FW(ZO)353
Wildlife Management

SUSTAINED YIELD

Life table information, especially that concerning r, is useful in designing harvest schemes. Most management programs aim for some sort of sustained yield (SY), which means that the same number of animals is harvested each year (the same yield is sustained for year after year). Managing for sustained yield is easier than managing for different yields each year. Why? Once managers have figured out about how many animals can be harvested each year and maintain a constant population size, figuring out how many permits can be sold, and so forth, can be calculated relatively easily from harvest results from previous years.

Sustained yield is attained when the instantaneous rate of harvest (H) equals r for the same population without hunting. H is the rate at which harvest could occur through the year for a population that reproduces throughout the year. Since most populations reproduce seasonally and fluctuate seasonably, H is not of practical value. When harvest is restricted to a small number of seasons (usually 1 or 2), then the actual harvest rate (h) is less than H.

Figure 1. Relationship between population density of white-tailed deer does and the average number of embryos per adult and fawn doe.

For each density at which a population is maintained, there is a corresponding SY. One SY is the maximum sustained yield (MSY) and is the absolute highest yield that a population can maintain under the given conditions. MSY can be maintained only when the population size is just right. Several types of population models can be used to estimate MSY. The logistic model of population growth assumes that each new recruit to the population reduces the survival and fecundity of all members of the population equally. Although this assumption is seldom strictly true, increased population size usually leads decreased mx in populations of most wildlife, including white-tailed deer as shown in Figure 1. Thus, the assumption of the logistic model is not too far off. Note that Figure 1 is not an mx graph; it shows, instead, how population density affects fecundity of young deer and adult deer. Your demography handout showed that mx curves for hooved mammals often have a plateau for most adult females (that is, mx is the same for most adult ages). The assumption that each new recruit to the population reduces the survival and fecundity of all members of the population equally leads to a carrying capacity (K) for the population. K is the population size at which each new recruit reduces survival and fecundity exactly to match r, consequently leading to a stable population that neither declines or grows. The equation for the logistic model is


To estimate MSY with the logistic equation, one needs to know K and r. Figure 2A illustrates the relationship between population size and time for a population that starts out small and that exhibits logistic growth and shows the relationship between SY and population size for that population. The slope of the curve at any point in Figure 2A is the rate of population growth at that time. Figure 2B plots the rate of population growth (the slope of the curve in Figure 2A) against population size, showing the sustained yield possible at each population size. Note that a large population and a small population will have the same sustained yield because they grow at the same rate. The small population grows less than maximally because population size, N, is too small, making rN small. The large population grows less than maximally because the population size, N, is too large, leading to too much negative feedback on population growth; (K-N) is close to 0. Where rate of population growth is maximal, sustained yield is maximal (MSY).

Figure 2a. Population size vs time for a population exhibiting logistic growth. The slope of the curve at any point is the rate of population growth at that time. Note that the same rate of population growth can occur at very different population sizes. The population grows at a maximal rate when it has grown to 1/2 of carrying capacity, or grown to K/2.Figure 2b. Sustained yield (or rate of population growth) vs population size for the populations graphed in Figure 2a. Note that a large population and a small population will have the same sustained yield because they grow at the same rate. Maximum Sustained Yield (MSY) occurs at population size K/2.

More complex models of population growth are available that incorporate interactions between trophic levels. Such models may incorporate predation, competition, food, and other factors. MSY estimates from these models are generally lower than those from obtained from logistic models. Thus, model choice is critical to effective management of populations and estimates of MSY from the logistic model can only be used with caution or can be used as estimates of the upper limit for MSY.

When fecundity and mortality change rapidly with changes in populationdensity, MSY can sometimes be estimated from yield/effort ratios. A population must exhibit rapid turnover, however, and many, many estimates of yield/effort must be obtained over a wide range of effort intensities in order to estimate MSY with this method.

Sometimes a manager wishes to partition mortality rate into components, such as hunting and "natural" mortalities. One might express this:

    qx = hx + nx
.
where qx is mortality rate for individuals of age x (remember?), hx is hunting mortality for individuals of age x, and nx if natural mortality. BUT, these components are not independent and thus they can not legitimately be added. If hunting ceases, natural mortality will increase in compensation. Expressions are available that do weigh these components independently. For example, let hx be the proportion of age class x that would die from hunting if no other mortality occurred, and let nx be the proportion dying naturally if no hunting occurred. Then

qx = hx + nx - hxnx,

or
px = (1-hx)(1-nx)
.
Then hxnx term in the qx equation represents the overlap of the 2 mortality factors when they occur together. Since px = 1- qx, getting to the second equation is simple algebra.

Maximum sustained yield is less often the goal of wildlife managers now than it was in the past. As more and more people share in non-hunting and non-trapping uses of wildlife, management goals reflect these changes in uses of wildlife. MSY, as a rule of thumb, is possible when a population is at about of K, or K/2. Though hunters like being able to have the maximum chance of harvesting game, failure to bag game is often offset by being able to see the game being hunted. Therefore, hunters may actually prefer to have lower bag limits and a population size slightly greater than K/2. Wildlife observation is usually easier and more rewarding when populations are higher that K/2. When a population reaches K, it is limited by food and and some animals will starve. Consequently, wildlife observation is most rewarding at some level less than K. Wildlife managers now must determine the optimum sustained yield (OSY) for a population, which incorporates interests of hunters and trappers and of those who do not hunt or trap. Determining MSY is difficult for most populations because the necessary life table parameters are unknown. MSY is most often determined through trial and error and through manipulation of hunting and trapping regulations over many seasons until MSY is approximated. OSY is even more difficult to determine because optimal population size comes from a compromise between conflicting interests that often can not be quantified. Once an OSY is determined, however, it can be treated the same as any SY as far as calculations, setting of regulations, and so forth.

What about harvesting populations of animals that live in social groups? Two alternative strategies exist for harvesting such populations: harvest entire social groups and leave other groups intact, or harvest only one or a few individuals from each group. By harvesting animals, one can increase the resources available to each individual not harvested. Consequently, one should harvest in a manner that maximizes this increase in resources for a given number of animals harvested. The number of individuals that should be harvested should be determined using principles such as those discussed in this handout. The best strategy for harvesting animals from groups depends on the behavior and ecology of the animals to be harvested. If social groups overlap in their use of space, the best strategy is probably to harvest entire groups. This harvest scheme will cause minimal social upheaval in groups from which no animals were harvested and will maximize the amount of food made available to those animals. If groups are dispersed and mobility is low (if groups are territorial, for example), only one or a few individuals should be harvested from each group. This harvest scheme for animals that live in territorial will decrease the size of each group, thereby increasing the amount of food available for animals not harvested. If entire territorial groups were harvested, 'holes' would be left in the social landscape where food would be abundant, but food available for groups not harvested would not be affected.

What about fluctuating conditions? In a widely fluctuating environment, population density may not be a good measure of available resources nor will population size or density this year be an index of rate of population increase next year. Two basic methods exist for managing such populations.

1) Ignore fluctuations and consider a population at its mean, or average, level. This strategy is best when the amplitude of the fluctuations is low and the fluctuation period is short. The biggest danger is to allow too high a harvest, which can be avoided by choosing a harvest rate somewhat below that which would be appropriate for the mean population.

2) A more conservative approach is to track r and to set harvests accordingly each year. This alternative is especially advisable when little is known about a population. It may be the only alternative when fluctuations are large and of long periodicity.

What about selective harvests? Ideally a manger seeks to attain optimal harvest on all segments of a population. A sustained yield harvest can be apportioned among age classes in a variety of ways. To attain OSY one must strike a balance between harvesting individuals from ages with low fecundity and setting up the optimal future age distributions for future population production. This can be done by having low harvest on age classes with high vx. Selective harvest of age classes, however, seldom increases sustained yield. This is because few populations have sharp vx peaks (see your Demography handout) and even for those that do, distinguishing adults of different ages is usually difficult. Exceptions occur when fecundity decreases sharply after a certain age or when removal of present young increases the viability of future young.

Harvest programs are often sex-selective. In populations in which males and females do not establish and maintain long-term pair bonds, more males may exist than are needed to inseminate all reproductively active females. Mature males in their primes who have lost in the competition for mates have little potential to contribute to the population and can be harvested with little effect on the population. In this situation, MSY can be a bit higher if harvest is increased by harvesting adult males with low reproductive potential. This harvest scheme has drawbacks, however. First, identifying adult males with low reproductive potential can be difficult. To a hunter (and to most humans), those males may appear no different than the males with high reproductive potential. Young males should not necessarily be harvested because 1) some of them will have high reproductive potential in the future and 2) many males should exist in a population to challenge reproductive males and to test the vigor and health of reproductive males. Second, one must remember that the level to which males can be reduced is affected by population density. Figure 1 shows that reproduction in white-tailed deer decreases with density of does in the population. K, however, is a measure of total population density. Thus, the more bucks are harvested and not does, the greater the proportion of does in the population and lower the reproductive output of those does. It turns out the MSY for white-tailed deer comes when the sex ratio in the population and in the harvest is close 50:50. Bucks only seasons increase SY only for populations that are well below the density at which there could be MSY. This means that bucks only seasons generally do no good unless a deer population is a tiny percentage of K. Almost no deer populations exist in that condition now in the US.