Robust population management under uncertainty for structured population models.

Structured population models are increasingly used in decision making, but typically have many entries that are unknown or highly uncertain. We present an approach for the systematic analysis of the effect of uncertainties on long-term population growth or decay. Many decisions for threatened and endangered species are made with poor or no information. We can still make decisions under these circumstances in a manner that is highly defensible, even without making assumptions about the distribution of uncertainty, or limiting ourselves to discussions of single, infinitesimally small changes in the parameters. Suppose that the model (determined by the data) for the population in question predicts long-term growth. Our goal is to determine how uncertain the data can be before the model loses this property. Some uncertainties will maintain long-term growth, and some will lead to long-term decay. The uncertainties are typically structured, and can be described by several parameters. We show how to determine which parameters maintain long-term growth. We illustrate the advantages of the method by applying it to a Peregrine Falcon population. The U.S. Fish and Wildlife Service recently decided to allow minimal harvesting of Peregrine Falcons after their recent removal from the Endangered Species List. Based on published demographic rates, we find that an asymptotic growth rate lambda > 1 is guaranteed with 5% harvest rate up to 3% error in adult survival if no two-year-olds breed, and up to 11% error if all two-year-olds breed. If a population growth rate of 3% or greater is desired, the acceptable error in adult survival decreases to between 1% and 6% depending of the proportion of two-year-olds that breed. These results clearly show the interactions between uncertainties in different parameters, and suggest that a harvest decision at this stage may be premature without solid data on adult survival and the frequency of breeding by young adults.

Effects of supplemental L-tryptophan on serotonin, cortisol, intestinal integrity, and behavior in weanling piglets.

Stress occurs in intensive pig farming when piglets are weaned and mixed. In this study, we investigated whether this stress might be reduced with elevated dietary levels of Trp. The effects of supplemental dietary Trp (5 g/kg of feed, as-fed basis) were tested on the neuroendocrine system, intestinal integrity, behavior, and growth performance in nursery pigs, both before and after mixing. Mixing occurred 5 d after weaning and diet introduction. On d 4, 5, and 6, Trp-fed pigs vs. control pigs showed approximately a 2-fold elevation in plasma Trp concentrations (68 +/- 7 vs. 32 +/- 2 micromol/L; P < 0.001), a 38% increase in hypothalamic serotonin turnover as measured by 5-hydroxyindoleacetic acid:5-hydroxytryptamine (P < 0.001), and an 11 to 18% increase (P < 0.05) in the intestinal villus height:crypt depth. Before (d 4) and at (d 5) mixing, saliva but not plasma cortisol concentrations were reduced (P < 0.02) by approximately 2-fold in Trp-fed pigs vs. control pigs. Intestinal paracellular (horseradish peroxidase) and transcellular (fluorescein isothiocyanate) transport of macromolecules were not affected by dietary treatment, but mixing induced a 2-fold reduction (P < 0.05) in transcellular transport. Behavioral responses (lying and standing) at mixing were not affected by dietary treatment, except on d 10 after diet introduction when Trp supplementation induced more lying and less standing (P < 0.02). Average daily gain and ADFI were not different among dietary groups (P > 0.10). In conclusion, supplemental dietary Trp (5 g/kg) to piglets increased hypothalamic serotonergic activity, reduced the salivary cortisol response to mixing, improved intestinal morphology, and reduced physical activity 10 d after diet introduction. Consequently, diets containing high Trp levels improved neuroendocrine components of stress and increased gastrointestinal robustness but did not affect behavioral reactivity in nursery pigs during weaning and mixing.

Estimation of the stoichiometry of volatile fatty acid production in the rumen of lactating cows.

The purpose of this study was to improve the prediction of the quantity and type of Volatile Fatty Acids (VFA) produced from fermented substrate in the rumen of lactating cows. A model was formulated that describes the conversion of substrate (soluble carbohydrates, starch, hemi-cellulose, cellulose, and protein) into VFA (acetate, propionate, butyrate, and other VFA). Inputs to the model were observed rates of true rumen digestion of substrates, whereas outputs were observed molar proportions of VFA in rumen fluid. A literature survey generated data of 182 diets (96 roughage and 86 concentrate diets). Coefficient values that define the conversion of a specific substrate into VFA were estimated meta-analytically by regression of the model against observed VFA molar proportions using non-linear regression techniques. Coefficient estimates significantly differed for acetate and propionate production in particular, between different types of substrate and between roughage and concentrate diets. Deviations of fitted from observed VFA molar proportions could be attributed to random error for 100%. In addition to regression against observed data, simulation studies were performed to investigate the potential of the estimation method. Fitted coefficient estimates from simulated data sets appeared accurate, as well as fitted rates of VFA production, although the model accounted for only a small fraction (maximally 45%) of the variation in VFA molar proportions. The simulation results showed that the latter result was merely a consequence of the statistical analysis chosen and should not be interpreted as an indication of inaccuracy of coefficient estimates. Deviations between fitted and observed values corresponded to those obtained in simulations.

Growth responses to dietary lysine at high and low ambient temperature in male turkeys.

Several researchers have postulated that dietary lysine requirements for turkeys are dependent upon ambient temperature. To test and quantify this hypothesis, a factorial experiment was designed with four dietary lysine levels (75, 90, 105, and 120% of NRC lysine recommendations) from 1 d of age onward and two ambient temperatures (15 vs. 30 degrees C) from 4 wk of age onward. Growth performance and carcass yields were measured, and requirements were derived from the fitted exponential response curves at 95% of the maximum possible response above that of the basal diet. In the entire experiment no significant interaction effects between temperature and lysine were observed for feed intake, BW gain, and feed:gain ratio. Exponential curves gave a very good fit (R2 > 0.89) for feed intake, and BW gain responses to dietary lysine concentrations in all age intervals. The dietary lysine requirement was estimated to be 1.67 +/- 0.09%, 1.19 +/- 0.13%, 1.08%, and 0.94 +/- 0.35% from 29 to 56 d, 57 to 84 d, 85 to 114 d, and 115 to 140 d of age, respectively. High temperature decreased all absolute processing yields in kilograms but relative cold carcass yield and relative yields of thighs, drums, and wings were increased by high temperature. Relative breast meat yield and abdominal fat were decreased by high temperature. Turkeys at low temperature responded with more breast meat to high lysine than at high temperature.

The effects of potassium diformate and its molecular constituents on the apparent ileal and fecal digestibility and retention of nutrients in growing-finishing pigs.

Five 43-kg barrows [(Dutch Landrace x Yorkshire) x Yorkshire] were fitted with steered ileocecal valve cannulas to compare the effects of K-diformate (KDF), a specifically conjugated salt vs its molecular constituents, namely, formic acid and K-formate, as acidifiers in lysine-deficient diets on the apparent ileal (ID) and fecal digestibility, retention of nutrients, and manure production. The animals were randomly assigned to five dietary treatments according to a 5 x 5 Latin square design as follows: 1) control-no acidifier; 2) 1% KDF (= 0.65% K-formate + 0.35% formic acid, or 0.7% [HCOO-] + 0.3% [K+]); 3) 0.65% K-formate (= 0.35% [HCOO-] + 0.3% [K+]); 4) 0.35% formic acid (= 0.35% [HCOO-]); and 5) 1.3% K-formate (= 0.7% [HCOO-] + 0.6% [K+]). Diets were formulated with barley, wheat, soybean meal, and canola meal as major ingredients, and provided all nutrients at adequate levels, except for lysine (24% less than estimated requirement). Feeding level was equal to 2.5 x maintenance requirement (MR) for ME (MR = 418 kJ ME x BW(-0.75)), and daily rations were given in two portions after mixing with water in a ratio of 1:2.5. Chromic oxide was used as an indigestible marker. No clinical health problems due to the dietary treatments were observed. Irrespective of the additive, there were no differences (P < or = 0.10) in the ID of DM, OM, CP, or essential amino acids compared to the control, except for phenylalanine (P < or = 0.05). Among nonessential AA, only the ID of tyrosine tended (P = 0.092) to increase (up to 3.9 percentage units). The fecal digestibility of ash and K were greater (P < or = 0.001) in pigs fed supplemental K, irrespective of its source. The greater intake and fecal digestibility of K corresponded with greater (P < or = 0.05) losses of K in urine. Body retention of N, Ca, total P, and K was similar (P > or = 0.10) among treatments. As estimated from a separate nonorthogonal analysis, supplemental K improved (P < or = 0.05) body N by 3.7 percentage units compared to the control. The results of this study do not provide a clear explanation for the improved growth performance reported previously with KDF and its molecular constituents, and further research on their in vivo mode of action will require methodological refinement, especially with regard to the efficiency of AA utilization.

The effects of calcium benzoate in diets with or without organic acids on dietary buffering capacity, apparent digestibility, retention of nutrients, and manure characteristics in swine.

Eight barrows (Yorkshire x [Finnish Landrace x Dutch Landrace]), initially 30 kg BW, were fitted with ileal cannulas to evaluate the effects of supplementing Ca benzoate (2.4%) and organic acids (OA) in the amount of 300 mEq acid/kg feed on dietary buffering capacity (BC), apparent digestibility and retention of nutrients, and manure characteristics. Swine were allotted in a 2 x 4 factorial arrangement of treatments according to a cyclic (8 x 5) changeover design. Two tapioca-corn-soybean meal-based diets were formulated without and with acidogenic Ca benzoate. Each diet was fed in combination with OA (none, formic, fumaric, or n-butyric acid). Daily rations were equal to 2.8 x maintenance requirement (418 kJ ME/BW(.75)) and were given in two portions. Chromic oxide (.25 g/kg) was used as a marker. On average, Ca benzoate lowered BC by 54 mEq/kg feed. This salt enhanced (P < .05) the ileal digestibility (ID) of DM, OM, arginine, isoleucine, leucine, phenylalanine, alanine, aspartic acid, and tyrosine (by up to 2.4 percentage units). Also, the total tract digestibility (TD) of DM, ash, Ca and GE, and Ca retention (percentage of intake) was greater (P < .05) in swine fed Ca benzoate, whereas N retention remained unaffected. Addition of all OA (formic and n-butyric acid, in particular) exerted a positive effect (P < .05) on the ID of amino acids (except for arginine, methionine, and cysteine). A similar effect (P < .05) was found for the TD of DM, OM, CP, Ca and total P and for the retention of N and Ca. In swine fed Ca benzoate, urinary pH decreased by 1.6 units (P < .001). In conclusion, dietary OA have a beneficial effect on the apparent ileal/total tract nutrient digestibilities, and Ca benzoate increased urine acidity, which could be effective against a rapid ammonia emission from manure of swine.

Follicular dynamics, repeatability and predictability of follicular recruitment in cows undergoing repeated follicular puncture.

The aim of our study was to characterize follicular recruitment and growth in response to the repeated removal of follicles. All tertiary follicles (> 2 mm of diameter) in the ovaries of 10 non-lactating Holstein Friesian cows were punctured at midcycle (Day 0) by means of an ultrasound-guided needle. Puncture sessions were scheduled twice weekly at 3- or 4-d intervals over 3 mo. In the middle of the experiment, i.e., Week 7, the effects of 2- and 5-d intervals between follicular punctures were tested and compared with the previous 3- and 4-d intervals. After this period, 6 animals were slaughtered to study the effect of puncturing on gross ovarian morphology. The protocol of puncturing follicles with 3- to 4-d intervals was continued for an additional 3 mo in the remaining 4 animals. Twice-weekly puncturing of all tertiary follicles abolished estrous cycles and lead to an increase in follicular wave frequency without apparent negative effects on either the reproductive tract or ovaries. After puncture the new follicular wave attained full numerical development within 3 d. Two-day intervals resulted in a lower number of follicles than the 3-d interval (11.0 -/+ 3.8 vs 15.4 -/+ 6.1; P < 0.05). In contrast 4- and 5-d intervals between puncture resulted in an increase in follicle size when compared with that of the 3-d interval. The mean+SD number of recruited follicles varied between animals ranging between 78 +/- 2.5 to 19.2 -/+ 6.0. The mean number of follicles recruited increased from the first month (March) to the third month (May) of sampling (11.8 +/- 4.7 vs 16.4 +/- 6.5; P < 0.01), and then decreased between the third (May) and the sixth (August) month of sampling (21.5 +/- 4.7 vs 16.8 +/- 5.0; P < 0.01). During the experiment, the number of recruited follicles varied cyclically, with waves having a length of 6 puncture session (PS) or 3 wk (i.e., the mean length the bovine estrous cycle). Follicular recruitment after repeated ovum pick-up showed a high repeatability (r = 0.576) A model was also developed showing good predictability of the potential of animals to recruit follicles on the basis of the first 4 to 6 PS. Our results showed that despite large variation in follicular recruitment between animals, the high repeatability and good predictability of follicle recruitment demonstrates the possibility of characterizing animals on their potential for follicle growth.

Modeling gas production kinetics of grass silages incubated with buffered ruminal fluid.

Time course measurements of in vitro gas production of feedstuffs incubated with buffered ruminal fluid give information about the rate at which the feed is fermented. To compare gas production kinetics from different feeds, a mathematical model was needed to describe the data. We investigated several existing models (exponential, logistic, Gompertz, Richards, Schnute), fitting them to 50 gas production curves obtained with grass silages. None of them gave a satisfactory description of the data. A new model was developed (modified Gompertz model; mGom) that basically divided gas production into two fractions, one arising from rapidly fermentable feed components and the other from slowly fermentable feed components. Residual mean squares (RMS) for the mGom model were lower (P < .05; n = 50) than the RMS for the other models. A good statistical comparison of kinetic gas production data is made possible with the mGom model.