Wildlife Harvesting

1. Wildlife Harvesting

2. Principles of Harvesting • The harvest rate = increase at zero = the rate of population increase if no harvest • If er = 1.20, (i.e., the finite rate of increase) • ln 1.20 = r = 0.182 • H = r and r = H; r = 0.182, H (instantaneous annual harvest rate) = 0.182 • If N = average population during the year • HN = Sustained Yield (SY)/year. • So, SY for an N = 5000*0.182 = 910/year

3. Specific period • If harvest is limited to a specific season, then the isolated harvest rate (h) must be used to calculate the SY • where: isolated rate (h) = 1 - e-H • If, H = 0.182, e-H = .834, then h = 1- 0.834 = 0.166 = isolated harvest rate, for a single season • So, 5000*.166 = 810

4. Split season • If a split season, the rate is calculated as h = 1 - e-H/2; or h = 1 - e-0.182/2; or h = 1 – e -.091; or h = 1 - .913 = .087, • So, hN = 5000*.087 = 435 • This can be calculated over multiple years (e.g., 3) or days ( e.g., 365) or weeks (e.g., 52) depending on objectives.

5. Rules of Harvesting • SY is calculated from instantaneous rate H = r • If year is divided into intervals, then h = 1 - e-H/y • However, most populations do not have a positive rate of increase. • Hence, to induce a positive r we must reduce the population below K.

6. Fixed Quota Harvest • An unharvested population at or near K will have a rate of increase of zero, a population must be stimulated to increase. • Options include increasing a limiting resource or, rarely, reduce predation. • Harvesting can reduce competition for resources and increase fecundity.

7. For every density below k, there is a corresponding harvest rate of h = r that holds the population stable • In terms of yield, although H tends to increase as density is lowered, SY does not do the same. • Remember HN = Sustained Yield (SY)/year.

8. Potential Growth Curve • Curved line represents values of r and the potential for increase along the symmetrical curve. • MSY occurs at K/2. • Linear line represents continuous values from year A to B

9. The Same SY occurs at both A & B • SY at A is high % of small population, while SY at B is small % of larger population. • So, SY =HN at some point in time. • Remember, r = H

10. Yields vs Density • The lower the density, the higher the yield is as a percentage of population density (assuming constant yield) • Maximum sustainable yield (MSY) can only occur when resources are maximized. • Resources are maximized when population densities are low.

11. Maximizing Yield • Intermediate population densities tend to lead to a MSY harvests. • Fixed harvest attempts to remove the net recruitment. • However, this assumes that net recruitment is actually a surplus.

12. Sustained Yield • Under a constant-quota harvest scenario, 2 densities provide a sustained yield. • The low-density point requires more effort for harvesting the same quota than at the higher density. • Any reduction below the population density for the low point produces an overharvest.

13. MSY • The peak net recruitment curve indicates the MSY for a population. • Harvesting at this level produces instability in the population because fluctuations in density due to stochastic events can lead to overharvest.

14. Estimate potential harvest • Because SY = HN, MSY is harvested from a population of N = K/2 at H = r/2 (to yield HN = rN - (r/K) N2); thus K and r are needed to estimate MSY.

15. Harvesting example • SY known for two levels of harvest • N 4800 3900 • SY 384 546 • h .080 .140 • H .083 .151 • K ={H1N2 - H2N1}/{H1 - H2 }= 5900 • r = KH/K - N = .45; H = r /2 so H = .45/2 = .22 • MSY = h(K/2); h = 1 - e-.22 = 0.20; • thus, MSY = .20(2950) = 590

16. Selective Harvesting • Need large pieces of property • Selective harvesting by age is impractical under most circumstances; • Selective harvesting by sex is practical and profitable. • Most populations have more than enough males (i.e., white-tailed deer) • Hence males can be disproportionally harvested without affecting fecundity.

17. How much, is affected by DENSITY and RATIO of males to females • R = Nm/Nf • k = maximum number of times a male can copulate per season • kR = mean number of copulations/female and determines the proportion of females that will be fertilized. • Thus, kR - g = P, the proportion of females fertilized, where g = untapped males.

18. Let P = proportion females fertilized • P = kR - g; where females copulate once B. P = 1 - e-kR; The proportion of females that breed 0, 1, 2, etc. is a Poisson. P = 1 - e-2 = .865, kR = 20(.1) = 2 P = 1 - e-1 = .632, kR = 20(.05) = 1 Even with only 5% males, most females are still fertilized P = 1 - e-4 = .982, kR = 20(.2) = 4

19. Calcualtion of Yield • Population with 1:1 sex ratio (Pf = 0.5) at SY density, • m = 0.5, p = 0.8 when unharvested; when population (N) is harvested right after birth pulse to leave 1000 • (m=fecundity – potential reproductive capacity; p=survival) • Thus, 1000(0.8) = 800 just before pulse and is increased by 800(0.5) = 400 = Npm (recruitment) • The multiplier here is .5 because only females reproduce. • The 800 + 400 = 1200, then SY of 200 is removed to reduce population back to 1000, to repeat cycle. • Hence, SY = Np + Npm - N = 1000(.8) + 400 - 1000 = 200 • and, h = 200/1200 = 0.167 (h = SY/N)

20. Sexes seperately • If, N at 1000, with 600 females and 400 males, Pf = 0.6. (Changing sex ration will change the harvest) • SYf = = 120 females • SYm = 160 males • This demonstrates males can be harvested at a higher rate than females!

21. The relationship of SY and the proportion of the population comprised of females for three sets of fecundity and survival values. • As Pf increases the response differs depending on p and m.

22. Harvesting and the Population I. A population held at I will be a young due to the high productivity - “r” selected population (unstable environment with many offspring). • Thus, heavy harvest results in a population with a high proportion of young animals. • This can render a population very sensitive to annual changes in reproductive success.

23. Harvesting and the Population III. This can also affect productivity, depending on the relationship of age and reproductive capacity. IV. A light harvest may permit age structure with higher percent of older animals - because survival is higher, and productivity lower, there are more trophy animals – “K” selected species (stable environments with few offspring) .

24. Optimal Yield • MSY has tended to dominate fisheries management because of the food based economics involved. • But MSY is not always the most desirable: • Where big bass and big bucks, or even biodiversity are the desired end products, MSY may not be the appropriate strategy. • This is because you alter the ecosystem and food web

25. Optimal Yield • A multi-species fishery is virtually impossible to manage for all MSY: some will be overfished, others underfished. • Hence, optimal yield may not be MSY. • Occasionally, MSY will be the optimal yield

26. MSY – is at the top and you will not realize you are on the downsize of the curve until too late. • Good for fish – bad for ungulates

27. BOYD and LIPSCOMB 1976 • OBJECTIVE: To increase trophy animals, using the loose correlation of age and rack size. • Change of age structure • Use regulation change to achieve management goals • [We know now that body size is a better determinant of age – because of the impacts of nutrition, age, and genetics]

28. Percent of Kill Percent of Kill Percent of Kill • KILL 800 KILL 320 KILL 500 SUCCESS 32% 17% 23%

29. CONSEQUENCES: Four point regulation was needed to accomplish objective, illegal kill was highest ever. Protected 1 year old animals • 1. Four point regulation achieved objective • 2. Population stabilized at 7300 • 3. Harvest stabilized at 500 • 4. Protection of young bulls results in some decreased productivity

30. Walters and Bandy (1972) • Yield Optimization • 1. Reproductive potential of ungulates increases with age. • 2. Harvest shifts age structure toward young. • 3. Mortality rates lowest among middle aged. • 4. Population changes may be density-dependent.

31. For deer – every 2 years will produce a larger SY • Quality = increased ages of the population (i.e., more trophy aged animals) and success from larger population. • Trophy deer management on private lands in the southeast.

32. Private Lands • Jenks et al. (2002) at Oak Ridge Reservation, TN evaluated managing males for trophies or MSY. • Results support the hypothesis that sustained production of trophy males is a consequence of MSY of either-sex harvests when males are considered trophy with >8 points, when annual recruitment at MSY consistently approaches unity, and when hunters show no selectivity bias.

33. Stock Recruitment • The stock-recruitment model is based on a deterministic, sigmoid population growth curve. • Small population = high growth • Large population = slow growth approaching zero as it nears K. • the net number of recruits (R) is low initially, rises to a maximum, then decreases to zero. • If the shape of the sigmoid growth curve is known, the R can be predicted from the residual population (post-harvest, or pre-recruitment).

34. McCullough (1984) • Fig. 1. Sustained yields of the George Reserve deer herd as a function of residual (post-hunt) population size. • Notably, MSY is displaced slightly to the right of K/2 - likely a result of lowered reproductive potential.

35. Fixed Number Harvest • Fig. 2. The sustained yield curve of the George Reserve herd, with the horizontal line indicating a fixed number harvest. Proportional harvests are illustrated by lines A and B, with the slope indicating the proportion harvested. A is the SY proportion, where b ~0.9 = r. Slopes >r or MSY lead to extinction. “C” is the MSY proportion.

36. 2 Important points • If a fixed number, less than MSY, is harvested when the residual population is below I, the population is inherently unstable. • If a fixed number less than MSY is harvested from a residual population above I, the population is inherently stable. The population will move up or down along the SY curve and equilibrate between I and K.

37. Management Problems • The shape of the SY curve means there are two residual populations for each SY value, one above, and one below I. This creates an ambiguity and a quandary for the manager, who cannot be certain whether the population is in the stable or unstable zone, unless K and N are known. The resolution to the manager’s dilemma is the PROPORTIONAL HARVEST (b). • Stable SY = b < r. If b is greater than r, the population will grow to extinction. • Stability results because the population will move along the SY curve to the residual population size corresponding to a given b and will stay there until b changes.

38. Example 1 and 2– Figure 1

39. Using McCullough’s empirical model, b could range from near zero to about 0.8 or 0.9, with an MSY about 50% of the residual population (Fig. 3). • If the SY curve shape and b are a species characteristic, then K could vary among populations and areas without changing the range of b for MSY.

40. Management Implications • Proportional harvesting provides the manager with a framework for selecting harvest and population size objectives. • For example, managers needing to provide recreation for both hunters and non-hunters could set a light harvest quota (b<0.5). This would maintain a high population level (lots of visible deer) and still ensure fair hunter opportunity and a healthy herd.

41. Management Implications • By contrast, managers facing a substantial depredation by deer could select a b ~ 0.8. • Such a heavy harvest would maintain low population density (with reduced depredation potential), and provide limited hunting recreation. • In some situations, it may be impossible to attain the high harvest proportions desired when proportional harvesting is initiated as a strategy. • High density populations may be difficult to hunt with sufficient pressure to achieve the desired effect. Harvests of >50% can be achieved in short seasons, however.

42. QDM • Protect young “basket rack” bucks” (read “don’t shoot”) • Harvest all “spike” & “cowhorn” bucks (unbranched antlers) • Harvest does in equal numbers to the bucks taken • Harvest the trophy (8+ point antlers w/spread beyond the ears)

43. But what about… • The evolutionary consequences • Impacts on other biota • Can you live with that as a future wildlife biologist? Should you? • Giest