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- 3. Analysis Methods
- Mortality Estimates

# Mortality as the Provider of Shell to Reef Structure

Shell is provided to the underlying reef structure through mortality. It is therefore critical to make good estimates of this parameter. Traditional methods have employed counts of

Estimating mortality from demographics** :** Mann et al. (2009b) use the age-at-length estimator to recast length demographic plots as graphs of year classes for each year and reef in the James River for the period 1998-2006. Where live cohorts could be followed for more than two successive years, the number of individuals per m2 was recorded in successive year classes. Survivorship and mortality were thus estimated by the following relationships as a proportion with values ranging from 0 – 1.0:

(1) Survivorship = #Live (t+1)/#Live(t)

(2) Mortality = #Live(t) – #Live (t+1)/#Live (t)

where #Live(t) equals the number of live oysters at time t (t, units of 1 yr). Thus mortality can be estimated provided >2 successive years of data are available, and an alternative to box count data provided. An error inherent to the approach of using just year class data is

Estimating mortality from articulated valves (box counts): So why not use the traditional and widely used approach of counting boxes? Box-length demographics can be converted to age demographics employing the assumption that all boxes are <1 year old in order to categorize the boxes into the same age classes as the live animals (that is valves disarticulate within one year of the death of the oyster). Thus live oysters with lengths x through y and boxes with lengths x through y are assumed to represent the same year class and are only counted once. If December is the end of the growing season and the surveys are in the preceding October-November, then all boxes represent mortality in that calendar year with the bulk of mortality being in the warmer months (predation, especially on the smaller individuals) and in the late summer (disease). This assumption is central to the approach that all boxes can be used in mortality estimation, although the longevity of undisturbed hinges in articulated valves has not been critically examined, and there is no requirement to estimate the “age” of new boxes as proposed by Volstad et al. (2008). We suggest that employing spat box densities may underestimate mortality in that size range because of both the fragility of the articulated box (it disarticulates quickly) and that predation related mortality does not leave an intact box in very small oysters.

If boxes are assigned to year classes and only counted once then mortality can be estimated by a second relationship as follows, again expressed as a proportion with values ranging from 0 – 1.0:

(3) Mortality = #Box(t) / [#Box(t) + #Live(t)]

The two mortality estimators are related by use of the #Live(t) value. A comparison of data from both estimators is presented in Figure 9 of Mann et al (2009b). There is a notable disparity between these two estimators with box counts providing consistently lower estimates by a substantial margin. We acknowledge the widespread use of box count data when no other data are available; however, box counts arguably underestimate mortality. Age-based data, as described above, is also not without its limitations.

The age-based demographic approach does not distinguish the contributions of natural (M) versus fishing (F) mortality. Thus generated mortality estimates are (M+F). For management purposes both are desirable in that F can be controlled, M generally cannot. Estimates of F require fishery reporting. In Virginia, the quality of this data is, unfortunately, less than optimal. Until such times as fishery-dependent data collection improves critical estimates of F are difficult to generate.

Estimating mortality from longevity: Hoenig (1983) provides a reasoned argument for the estimation of natural mortality rates based on species longevity. These are discussed for oysters by Mann et al. (2009a), who both review historical records of oyster age (10-20y, Powell and Cummins 1985) and size (up to 450 mm, DeBroca 1865) prior to the impact of harvest and, more recently, disease epizootics. Under a scenario where life expectancy is matched with a constant mortality for age classes >1y (to avoid the complication of density-dependent YOY predation loss and include the predation refuge size of 25+ mm (Eggleston 1990)) we can describe annual mortality rate, M, as a proportional value between 0.0 (all survived) and 1.0 (all died). Survival, S, is (1-M) for a period of one year or (1-M)q for a period of q years. Recalling that the plot of S versus time is exponentially declining, a 2% value for S is reached with the corresponding values for age and M: 5y at M= 0.55, 7y at M= 0.45, 9y at M = 0.35, 13y at M = 0.25, >20y at M = 0.15. Note that longevity values approaching 20 years are not unreasonable for pre-colonial oyster populations in that the maximum length of 450 mm SL from DeBroca (1865) corresponds with an age of 19y and SL of 433 mm using the modern growth curve from Mann et al. (2009b). Yet such longevity, a product of 50 million years of evolution (see discussion in Mann et al. (2009a) with respect to the role of longevity in shell production and reef accretion through positive shell budgets) is not commensurate with current observations. For almost half a century significant efforts have been underway to first understand and secondarily combat the impacts of two oyster diseases in the Chesapeake Bay, these being Dermo (*Perkinsus marinus*) and MSX (

*Haplosporidium*nelsoni ). What is evident about both diseases is that they typically can kill their hosts within the first 2-3 years of life, thus massively truncating the age demographic of the population. Such disease-compromised populations cannot, unfortunately, be modeled using mortality estimators developed from the sound life history based arguments discussed earlier.

So what drives the mortality observations of recent (50 years!) studies and how are the mortality estimators from the above equations of use? Numerous studies have used tray held oysters to assess mortality over time in conjunction with disease assays in the experimental populations. In addition, studies have examined the temporal and spatial variability in disease prevalence and intensity in field populations. With the advent of age structure description and the subsequent estimation of age-specific mortality, the option exists to match the mortality data with parallel disease date. The limitation is the ability to subtract the impact of harvest removal on a site and time specific basis and thus correct the estimate of disease-related mortality.