasitism based on the observed proportion of BTM larvae that died due to emergence of each parasitoid species (as presented in Table 1) and the corresponding estimate of percent parasitism based on the marginal attack rate. In both tables the total percent parasitism is the same. It is equal to the sum of the observed percent parasitism of each of the three tachinid species and it is equal to 100*(1-(1-mcc)(1-mcl) (1-mtn))where mCc mCl mTn are the respective marginal attack rates of the three tachinid species expressed as proportions instead of percentages.

We used the proportional hazards assumption to calculate marginal attack rates for C. concinnataand C. laxifrons (Table A1). The resulting estimates differ very little from the observed percent mortalities presented in Table 1. This occurred because the marginal attack rates among two contemporaneous parasitoids differ significantly from the proportions of hosts dying from each parasitoid only when both species have large attack rates, which is not the case for C. laxifrons in this data. For the same reason, the estimated marginal attack rates of C. concinnata and C. laxifrons in our experimental populations (Fig. 2) differed by only a few percentage points from the values we would have obtained had we computed cumulative mortality from the observed proportions that died during each two-week interval. Furthermore, both species emerged and killed their BTM host almost exclusively following the last larval collection. Thus the estimate of cumulative mortality for each parasitoid species across all collections was nearly identical to the marginal attack rate calculated for that parasitoid in the last larval collection.

In contrast to C. concinnata and C. laxifrons, the assumption of sequential emergence substantially affects our estimates of mortality from T. nidicola. In the original data (Table 1), the mean proportion of larvae that died from T. nidicola was 14.3% in coastal towns and 4.9% in inland towns. The estimated attack rate of T. nidicola was 16.3% in coastal areas, and 11.6% in inland areas. Our interpretation is that a large part of the apparent decline in percent parasitism by T. nidicola between coastal and inland habitats evident in Table 1 occurred because many of the BTM larvae in inland populations died first from C. concinnata.


TABLE A1. Percent parasitism based on the observed percentage that died and on the estimated marginal attack rate by tachinid parasitoids of browntail moth in coastal and inland New England habitats, 1923 (modified from Burgess and Crossman 1929).

Location

Compsilura concinnata

Carcelia laxifrons

Townsendelliomyia nidicola

Total Tachinids

Coastal habitat

% Dying

Marg . %

% Dying

Marg . %

% Dying

Marg .%

% Dying

Brewster , MA

3

3.11

7

     7.11

27

    30.00

37

Bourne, MA

5

5.66

22

   22.62

29

    39.73

56

Hampton , NH

1

1.03

5

     5.03

6

      6.38

12

Kingston , MA

0

0.00

0

     0.00

13

    13.00

13

Salisbury , MA

2

2.01

1

     1.01

 3

      3.09

  6

Sandwich , MA

0

0.00

0

     0.00

18

    18.00

18

Scituate , MA

1

1.00

0

     0.00

19

    19.19

20

York , ME

0

0.00

3

     3.00

 1

      1.03

  4

Mean-Coastal

1.5

1.6

4.8

     4.8

14.5

    16.3

20.8

 

 

 

 

 

 

 

 

Inland habitat

 

 

 

 

 

 

 

Andover , MA

63

63.00

0

0.00

2

  5.41

65

Burlington , MA

77

77.00

0

0.00

10

43.48

87

Dedham , MA

16

16.00

0

0.00

19

22.62

35

E. Kingston , NH

45

45.00

0

0.00

9

16.36

54

Newbury , MA

53

54.02

3

4.30

1

  2.27

57

Rowley , MA

28

28.32

2

0.00

8

11.43

38

Sherborn , MA

66

66.91

2

3.30

1

  3.13

69

Stratham , NH

13

13.00

0

0.00

0

  0.00

13

Weston , MA

20

20.00

0

0.00

0

  0.00

20

Mean-Inland

42.3

42.6

0.7

0.8

4.9

11.6

48.7

† State abbreviations are: MA = Massachusetts, NH = New Hampshire, and ME = Maine.



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