1 / 43

Wildlife Harvesting

Wildlife Harvesting. Principles of Harvesting. The harvest rate = increase at zero = the rate of population increase if no harvest If e r = 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

Gabriel
Download Presentation

Wildlife Harvesting

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related