Douglas P. Peterson, Bruce E. Rieman, Michael K. Young, and James A. Brammer. 2010. Modeling predicts that redd trampling by cattle may contribute to population declines of native trout. Ecological Applications 20:954–966.

Appendix A. Derivation of finite mortality for cutthroat trout embryos resulting from redd trampling by cattle.

Roberts (1988) and Roberts and White (1992) present laboratory data on the effects of single- and multiple-wading events by anglers on egg-to-fry survival of Yellowstone cutthroat trout (Oncorhynchus clarkii bouvieri), brown trout (Salmo trutta) and rainbow trout (Oncorhynchus mykiss). To derive mortality estimates for stream-resident cutthroat trout resulting from redd trampling by cattle we proceeded as follows:

1. We assumed that the finite (and instantaneous) mortalities associated with angler wading and cattle trampling were equivalent, as empirical data for the latter are not available.
2. We used data from single-wading events to derive estimates for stage-specific mortality.
3. We defined discrete developmental stages from egg-to-fry based on the progression of embryonic development and sensitivity to wading effects. The duration of any particular stage is controlled by the accumulation of Celsius temperature units (CTU), defined as the sum of mean daily temperatures in degrees Celsius.
4. We used experimental data for Yellowstone cutthroat trout, supplemented by data for a closely related species (rainbow trout) when estimates for important or sensitive developmental stages were lacking for cutthroat trout.
5. We assumed a type-2 fishery model (Ricker 1975) to decompose wading (trampling) effects from natural mortality in the absence of wading.

The sensitivity of trout embryos to mechanical disturbance varies by developmental stage (Roberts 1988, Roberts and White 1992). The green egg stage (0–175 CTU) experiences comparatively low mortality and low sensitivity to wading, except around the time of blastopore closure, between about 80–100 CTU.  Since experimental data for cutthroat trout were not available during this period, the estimate for finite mortality at this stage was supplemented with data for rainbow trout (Table A1).  The eyed egg stage experiences two discrete periods of sensitivity to mechanical impacts, so we further divided this stage into two parts.  The eyed egg 1 stage (176–260 CTU) roughly corresponds to start of the eyed stage until the start of chorion softening, and is less sensitive than the eyed egg 2 stage (261–300 CTU) that occurs between the start of chorion softening and hatching.  The pre-emergent sac fry stage (331–500 CTU) encompasses the post-hatching period when sac fry remain in the stream gravels, and is more sensitive to mechanical impacts than the green egg and eyed egg 1 stages.  Data for the comparatively short hatching stage (301–330 CTU) are not available for cutthroat trout, however data for rainbow trout and brown trout both suggest that sensitivity during this stage is intermediate between the eyed egg 2 and pre-emergent sac fry stages.  We thus assumed that wading (and trampling) effects for hatching cutthroat trout would also be intermediate (Table A1).

Total instantaneous mortality in the absence of trampling (Z_NT) is an estimate for the controlled laboratory conditions of Roberts and White (1992), but provides an approach to partition stage-specific mortality in a natural population (i.e., estimate the Z_NT(i)).  Based on the sum of stage-specific natural mortalities    the finite mortality during the n = 5 developmental stages from egg-to-fry in the lab was  which likely underestimates mortality in many wild populations.  However, the stage-specific estimates of natural mortality derived from the laboratory conditions (Table A3) can be used to scale the corresponding estimates for a wild population with a given (assumed) finite mortality.  Assuming the relative mortality is similar in laboratory and field settings then, for example, 9.22% of the total mortality occurs in the green egg stage (Table A3).   For example, a wild population with 0.95 total finite mortality would have Z_NT= -ln(1-0.95) = 2.996, so the instantaneous mortality during the green egg stage would be 0.0922 × 2.996 = 0.276.  Instantaneous rates for the other developmental rates in the wild population could be similarly calculated.  Then, total instantaneous mortality would be calculated as .

TABLE A1. Mortality of rainbow trout (RBT) and Yellowstone cutthroat trout (YCT) in response to a single wading event during a particular stage of embryonic development based on data from Roberts (1988) and Roberts and White (1992).

Note:  Total finite mortality (A_i) was mortality estimated for treatments subjected to a single wading event, while natural finite mortality (M_i) was mortality in the controls (no wading).  The mortality estimates for the controls (M_i) were not adjusted for handling effects.

† Laboratory experiments of Roberts (1988) and Roberts and White (1992) that estimated mortality from single wading events were repeated for some species (test 1 and 2 for RBT) and conducted in enclosures of two different sizes (0.3 and 1.0-m wide).

TABLE A2. Mean finite mortality based on data from Table A1.

Note: Experimental data for the hatching stage were not available, so estimates are based on interpolation (average) between the estimates for eyed egg 2 and pre-emergent sac fry.

TABLE A3. Stage-specific estimates for instantaneous mortality of cutthroat trout in the presence Z_TR(i) or absence Z_NT(i) of a single trampling event by cattle.

Notes: Values were based on finite estimates presented in Table A2, as estimated in laboratory conditions. Total instantaneous mortality is the sum of natural and trampling-related instantaneous mortalities, so a redd trampled during each developmental stage would experience instantaneous mortality equal to 1.2392 plus the total natural mortality (0.7929 in this example).

LITERATURE CITED

Ricker, W. E. 1975. Computation and interpretation of biological statistics of fish populations. Bulletin 191, Department of the Environment, Fisheries and Marine Service, Ottawa, Canada.

Roberts, B. C. 1988. Potential influence of recreational use on Nelson Spring Creek, Montana. Master’s thesis. Montana State University, Bozeman, Montana, USA.

Roberts, B. C., and R. G. White. 1992. Effects of angler wading on survival of trout eggs and pre-emergent fry. North American Journal of Fisheries Management 12:450–459.