K Factor Analysis

Population Dynamics – Practical 2 ReportDivya Krishnamohan

Student ID: 200292988

K- Factor Analysis: The holly-leaf miner

(Phytomyza ilicis)

Practical 2 Report

POPULATION DYNAMICSBLGY 5101

(MSc. Biodiverity & Conservation)

Divya KrishnamohanStudent ID: 200292988



K- Factor Analysis: The holly-leaf miner ( Phytomyza ilicis)

Introduction:

The aim of this study is to determine the major causes of mortality in the holly-leaf miner (Phytomyza ilicis) in the area of Leeds, by performing a k-factor analysis on data obtained by dissecting local holly leaves.

The k-factor analysis is used to identify which of several mortality factors contribute most significantly towards determining the population size of P. ilicis, as well as whether the mortality factors involved are density dependent.

Life Cycle of P. ilicis

The holly-leaf miner is an agromyzid fly. During June, the female fly lays a single egg on the base of the midrib on the underside of the leaves of the holly tree (Ilex aquifolium). When the larva hatches, it slowly eats its way through the central tissue and eventually into the outer parenchyma, where it remains beneath the epidermis, feeding on the parenchymatous tissue. The ‘mine’ so formed appears irregularly shaped and pale in colour, attaining its maximum size in the month of March. Before pupating, the larva prepares a thin triangular area on the leaf cuticle against which it fits a hinged emergence plate. The larva then forms a puparium which lies pressed against the epidermis, with its anterior spiracles projecting through the attenuated area of the cuticle. The adult form emerges from the puparium by breaking through the hinged plate. The emergence of the adult is therefore identifiable on the leaf surface by a characteristic raised triangular flap.

During its larval phase, P. ilicis is subject to various threats to its survival. Several hymenopterous wasps parasitise either the larva or the pupa of P. ilicis and can be identified by the presence of a pupa characteristic of the parasitic species, or the presence of an emergence hole (usually a neat, round hole) that differs from that made by adult P. ilicis.

Another significant cause of mortality (especially during the last instar) is bird predation. The blue tit (Parus caeruleus), in particular, is adept at ripping open mines and feeding on the larvae. A mine surface that is torn is indicative of bird predation.

Further, an unknown number of diseases are seen to affect the holly-leaf miner larvae and pupae. An intact mine or puparium containing no intact insect usually indicates that the individual has succumbed to some disease.

In the following study, leaf mines present on leaves from 9 different holly trees were dissected and the fate of the insect determined. The number of survivors (successful emergents), and number of deaths attributed to parasitic wasps Chrysocharis gemma, Chrysocharis syma and Sphegigaster flavicornis; bird predation; larval disease; and pupal disease were recorded. The data were then analysed to identify the key factors of mortality influencing the population of P. ilicis under study.



Method:

The method followed was as specified in the practical handout, Practical 2. K-factor Analysis: The holly-leaf miner (Phytomyza ilicis) by Dr. K. C. Hamer.

The methodology outlined was followed with the exception of one deviation – data collected by Group- Tree 1 was transformed for the purpose of performing the necessary calculations of the analysis, i.e., as no survivors were found, calculating the mortality factor k5 was not possible; to resolve this, a value of +1 was added to the cumulative data collected by Group- Tree 1, achieved by assuming that 1 survivor was found.



Results:

Table 1.

Raw data, cumulative numbers and k values for data collected by Group- Tree1.

Life stage (cause of

mortality)

Numbers(raw data)

Cumulative numbers (a0-6)

Log numbers (of a0-6)

k value

C. gemma

Larval disease

S. flavicornis

C. syma

Pupal disease

Bird predation

Survivors

3

11

0

0

1

5

1

21

18

7

7

7

6

1

1.322

1.255

0.845

0.845

0.845

0.778

0

0.067

0.41

0.00

0.00

0.00

0.067

0.778

Total 21 K=1.322

Table 2.

Cumulative data and k values of trees 1-9.

C. gemma Larval disease

S. flavicornis C. syma Pupal disease

Bird predation

Tree a0 k0 a1 k1 a2 k2 a3 k3 a4 k4 a5 k5 K

1

2

3

4

5

6

7

8

9

21

26

23

27

18

15

16

25

22

0.067

0.073

0.040

0.000

0.000

0.000

0.058

0.018

0.000

18

22

21

27

18

15

14

24

22

0.410

0.388

0.368

0.477

0.079

0.273

0.243

0.339

0.439

7

9

9

9

15

8

8

11

8

0.000

0.000

0.051

0.000

0.062

0.058

0.058

0.000

0.000

7

9

8

9

13

7

7

11

8

0.000

0.477

0.000

0.000

0.000

0.000

0.000

0.000

0.000

7

3

8

9

13

7

7

11

8

0.067

0.176

0.000

0.255

0.160

0.243

0.243

0.041

0.204

6

2

8

5

9

4

4

10

5

0.778

0.301

0.301

0.097

0.176

0.602

0.301

1.000

0.699

1.322

1.415

0.760

0.829

0.477

1.176

0.903

1.398

1.342



Total

193 0.028 181 0.333 84 0.027 79 0.034 73 0.14 53 0.423 0.985

0.080.060.040.020.00

Mortality caused by C. gemma (k0)

1.50

1.25

1.00

0.75

0.50

Total life-time mortality (K)

0.500.400.300.200.10

Mortality caused by Larval Disease (k1)

1.50

1.25

1.00

0.75

0.50

Total Life-time Mortality (K)



0.070.060.050.040.030.020.010.00

Mortality caused by S. flavicornis (k2)

1.50

1.25

1.00

0.75

0.50


0.400.200.00

Mortality caused by C. syma (k3)

1.50

1.25

1.00

0.75

0.50




Fig.1. Relationship between the mortality factors (k0-5) and total life-time mortality (K) to determine which mortality factors are key factors.

0.300.250.200.150.100.050.00

Mortality caused by Pupal Disease (k4)

1.50

1.25

1.00

0.75

0.50


1.000.800.600.400.200.00

Mortality caused by Bird Predation (k5)

1.50

1.25

1.00

0.75

0.50Total life-time mortality (K)



28.0026.0024.0022.0020.0018.0016.00

Cumulative population (a0)

0.08

0.06

0.04

0.02

0.00

Mortality caused by C. gemma (k0)

27.5025.0022.5020.0017.5015.00


0.50

0.40

0.30

0.20

0.10

Mortality caused by Larval

Disease (k1)



15.0012.5010.007.50


0.07

0.06

0.05

0.04

0.03

0.02

0.01

0.00

Mortality caused by S. flavicornis

(k2)

13.0012.0011.0010.009.008.007.00


0.40

0.20

0.00

Mortality caused by C. syma (k3)



Fig. 2. Relationship between cumulative populations (a0-5) and mortality factors (k0-5) to determine density dependence of mortality factors.Table 3.

Kendall’s tau_b correlations between total life-time mortality (K) and mortality factors (k0-5) to determine which mortality factors are key factors.

K correlated with Kendall's tau_b Sig.

k0 0.365 0.189

k1 0.278 0.297

k2 -0.567 0.049

k3 0.471 0.121

k4 -0.141 0.600

k5 0.551 0.043

12.50010.0007.5005.0002.500


0.30

0.25

0.20

0.15

0.10

0.05

0.00

(k4)

10.0008.0006.0004.0002.000


1.00

0.80

0.60

0.40

0.20

0.00Mortality caused by Bird

Predation (k5)

Mortality caused by Pupal Disease



Table 4.

Kendall’s tau_b correlations between mortality factors (k0-5) and their initial densities or cumulative populations (a0-5) to determine which mortality factors are density dependent.

ax correlated with kx Kendall's tau_b Sig.

a0, k0 0.122 0.661

a1, k1 0.514 0.058

a2, k2 0.110 0.718

a3, k3 0.191 0.551

a4, k4 -0.120 0.667

a5, k5 0.209 0.452

key factor not a key factor

density dependent

densityindependent

Fig. 3. Classification of mortality factors affecting the population of P. ilicis in Leeds.

-- Larval disease

Bird predation C. symaS. flavicornis C. gemma

Pupal disease



Discussion and Conclusion:

Of a total of 193 holly-leaf mines examined, 10.36% of the cases were identified as having adult P. ilicis emerge successfully. It is evident that the population of holly-leaf miners under study are subject to a very high mortality rate.

The k-analysis revealed that there were two key mortality factors – bird predation, with a positive correlation value of 0.551 (P=0.043) and S. flavicornis, with a negative correlation value of -0.567 (P=0.049). (Refer Fig. 1, and Table 3).

The incidence of bird predation was recorded in 17.1% of the cases; however the ‘killing power’ of this mortality factor was seen to be 62.26% (almost 10% more than the next most significant mortality factor, larval disease). A positive, significant correlation indicates that an increased incidence of bird predation would significantly influence the total life-time mortality, causing it, in effect, to rise.

In contrast, S. flavicornis was recorded in 2.59% of the cases, having a ‘killing power’ of 5.95%. A negative but significant correlation could indicate that a lower occurrence of S. flavicornis could result in a higher total life-time mortality value. An interpretation of this result could be that given that the causes of mortality occur in a time series, i.e., each successive mortality factor acts on the proportion of survivors that have escaped the influence of the preceding mortality factor, a higher percentage of cases with S. flavicornis infections means that there are fewer individuals that are subject to mortality caused by a factor further down the time series (such as bird predation) which has a killing power with an influence 10 fold that of S. flavicornis.

Correlations of the different mortality factors with their initial densities revealed that only one factor was density dependent (marginally) – larval disease, 0.514 (P=0.58). Logically, one can conclude that an increased density of P. ilicis results in a higher proportion of individuals that get infected with larval disease as higher densities favour rapid spread of contagion.

Of the four possible types of mortality that can act on the holly-leaf miner (refer to Fig.3), P. ilicis in Leeds is affected by three types – density independent key factors, and non key factors that are both density independent and dependent. Larval disease is the one factor that is density dependent and though it is a not a key factor it may be noted that it was recorded in 50.25% of the cases.



Recommendations:

In the event that Phtyomyza ilicis is considered a pest species:

Studies have shown that a good bio-control agent should impose spatially density-dependent mortality on the victim population (Beddington et. al 1978). In this study however, larval disease is seen to be the only density-dependent factor, albeit, a non-key factor. Larval disease therefore, cannot be used as a bio-control agent as the analysis reveals that it does not significantly influence life time mortality, added to which the specific disease is unknown (it could be one of several that afflict P. ilicis).

Of the factors analysed, bird predation is seen to contribute most significantly towards the life time mortality rate of P. ilicis. The blue tit, (Parus caeruleus) is a well known predator of the holly-leaf miner. One may recommend encouraging bird predators such as the blue tit in areas targeted for reducing P. ilicis by erecting nest boxes (rather than placing bird feeders). Blue tits are aggregate feeders and providing nesting sites beside a potential food source such as an Ilex stand (having leaf mines) is likely to have the desired effect of reducing P. ilicis numbers.

Elsewhere, the use of the parasitoid wasp Chrysocharis gemma has proven successful (Clausen 1978). Other studies have indicated that C. gemma is a density dependent key factor. A possible explanation for the discrepancy in results is the scale of this study and perhaps a prevalence of habitat variables that do not encourage C. gemma in the locality from which samples were obtained.

In the event that Phytomyza ilicis is considered an important and threatened species:

In order to conserve the holly-leaf miner, it would be imperative to reduce the factors that threaten its survival. From this study it is apparent that bird predation poses a significant risk, and measures to reduce the incidence of birds feeding on P. ilicis, such as providing alternative food sources, or discouraging aggregations, may reduce larval mortality caused by this source.

Further, narrow spectrum insecticides, or even the use of pheromone baiting, may be employed to target the parasitoid wasp species (assuming they exist).

Research on the diseases that affect P. ilicis may provide valuable information on how to control and treat larval and pupal diseases.

Increasing plantations of the food plant Ilex aquifolim may help in boosting P. ilicis populations, though little is known about how host selection takes place or what specific characteristics of the host plant are desirable.



References:

Books and journals:

Heads, P. A., & Lawton, J. H. (1983). Studies on the natural enemy complex of the holly leaf-miner: the effects of scale on the detection of aggregative responses and the implications for biological control. Oikos, 40, 267-276.

Lewis, T., & Taylor, L.R. (1967). Introduction to Experimental Ecology. London: Academic Press.

Valladares, G., & Lawton, J. H. (1991). Host-Plant Selection in the Holly Leaf-Miner: Does Mother Know Best? The Journal of Animal Ecology, 60, 227-240.

Websites:

Flint, M. H., & Doane, C.C. (1996). Understanding semiochemicals with emphasis on insect sex pheromones in integrated pest management programs. Retrieved November 21, 2006 from the University of Minnesota, Radcliffe’s IPM World Textbook website: http://ipmworld.umn.edu/chapters/flint.htm

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