10. Using Matrix Models to Focus Research and Management Efforts
163
were very sensitive to changes in survival rates of medium to large fish (Fig.
10.4b, c); increases in medium to large fish survival resulted in more large fish in
the equilibrium population.
The factorial examination of population response to combinations of anthropogenic impacts revealed important information for management. Potential
Brook Trout responses to Rainbow Trout competition and predation included a
decrease in survival rate of small fish, a change in density dependence in survival
of small fish, and a decrease in growth rates of all sizes. Population size tended to
decrease with an increase in small-fish growth rate (producing a population with
fewer but larger fish), but there was an interaction between the effect of small-fish
growth rates and small-fish survival rate on ultimate population size. Brook Trout
responded to decreases in pH, with decreased growth rate in all size classes,
decreased survival rates of small fish, and decreased egg-to-larva survival rates.
This combination of effects, at magnitudes documented in laboratory experiments, had severe negative impacts on the model population. Relatively small
effects of changes in pH for Rainbow Trout resulted in local extinctions. By
contrast, neither the increase in large fish mortality associated with sport harvesting nor the increase in egg-to-larva mortality associated with sedimentation
caused local extinctions.
Discussion
Resources are limited to conduct research on population ecology of threatened,
endangered, and other species of concern to conservation biologists. As a result,
we need to invest our financial and human resources wisely, to maximize our
ability to forecast population change. The age- and stage-based matrix modeling
approaches we have outlined in this chapter and, in particular, the elasticity
analyses of these matrices, provide guidance to focus research efforts. The analysis allows us to identify sensitive life stages and processes; these parameters have
disproportionate effects on population responses and so need to be better understood to increase our confidence in making forecasts. For example, it is relatively
inexpensive to estimate survival rates for sea turtle eggs or annual fecundity of
female sea turtles, but the population growth rate is relatively insensitive to these
components of the model (Crouse et al. 1987; Crowder et al. 1994). We would be
much better off enhancing our understanding of survival rates in the small and
large juvenile stages, although these data will be difficult to acquire. Similarly, in
fish, it appears that we need to focus our efforts on making better estimates of
survival in the juvenile stages. It is easier to work on adults (which can be tagged)
or early larvae (for which estimates can be made using netting techniques), but the
survival in the juvenile stage is often the most sensitive component in the model.
If it is generally true that fish population growth rates are relatively sensitive to
survival in the late larval and juvenile stages, this will be challenging to study
because in many fishes these are difficult stages to assess quantitatively (Crowder
et al. 1992). In the meantime, the elasticity analysis may help us focus interim
163
were very sensitive to changes in survival rates of medium to large fish (Fig.
10.4b, c); increases in medium to large fish survival resulted in more large fish in
the equilibrium population.
The factorial examination of population response to combinations of anthropogenic impacts revealed important information for management. Potential
Brook Trout responses to Rainbow Trout competition and predation included a
decrease in survival rate of small fish, a change in density dependence in survival
of small fish, and a decrease in growth rates of all sizes. Population size tended to
decrease with an increase in small-fish growth rate (producing a population with
fewer but larger fish), but there was an interaction between the effect of small-fish
growth rates and small-fish survival rate on ultimate population size. Brook Trout
responded to decreases in pH, with decreased growth rate in all size classes,
decreased survival rates of small fish, and decreased egg-to-larva survival rates.
This combination of effects, at magnitudes documented in laboratory experiments, had severe negative impacts on the model population. Relatively small
effects of changes in pH for Rainbow Trout resulted in local extinctions. By
contrast, neither the increase in large fish mortality associated with sport harvesting nor the increase in egg-to-larva mortality associated with sedimentation
caused local extinctions.
Discussion
Resources are limited to conduct research on population ecology of threatened,
endangered, and other species of concern to conservation biologists. As a result,
we need to invest our financial and human resources wisely, to maximize our
ability to forecast population change. The age- and stage-based matrix modeling
approaches we have outlined in this chapter and, in particular, the elasticity
analyses of these matrices, provide guidance to focus research efforts. The analysis allows us to identify sensitive life stages and processes; these parameters have
disproportionate effects on population responses and so need to be better understood to increase our confidence in making forecasts. For example, it is relatively
inexpensive to estimate survival rates for sea turtle eggs or annual fecundity of
female sea turtles, but the population growth rate is relatively insensitive to these
components of the model (Crouse et al. 1987; Crowder et al. 1994). We would be
much better off enhancing our understanding of survival rates in the small and
large juvenile stages, although these data will be difficult to acquire. Similarly, in
fish, it appears that we need to focus our efforts on making better estimates of
survival in the juvenile stages. It is easier to work on adults (which can be tagged)
or early larvae (for which estimates can be made using netting techniques), but the
survival in the juvenile stage is often the most sensitive component in the model.
If it is generally true that fish population growth rates are relatively sensitive to
survival in the late larval and juvenile stages, this will be challenging to study
because in many fishes these are difficult stages to assess quantitatively (Crowder
et al. 1992). In the meantime, the elasticity analysis may help us focus interim