Sin ttulo de diapositiva

1
Estimation of Death Rates in Apis mellifera
(HymenopteraApidae) Colonies exposed to Varroa
destructor (MesostigmataVarroidae), using a
Recurrence Data Approach

• Dulce M. Bustamante1, José D. Villa2 and Luis A.
  Escobar1.
• Department of Experimental Statistics, Louisiana
  State University, Baton Rouge, LA
• USDA-ARS Honey Bee Breeding, Genetics and
  Physiology Laboratory, Baton Rouge, LA

• INTRODUCTION
• Observations of unmanaged or feral honey bee
  colonies established and observed through time
  generate data structures which are not very
  compatible with standard survival analyses
  because colonies are founded by swarms in
  different months. An additional complexity arose
  from the movement of the parasitic mite, Varroa
  destructor, into the area at the end of the third
  year of observations, increasing the potential
  risk to surviving colonies at different points in
  their life span.
• The present study was conducted to explore a new
  approach to analyze survival data of honey bee
  colonies and to describe the possible effects
  that the appearance of V. destructor had in the
  mortality rates of the colonies.
• METHODS HONEY BEE COLONIES
• The field study was conducted in southeastern
  Louisiana. One hundred and four (104) swarms
  were established during nine swarming seasons
  (Spring) from 1990 to 2000.
• Swarms originated from an undetermined
  combination of feral and managed colonies in East
  Baton Rouge and Iberville parishes. After the
  arrival of parasitic mites an effort was made to
  avoid swarms from colonies artificially selected
  for resistance to V. destructor and most swarms
  were captured in St. Tammany and Tangipahoa
  parishes, in areas with little or no beekeeping.
• Colonies were monitored regularly to determine
  their status (life or death). Colonies received
  no management and no treatment to control mites
  was applied, trying to emulate feral conditions
  (Figure 1). Observations were recorded until
  September 2004.

• Using maximum likelihood methods to compare the
  adjustment of one single curve versus two curves
  to the non-parametric estimate, it was determined
  that two HPP described the curve better than a
  single HPP (Likelihood Ratio Test 14.75, 1 df,
  p0.00012) (Figure 4).
• The inverse of the maximum likelihood parameters
  from the two HPP curves provided the death rates
  of the two discrete sets of colonies.
• These maximum likelihood parameters can also be
  interpreted as the scale parameters of
  exponential distributions. This implies that the
  inverse value is also the probability that a
  colony will die in the next interval of time.
• The death rates (or probability of death) for the
  two sets of colonies were
• - NoEarly Varroa 0.087 deaths per month
  per colony
• - Late Varroa 0.037 deaths per month per colony
• DISCUSSION AND CONCLUSIONS
• Recurrence-data methods provided a satisfactory
  framework to address the problem of staggered
  entries in estimating death rates of honey bee
  colonies and are recommended for similar studies.
  
• There was a reduction in the mortality rates of
  the studied colonies five years after the arrival
  of V. destructor from 0.087 to 0.037 deaths per
  month per colony. Other factors can not be ruled
  out and future analysis of this data set should
  investigate the contribution of environmental
  variables in explaining the observed mortality
  rates.
• The results suggest the possible emergence of
  resistance to V. destructor in honey bee
  populations in the U.S., or the development of
  reduced virulence in the mite populations (Oldroy
  1999 Seeley 2004).

Figure 1. Unmanaged honey bee colony emulating
feral conditions. (Photo by J. Villa)

• Figure 2. Life times in months of 104 honey bee
  colonies.
• Each horizontal line represents a colony. The
  beginning of the line is the date when the colony
  was established and the end of the line is the
  date of death or censoring of the colony (time
  zero is March of 1990).
• The symbol x indicates colonies that died and the
  symbol - correspond to the censored colonies.
• For instance, the first colony is represented by
  the first horizontal line, it was established in
  March of 1990 and died in February 1993, which
  corresponds to a life time of 35 months.
• Varroa destructor appeared in the Fall of 1992
  (after month 30).
• The plot emphasizes the staggered entry of the
  sets of colonies into the study at different
  times.

• METHODS DATA STRUCTURE AND ITS COMPATIBILITY
  WITH RECURRENCE DATA
• The data obtained from the experiment were the
  life times (in months) of each of the 104 honey
  bee colonies
• 97 seven exact life times (start and end time of
  the colony is known)
• 7 right censored times (colonies that were alive
  at the end of the experiment)
• The colonies entered the study in a staggered
  manner, with colonies being established from
  swarms in different months and years throughout
  the 10 years of the study (Figure 2).
• Recurrent events include, for instance,
  recurrence of parasitic infestations in an animal
  after being cured. One can study the
  distribution of time between events and the rate
  at which events occur as a function of time
  (Nelson 1998).
• Some recurrent events are recorded only in
  observation windows of time with gaps between
  the windows, even though the underlying process
  is continuous over time (Zuo et al. 2004).
• Observation windows and the gaps between them can
  have random length and there is no requirement
  for the observation windows to have the same
  beginning or ending points for different
  observational units (Zuo et al. 2004), meaning
  they can enter the study in a staggered way.
• Based on the window structure, the honey bee
  colony data addressed here can be interpreted as
  follows
• The data set consists of 104 independent units
  (colonies) each unit was observed in a single
  window with
• random length equal to its life time.
• For 97 of the units, only one event (death)
  occurred at the end point of the window. The
  other 7

• Figure 3. Non parametric estimate of the mean
  cumulative number of deaths and parametric fit
  using a Homogeneous Poisson Process.
• The step like curve is the non parametric
  estimate. Notice that its slope becomes less
  steep after month 91 (March 1997).
• The dashed line represents the parametric fit.
  It is evident that it is not a very good fit.

• Figure 4. Parametric fit using a Homogeneous
  Poisson Process for the periods NoEarly (before
  1997) and Late Varroa (after 1997).
• Compare with Figure 3, and notice the improved
  fit to the non parametric estimate when
  considering these periods separately instead of a
  single fit.