PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES rerurn on or before date due. DATE DUE DATE DUE DATE DUE - : "WSW 3%?— C: __7 J[_ll :7] MSU Is An Affirmative Action/Equal Opportunity Institution cmmhd AN EMPIRICAL AND THEORETICAL INVESTIGATION INTO THE ADAPTIVE SIGNIFICANCE OF HATCHING ASYNCHRONY AND BROOD REDUCTION IN THE TREE SWALLOW (IAQEXQINEIA EIQQLQB) BY Bryan Christopher Pijanowski A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Zoology 1991 gov-Jon's. ABSTRACT AN EMPIRICAL AND THEORETICAL INVESTIGATION INTO THE ADAPTIVE SIGNIFICANCE OF HATCHING ASYNCHRONY AND BROOD REDUCTION IN THE TREE SWALLOW (TAQHXQINEIA EIQQLQB) BY Bryan Christopher Pijanowski This thesis investigates whether the brood reduction hypothesis can adequately explain the adaptive signifi- cance of hatching asynchrony in the tree swallow (Igghygi; neg; bigolor). The first chapter discusses the major hypotheses proposed to explain the adaptive significance of hatching asynchrony in altricial birds. The second chapter presents the results of a four-year experimental study conducted in the Upper Peninsula of Michigan on the tree swallow. I established synchronous hatching and two degrees of asynchronous hatching (one of which is the most common in the population) in five nestling broods. Four levels of the brood reduction hypothesis were confirmed in tree swallows. First, several conditions favor brood reduced a reductzcr tive taCf Fourth, : that I pr chrcny CJ time c::;' My fie food was product;x nests the hAtcthg, reduction. Second, mechanisms allowing a brood to be reduced were evident. Third, survival-promoting reproduc— tive tactics were employed prior to brood reduction. Fourth, data were consistent with four adaptive scenarios that I propose for how brood reduction and hatching asyn- chrony can yield the most offspring in a parent's life- time compared synchronous hatching. My field experiments also showed, however, that, when food was more plentiful, synchronous hatching was the most productive brood. This result, common among field experi- ments that have adjusted broods to simulate synchronous hatching, is viewed as maladaptive by some researchers. The third chapter presents a model showing how hatching asynchrony can be adaptive if there are costs associated with asynchronous hatching when parents breed during unpredictably good and bad food years. I discuss the conditions for which asynchronous hatching produces more offspring than synchronous hatching. I test this model using data from the second chapter. The final chapter expands upon the model of the third chapter. I show, using computer simulations that, if parents breed in an environment where a continuous distri- bution of food years occur with moderate food years the most frequent, then in most cases, natural selection favors an adjustment in brood size over an adjustment in the degree of asynchronous hatching. I also use this model to shoe : or degree hatc.;:g to show how adult mortality, as a function of brood size or degree of asynchronous hatching, can select for the hatching condition and brood size that yields the most productive brood in a parent's lifetime. e D O BET :5 C 1991 Copyright by BRYAN CHRISTOPHER PIJANOWSKI 1991 FOR MY PARENTS AND MY WIFE vi I so; cozzxte mid Dona ACKNOWLEDGEMENTS I would first like to thank the members of my doctoral committee, Drs. Donald Beaver, Donald Hall, Thomas Getty, and Donald Straney for their continued patience and guid- ance. I was extremely fortunate to have been under the tutelage of Dr. Donald Beaver, the chair of my committee. He always knew what to say to relieve my frustrations when I came to a mental block. His good humor, patience and wisdom helped me to survive the pressures of graduate school. I know of no better scholar and teacher of natu- ral history. He was an excellent role model. Drs. Getty, Hall and Straney treated me politely and respectfully even after having been asked to read endless versions of model manuscripts and research proposals. Their guidance on these tasks has made me a much better scientist. I would also like to thank all the people involved in the Biological Science Department for their continued support and guidance. I would especially like to thank Andrea Pesce, Nancy Dykema and Jan Asmann for placing so much confidence in my teaching and leadership abilities. Their confidence in me gave me confidence. This degree would also not be possible without the vii support from Re: skas. The f‘ to keep Rogers, read ear Question: and press For 5, Pallucc; also yer. ski: he; support during this last year from The Museum, especially from Ken Dewhurst, Chris Carmichael and Laura Abraczin- skas. The following fellow graduate students also helped me to keep my sanity during my tenure here: Terry Trier, Beth Rogers, Rob Morell, and Pat Lederle. Karen and Dan Cebra read earlier versions of Chapter 3 and asked difficult questions that helped me to improve modeling techniques and presentation. For support in the field, I would like to thank Ron Palluconi, for his good humor and valued friendship. I am also very proud to boast that my father, Robert Pijanow- ski, helped during the last year of my field research. He provided me with much comfort and assistance during the very miserable and trying 1989 field season. The friendship, good times and good conversation with Bruce, Mary and Keith Johnston, Nadine Wojtowicz, Mic- hele Butterly and Jahan Eftekar are deeply cherished and valued. Last, and of course not the least, I owe the world of gratitude to my wife, Dawn, for her love, patience, con- tinued support and hard work, especially during these challenging last few years of my doctoral work. She always thought that my endeavors were "worldly" and never ques- tioned why I would spend so many hours behind a computer viii or livi: I He's. ported f Sigma-X;P Vallace acknowle System E Tasks 5.. or living out of tents for several weeks at a time. I would like to acknowledge that my research was sup- ported from funds from the Department of Zoology, a Sigma-Xi Research-in-Aid Grant, and the George and Martha Wallace Endowed Scholarship Award. I would also like to acknowledge logistical support from the ELF Communications System Ecological Monitoring Program, Small Vertebrates: Tasks 5.6 and 5.12A, subcontract No. E06595-88-006. ix V Q.- N‘ . - 0““ QQ-a #4 >4 +4 0 TABLE OF CONTENTS LISTOFTABLESOOOO0.0.00.0...OOOOOOOOOOOOOOOOOOOOOOO xiii LIST OF FIGURES ...... ........... . ..... ............. xv VOLUME I CHAPTER 1: INTRODUCTION TO CONCEPTS I. DEFINITION AND POSSIBLE CAUSES OF HATCHING ASYNCHRONYOOOO0.00.00.00.000COOOOOOIOOCOOOOO 1 II. BRIEF PRESENTATION OF HYPOTHESES EXPLAINING THE ADAPTIVE SIGNIFICANCE OF HATCHING ASYNCHRONY IN BIRDSOCOC.OCCOOCCOOOIOOOOCOCOO 4 III. OVERVIEWOF CHAPTERSCOOOOOOO0.00000000000000 7 CHAPTER 2: FIELD EXPERIMENTS ON THE TREE SWALLOW: A TEST OF THE BROOD REDUCTION HYPOTHESIS -I. INTRODUCTION..................... ....... ..... 9 II. MATERIALS AND METHODS........................ 17 Study Animal............................... 17 Study Site................................. 18 Natural Weight Hierarchies................. 19 Experimental Manipulations................. 21 Food Abundance............................. 22 Egg Weights................................ 27 Nestling Growth and Development............ 27 Feeding Behavior........................... 30 Parental Care.............................. 31 Statistical Procedures..................... 32 III. RESULTS.................................... 33 Natural Hatch Spreads...................... 33 Effects of experimental manipulation....... 34 Egg Weights................................ 38 Insect Abundances.......................... 38 X Fledging success and nestling death........ 57 Nestling growth and development............ 65 1. Growth of all nestlings............ 66 2. Growth of nestlings that fledged... 87 3. Dynamics of nestling weights....... 106 4. Nestling growth and daily food abundance..................... 118 Feeding Behavior........................... 118 Parental Care........... ....... ............ 127 IV. DISCUSSION.................................. 132 A. GENERAL RESULTS OF STUDY RELEVANT TO THE BROOD REDUCTION HYPOTHESIS......... 132 1. Natural Degree of Hatching Asynchrony......................... 132 2. Food Supplies...................... 132 3. Effects of Experimental Manipulations...................... 132 B. EXAMINING THE BROOD REDUCTION HYPOTHESIS.................... 138 1. Objectives of study................ 138 2. Conditions for Brood Reduction.... 138 3. Mechanisms of Brood Reduction...... 145 4. Reproductive Tactics Consistent with Brood Reduction.... 151 5. The Adaptive Value of Brood Reduction.......... ..... ..... 154 C. CONCLUSIONS...................0.0.0.0... 165 VOLUME II CHAPTER 3: A REVISION OF LACK'S BROOD REDUCTION HYPOTHESIS USING A GAME THEORY MODEL I. INTRODUCTION................................. 166 II. THEMODEL PRESENTATION....................... 170 III. RESULTS...................................... 178 xi 0' i. ' '- cuzr . no... ‘5 IV. DISCUSSION................................... 193 A. Introduction............................. 193 B. Model's Specifications................... 197 1. Assumptions........................ 197 2. Predictions........................ 204 V. SMARY......O.. ........ ..................... 217 CHAPTER 4: A MATHEMATICAL MODEL FOR HATCHING ASYNCHRONY AND BROOD REDUCTION I. INTRODUCTION................................. 220 II. EXTENDED MATHEMATICAL MODEL FOR BROOD REDUCTION AND HATCHING ASYNCHRONY............ 224 A. Introduction... ............. ............ 224 B. Food Year Type Continuum................ 225 C. Nestling Survival by Hatch Position..... 227 D. Annual Parental Mortality............... 231 III. RESULTS...................................... 233 A. Introduction............................ 233 B. Food Year Type Distribution on Nestling Survival.................. 233 C. Annual Parental Mortality............... 248 IV. DISCUSSION................................... 259 A. Introduction.................... ....... . 259 B. Food Year Distribution on the Most Productive Hatching Form and Brood Size........................ 261 C. Adult Mortality on the Most Productive Hatching Form and Brood Size........................ 263 D. Implications of the Model to Field Research........................ 264 E. Relationship of the Present Brood Reduction Model to Alternative Hypotheses................ 267 V. CONCLUSIONS................................... 268 LITERATURE CITED................................ 270 Taz.e Tatle 35 Table 4. Table 5. Table 6. Table 7 h A Table Table Table Table Table Table Table Table Table 2A. ZB. 3A. 3B. LIST OF TABLES Analysis of covariance examining the effects of the bolus collection experiments on the rate of linear phase of nestling growth.................... 40 Component loadings of nestling growth rates on the first and second principal axes..... ............. ... ......... 92 Component loadings for the age of nestling developmental events on the first and second principal axes ......... 92 Means of growth rate principal components and selected growth measures, by food year type.. .......... .............. 94 Means of age for developmental events principal components and selected growth measures, by food year type................. 94 Analysis of variance on the log transformed maximum nestlings weights. Levels tested are food year type (food yr), hatching treatment (tmt) and hatch position (hatch). ........... ..... ..... 105 Table of significant means from the analysis of variance for Table 4. Means are in their untransformed scale ..... 105 Analysis of variance on the log transformed age of maximum nestling weight. Sources of variation are food year type (food yr.), hatching treatment (tmt) and hatch position (hatch)............ 107 Table of significant means from the analysis of variance for Table 6. Means are in their untransformed scale..... 107 xiii Table Table 5 Table 1 W " 1; 155.9 . Table Table Table Table 10. 11. The expected yearly reproductive success of parents hatching nestlings synchronously and asynchronous in good and bad food years. The ratio presented represents the proportion of lifetime reproductive success that is gained during good food years............. ........ Factors that might increase or decrease the value of 'q' ....... .......... List of variables contained in model. ...... The B* and N* values for iterations of model's 'k' (survival difference between latter-hatched nestlings), 'z' (nestling survival across food continuum), 'a' (brood size dependent mortality constant) and 'u' (mean of food year distribution) variableSeeeeeeeeeeeeee ....... .. ..... ...... xiv 187 226 244 PIC I'R' ‘ul .flr" e N ‘U». ’a'.“ 24.5. 75"“ I b ‘V‘VAE- FYBv-ny. ngflL FAG'CRE 7 IC-LRE a HERE 9. :URE SURE :URE :URE SURE :URE EURE 10. LIST OF FIGURES Location of the study site in the Upper Peninsula of Michigan........ ....... 20 The relationship between the natural logarithm of daily IBI measures (in mg insect/100km of wind) and daily windspeeds at the plot ....... 26 Match clutch spreads, by calendar days, sizes 4 through 6 ....... . ......... 35 The coefficient of variation of weights of broods on the first noon (12:00 EST) after natural hatching. ....... 37 Mean egg weights (: 1 S.E.) by laying sequence. Shown are egg weights for clutch sizes of 4 through 6 ........... ........... 39 Daily IBI measures (mg of insect/lookm of wind) for each year of the study. Days that information is not available is designated with an asterisk ('*')......... 41 Mean IBI measures (mg dry weight of insects/100 km of wind) for each year (i 1 S.E.). Also given are the seven year averages for three of Hussell and Quinney's study sites................. 48 Size-taxa distribution of insects (in percent of total) captured my tow nets for the e................................. 49 Size-taxa distribution of insects (in percent of total) captured Hussell's version of the tow nets for the 1988 and 1989 seasons.............................. 51 Size-taxa distribution of insects (in percent of total) captured my the Manitoba traps for the 1988 and 1989 season........ 52 XV CFO -U'. rev" ,. I $6.; YF"F‘ I .bea anv‘v- u ‘09,- FIGURE F’fiv-nn . ¢€.flL ‘ IGL‘RE 1 FIGLFE 2 FTP'm ‘V\KE 2 SURE SURE SURE SURE SURE SURE SURE SURE SURE SURE SURE SURE 11. 12. 13. 14. 15. 16. 17. 19. 20. 21. 22. Daily dry weights of insects captured in the Manitoba traps for 1988 and 1989..... The daily numbers of insects captured in the Manitoba traps for 1988 and 1989..... Fledging success of nestlings for the four-year study by hatching treatment and hatch position........................ Nestling fledging success by food year type, hatching treatment and hatch position. Food year types are MORE FOOD and LESS FOOD.................. ...... Age of nestling deaths by hatching treatment and hatch position. Hatch position legend is located on the lower left corner of each plot............ Mean body weight measures (1 1 S.E. ) of all nestlings by age (days post-hatch, DPH)... ................... ......O......... Mean tarsus measures (i 1 S.E. ) of all nestlings by age (days post-hatch, DPH) .................... Mean ulna length measures (1 1 S.E. ) of all nestlings by age (days post-hatch, DPH).............. ...... Mean wing chord measures (1 1 S.E. ) of all nestlings by age (days post-hatch, DPH).................... Mean length of ninth primary (1 1 S.E.) for all nestlings by age (days post-hatch, DPH).................... Density plots of the linear phase of body weight growth for all nestlings by food year type and hatching treatment ........ Density plots of the linear phase of body weight growth for all nestlings by food year type and hatch position ..... xvi 53 55 59 61 63 67 69 71 73 75 78 80 ,‘F oil: anw dcv: TPH‘v '. ‘uvox. Tfi'fiw FAucflE VF... W .utnz 3 YPSMI ‘U¥5£ Le.) FIG'JRE L-p P132745 . FIGURE FIGURE FIGURE FIGURE FIGURE FIGURE FIGURE FIGURE FIGURE FIGURE FIGURE 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. Density plots depletion for of the age of yolk all nestlings by food year type and hatching treatment ... ...... 83 Density plots of the age of yolk depletion for all nestlings by food year type and hatch position ...... ....... 85 Density plots of the age of eye opening for all nestlings by food year type and hatching treatment .............. 88 Density plots of the age of eye opening for all nestlings by food year type and hatching treatment ........... ..... ... 90 Density distributions of PC(1) scores for rate of body growth by food year type and hatching treatment.0verlaid are normal probability plots to describe central tendency and dispersion ...... ..... 95 Density distributions of PC(2) scores for rate of feather growth by food year type and hatching treatment. Overlaid are normal probability plots to describe central tendency and dispersion............. ...... 99 Density distributions of PC(1) scores age that developmental events occurred by food year type and hatching treatment. Overlaid are normal probability plots............. 101 Density distributions of PC(2) scores age of feather growth initiation by food year type and hatching treatment. Overlaid are normal probability plots to describe central tendency and dispersion................... 103 The proportion of changes within each weight ranking by hatching treatment...... 108 The average coefficient of variations of nestling weights by hatching treatment..................... 111 The mean percent of nestling body weight (3 1 S.E.) deviating from the average body weight with respect to the day of brood reduction........................ 112 xvii FIGURE IGL'RE FIGL’RE FIGL’RE IGLFE I’ime FIGURE .r. J. J. FIGURE FIGURE FIGURE FIGURE FIGURE FIGURE Figure FIGURE FIGURE 34. 35. 36. 37. 38. 39. 40. 41. 42. The mean percent of nestling body weight (i 1 S.E.) deviating from the average body weight with respect to the day of brood reduction........................ 116 Size-taxa distribution of insects (in percent of total) in food boluses for the 1987, 1988 and 1989 seasons..................... ..... 120 The proportion of food delivered to each nestling according to its hatch position and by food year type for SINGLE AND DOUBLE ASYNCHRONOUS broods............ 123 The proportion of food and proportion of feeds delivered to each nestling according to its weight ranking by food year type for SYNCHRONOUS broods.......... 124 The (a) median percentage weight loss (from hatching to late in the nestling period) of females raising broods, by hatching treatment; (b) the average of the most percentage weight lost by females for (i 1 S.E.) evening weighings from hatching date; and (c) the average of the maximum weight lost by females (1 1 S.E.) from hatching date ......... . ........ 128 The percent weight change of females from their weights at hatching averaged with to the day of brood reduction. All hatching treatments and only those broods that fledged 4 young are included......... 131 Geometric means of fledging success for all four years, by hatching treatment ................................. 159 Payoff matrix for two alternative hatching strategies generated by the game theory model..................... 173 The (A) probability of each nestling surviving to reproductive age and (B) the total number of nestlings per brood surviving to their reproductive age, both as a function of brood size.......... 176 xviii FIGURE FIG'IRE FIGZRE FIGURE . FIGURE 4 Figure 4 Figure 4L Figure 5 SURE 43. SURE 44. SURE 45. SURE SURE gure gure gure 46. 47. 48. 49. 50. The HPR (hatching productivity ratio) as it varies with the frequency of good years. The threshold frequency of good years, T-, is also given and indicated by the dotted line. Parameter values are 'B'=5, 'a'=0.2, 's'=0.7, 'q'=0.7 and 'c'= 1.0...................... 180 Productivity of hatching asynchrony and hatching synchrony versus brood size. Parameter values are 'B'=5, 'a'=0.2, 's'=0.7, 'q'=0.7 and 'c'=1.0 ..... 182 HPR values (A) as a function of 'q' and 's' with parameter values of 'B'=5, 'a'=0.2 and 'c'=1.0 (for 's' iterations, 'q'=0.7 and for 'q' iterations, 's'=0.7); and (B) as a function of 'q' for brood sizes of 'B' and 'B-l', where RBA denotes the reduced brood size advantage, see text for details; (C) as a function of 'a' and 'c' ............. . ........... .......... 185 T- values (A) as a function of 'q' aAd 's' with parameter values of 'B'=5, 'a'=0.2 and 'c'=1.0 (for 's' iterations, 'q'=0.7 and for 'q' iterations, 's'=0.7); and (B) as a function of 'a' and 'c'...... ........ 189 Expected productivities of hatching synchrony (A) and asynchrony (B). Given are good food year (...), bad food year (- - -), and the mean (___) productivities between both year types... 192 Nestling survival values by hatch position for three different hatch forms... ...... .......... ........ .... 235 The expected proportion of brood productivity for each food year and different '2' values ................. 237 A productivity landscape as a function of brood size and hatching form. Also included is adult mortality plane described as a function of brood size and hatch...................... 249 xix Fi [re 51 . [re 52 . [re 53. The effect of different 'sd' and 'u' on the curvature of the productivity landscape along the 'N' and 'B' facets.... 253 The effect of different 'k' and '2' values on the curvature of the productivity landscape along the 'N' and 'B' facets ..... ...... ......... 255 The effect of different 'a' values on the curvature of the productivity landscape along the 'N' and 'B' facets............ ..... . ...... ........ 257 XX r1 CHAPTER 1 INTRODUCTION TO CONCEPTS I. DEFINITION AND POSSIBLE CAUSES OF HATCHING ASYNCHRONY Asynchronous hatching of a clutch of eggs was rst noticed by Dunlop (1913, in Magrath 1990) as an ian reproductive pattern. He observed that in some rds, many eggs of a clutch do not hatch at the same me. Rather, a group of eggs hatch together, and e or more eggs hatch later. The obvious result of ynchronous hatching is that broods are created where stlings differ in their ages and weights. The alter- tive hatching form is synchronous hatching, where gs of a clutch hatch on same day. All nestlings in nchronous broods are the same ages. Lack suggested that asynchronous hatching is a sult of the timing of incubation initiation. Most rds lay one egg per day (Lack 1947, 1948; Klomp 1970; ark and Wilson 1981) with the development of eggs curring once incubation raises the egg temperatures ove 25° C (see Magrath 1990). If incubation CORSET; those e er. Si tion (I those I commences before the completion of egg laying, then those eggs present when incubation begins hatch togeth- er. Since each egg requires the same amount of incuba- tion (Drent 1975), eggs laid later will hatch after those eggs present at the start of incubation. Alternative explanations for how hatching asyn- chrony is created do exist, although they have received little experimental or observational attention (Magrath 1990). Some researchers (see Magrath 1990) have sug- gested that asynchronous hatching results from unequal incubation temperatures applied to the clutch. Those eggs incubated at higher temperatures develop quicker and batch earlier. Yet, it is unlikely that this mechanism could produce eggs of a clutch hatching in the order that they were laid as has been commonly observed. In addition, it is also difficult to see how this mechanism could produce complete asynchronous hatching (each egg of a clutch hatching on a different day). Incubation temperatures would have to be very different between eggs to produce complete hatching asynchrony. Lastly, asynchronous hatching could also be the result of genetic differences in development rates for each egg of a clutch (James Asher, pers. comm.). Eggs developing faster than others will hatch first. This mechanism would be difficult to differentiate in the field Lack [. time c mechan; inq sec deranc notice field than the incubation initiation theory proposed by Lack (1947) because genetic differences in development time could correlate with egg laying sequence. Both mechanisms, thus, could give the same result of hatch- ing sequence matching the laying sequence. Lack (1947) was the first to discuss the prepon- derance of the asynchronous hatching in birds. He noticed that asynchronous hatching occurred only on a handful of birds, such as the Strigiformes and Falconi- formes. He initially treated hatching asynchrony as the exception in hatching forms. In subsequent works (Lack 1954, 1968), Lack presented cases where hatching asynchrony was prevalent in several Orders of birds, all nonpasserines. It was not until Clark and Wilson's (1981) review of 82 species of mostly altricial passer- ines that hatching asynchrony became viewed as the norm rather than the exception in avian hatching strategies. Their review revealed that nearly 80% of the birds included in their literature search hatch their clutch- es asynchronously. If this review is represents the avian Class as a whole, hatching asynchrony should be viewed as the rule of hatching situations rather than the exception. EXPLAI. pGCOSe ing as]I review have b{ level Ha seb’es II. BRIEF PRESENTATION OF HYPOTHESES EXPLAINING THE SIGNIFICANCE OF HATCHING ASYNCHRONY IN BIRDS To date, there have been nearly twenty hypotheses proposed to explain the adaptive significance of hatch- ing asynchrony in altricial birds (see Magrath 1990 for review). Many of the more recently proposed hypotheses have been variations of one or more hypotheses (Magrath 1990). Below, I present seven of the most commonly cited adaptive hypotheses that explain why hatching asynchrony exists in altricial birds. David Lack (1947, 1954) suggested that hatching asynchrony produces a beneficial competitive feeding hierarchy among nestlings within a nest. During times of food shortages, parents feed only the oldest and strongest nestlings, allowing the smallest nestling(s) to die. In synchronous broods, no competitive feeding hierarchy during periods of reduced food supply causes all nestlings in the brood to be malnourished. Entire broods risk starving. This hypothesis is called as the brood reduction hypothesis and is thought to be espe- cially relevant for species that rely on food, future levels of which are unpredictable at egg laying. Hahn (1981) proposed that hatching asynchrony serves to reduce sibling-sibling competition for food provided by parents. A feeding hierarchy is created by hat themse cordin are ea_ less f, hypoth: hypoths 'u (1972) tling ; sis, he becausg require % i that n:l | | benefic which a3 Th“. tr eXPOSEd failure by hatching asynchrony rather than by the nestlings themselves; an energetically expensive process. Ac- cording to Hahn (1981), broods hatched asynchronously are easier for parents to raise because they require less food than synchronously hatched broods. This hypothesis is called the sibling rivalry reduction hypothesis. The peak demand reduction hypothesis of Hussell (1972) centers on the short period during which nes- tling growth is most rapid. According to this hypothe— sis, hatching asynchrony may be beneficial to parents because it staggers nestlings' maximal energy demand so that not all nestlings concurrently peak in their food requirements. Thus, parents may rear larger broods using asynchronous hatching. The predation hypothesis (Hussell 1972, Clark and Wilson 1981) predicts that the early onset of incuba- tion, which results in asynchronous hatching, is beneficial to parents because it advances the date for which all but the last-hatched nestling can fledge. Thus, the amount of time earlier hatched nestlings are exposed to possible predation is reduced thereby in- creasing the chances of producing offspring. Similar to the predation hypothesis is the nest- failure hypothesis of Clark and Wilson (1981). The thesis is fat the eg than t period the m; ferred the egj 1962, ) hatchi: Occurre the ml hatche: all fir tling i insura: that ha last-ha the ear. nestlin: Derim, The ins; hypothesl i n. \ 6 thesis of this hypothesis is that hatching asynchrony is favored when the expected nest-failure rates during the egg period (i.e. incubation period) are greater than those of the nestling period. Decreasing the egg period is accomplished by commencing incubation during the middle of egg laying. There also exists a suite of explanations re- ferred to as insurance hypotheses. One form, called the egg-insurance hypothesis (Ingram 1959, Dorward 1962, Mead and Morton 1985, Anderson 1990), states that hatching asynchrony benefits parents expecting a high occurrence of infertile eggs in a clutch. If one of the first-laid eggs does not hatch, then the last- hatched nestling replaces it. On the other hand, if all first laid eggs hatch, then the last-hatched nes- tling is selectively starved. Likewise, the young— insurance hypothesis (Nisbet and Cohen 1975) states that hatching asynchrony allows parents to starve the last-hatched nestling if all of its siblings survive the early portion of the nestling period. If one nestling dies during the first half of the nestling period, then the last-hatched nestling replaces it. The insurance hypotheses, like the nest-crowding hy- pothesis, is a modification of the brood reduction hypothesis. Mead and Morton (1985) have also suggested that hatch; cient laying one he the st, I laying last-Ll drazatl | 999 1a I that t: | the ct: laying hormCte tation Starts it' The SIArt i degree With in hatching asynchrony could be a consequence of an effi- cient hormonal-control mechanism that occurs during egg laying and initiation of incubation. They propose that one hormone, instead of two, regulates egg laying and the start of incubation. They cited that, during egg laying, levels of prolactin increase until the very last-laid egg is ovulated and then these levels drop dramatically. Since ovulation occurs one day before egg laying, then prolactin levels decline on the day that the penultimate egg is laid. They propose that the change in prolactin during the late phases of egg laying also is what initiates incubation. Having one hormone to control two events is a physiological adap- tation and hatching asynchrony, because incubation starts before the end of egg laying, is a consequent of it. Their hypothesis predicts that most birds should start incubation on the penultimate egg and that the degree of hatching asynchrony should remain constant with increasing clutch size. III. OVERVIEW OF CHAPTERS This thesis investigates whether the brood reduc- tion hypothesis can adequately explain the adaptive significance of hatching asynchrony in the tree swallow (Igghxgingta bigglgr). The second chapter discusses the IE study The tr attes; adapt; ductiv years. model I a cont Icrta; 8 the methods and results of a four-year experimental study conducted in the Upper Peninsula of Michigan. The third chapter presents a game theory model that attempts to prove how hatching asynchrony can still be adaptive if there are costs associated with this repro- ductive tactic when parents breed during good food years. The forth and final chapter expands upon the model presented in the third chapter and considers how a continuous distribution of food years and adult mortality selects for hatching form and brood size. CHAPTER 2 A TEST OF THE BROOD REDUCTION HYPOTHESIS: FIELD EXPERIMENTS ON THE TREE SWALLOW I. INTRODUCTION The most cited explanation for the adaptive significance of hatching asynchrony in birds is the one proposed by David Lack (1947, p. 324-326). He observed that the last-hatched nestling of a clutch frequently dies. Lack suggested that asynchronous hatching may be an adaptation to protect parents from investing in large clutches during breeding seasons where food supplies may only provide sufficient food for part of the brood. If food becomes short, the youngest chick loses in its competition with its nestmates for food and dies. On the other hand, if all nestlings were of the same age, their competitive abilities may not differ and all nestlings might starve. Lack also added that asynchronous hatching would not be disadvantageous to parents when food supplies are good because well fed nestlings become inactive when they are satiated. Thus, the smallest nestling will not experience compe- tition and will receive food when resources are not limiting. This theory has been coined the "brood reduction hypothesis" by Ricklefs (1965). 9 asyncr condit brood cause shoulc seleci (1931 from lack nous broo ex;; Dopu Shot and PTO: hYpo the ShoUl ShOUl 10 For researchers to accept the brood reduction hypothesis as an adaptive explanation for hatching asynchrony, four conditions should be met. First, conditions that would benefit parents by reducing a brood using hatching asynchrony must be present. Be- cause hatching asynchrony is common in a population, it should not be assumed to be a direct result of natural selection. Williams (1966b) and Gould and Lewontin (1981) have argued that a beneficial trait could result from chance rather than by natural selection. Thus, a lack of the conditions necessary to produce asynchro- nous hatching would result in the rejection of the brood reduction hypothesis as a satisfactory adaptive explanation for the existence of the trait. Second, brood reduction should occur in the population by hatching asynchrony, which in turn, should produce a feeding hierarchy in a brood (Clark and Wilson 1981). If hatching asynchrony fails to produce a feeding hierarchy, then the brood reduction hypothesis is clearly not an adequate explanation for the existence of hatching asynchrony. Third, hatching asynchrony and brood reduction should have some adaptive value. An adaptive trait should benefit individuals because it increases lifet alter. consiS' “Y- If hatchil br00d 1 Ute to: br00d : levels able 3 is 3ft period ing prere: inSeCt hatch 11 lifetime reproductive success of parents compared to alternative traits (Williams 1966a). In addition, because it is easy for researchers to fit data to a hypothesis with complex and elaborate scenarios, the data should not be forced to fit the adaptive hypothe- sis (Gould and Lewontin, 1981). Therefore, an adaptive explanation should only be accepted if the data provide the researcher with a reasonable explanation. Lastly, other reproductive tactics should be consistent with brood reduction and hatching asynchro- ny. If another trait exists that counteracts either hatching asynchrony or brood reduction mechanisms, then brood reduction and hatching asynchrony cannot contrib- ute toward the overall fitness of parents. Lack hypothesized that hatching asynchrony and brood reduction should be beneficial when: (a) food levels for the upcoming nestling period are unpredict- able when the eggs are laid; (b) parental performance is affected by food levels; and, (c) when nestling periods are long so that parents have increased risk of being exposed to periods of food shortage. There is some evidence to suggest that these prerequisites do apply to a variety of birds. Many insectivores (see O'Connor 1978 for review), which hatch clutches asynchronously, rely solely on food 12 which is thought to be unpredictable. Brood reduction has also been frequently observed in species that have long nestling periods, such as the raptors (e.g. Stin- son 1979), ciconiiformes (e.g. Evans and McMahon 1987, Mock and Parker 1986), and large-bodied passerines (e.g. Haydock and Ligon 1986). Asynchronous hatching is also common in cavity nesting birds, which have long nestling periods associated with the reduced risk of predation (see Clark and Wilson 1981 for review). Lastly, food levels have been shown to affect a wide variety of reproductive performance measures such as clutch size (see review in Quinney 1983, and Quinney and Hussell 1986), egg laying date (e.g. YomTov 1975), feeding rates (e.g. Proctor 1975, Nisbet and Cohen 1975), and nestling growth rates (e.g. Hussell and Quinney 1987), to name a few. The second condition that must be met to accept the brood reduction hypothesis is that brood reduction mechanisms should exist and be due to hatching asyn- chrony. Ricklefs (1965) suggested that the older nes- tlings, because of their better competitive abilities, should always get fed first. Once older nestlings are full, then younger nestlings may get fed. However, if food becomes scarce, then parents will take more time foraging for food and older nestlings will become hungry by the time it is the youngest nestling's turn to ge 1984, hatch: becau: As a h hatchi feedin (Clark fueled brood: and s: adjust hiera: aSYnc? OVer, nous t ”agrat nestlii than in Searche t0 faci parents 13 to get fed. Several studies (Proctor 1975, Groves 1984, Forbes and Ankney 1987) have shown that last- hatched nestlings do not get fed when food is limited because their older nestmates compete better for food. As a result, the younger nestlings starve. There is a controversy, however, over whether hatching asynchrony is necessary to establish the feeding hierarchies that facilitate brood reduction (Clark and Wilson 1981). This controversy has been fueled by experimental studies that have manipulated broods to simulate synchronous hatching (see Amundsen and Stokland 1988, for review). In most cases, broods adjusted for synchronous hatching have developed weight hierarchies that are as great as those established by asynchronous hatching (Clark and Wilson 1981). More- over, partial brood loss was common in these synchro- nous broods. Many of these studies have shown (see Magrath 1990 for review), on the other hand, that nestling deaths in asynchronous broods occurred earlier than in synchronous broods, suggesting to some re- searchers that the function of hatching asynchrony is to facilitate the early deaths of nestlings so that parents provide less investment in nestlings that will eventually die. Thus, hatching asynchrony provides an efficient mechanism of brood reduction. which than re; brr- hr( br( 14 The third condition that must be met is whether brood reduction facilitated by hatching asynchrony has an adaptive value. Williams (1966) and Stearns (1976) recognized that an adaptive trait should be one in which parents produce more offspring in their lifetime than any alternative trait. However, in several stud- ies, broods manipulated to establish hatching synchrony have been more productive than the normal degree of hatching asynchrony, especially when food did not appear to be limiting (see Amundsen and Stokland 1988, for review). Some researchers (e.g. Amundsen and Stok- land 1988) have suggested that brood reduction should be viewed as maladaptive if it occurs during food plentiful conditions. Lastly, a researcher should determine if other reproductive tactics of the parents are consistent with brood reduction. Ricklefs (1965) recognized that, if brood reduction is adaptive, then the reduction of the brood should be complimented by other strategies not resulting in nestling death. For example, when food becomes reduced, parents could attempt to increase their foraging rate rather than resort to an immediate starvation of the last-hatched nestling (Ricklefs 1965). Several researchers have also argued that decreasing egg size with laying order, common to many altricial birds (see Slagsvold et al. 1984 for review), lm tic ti! 15 should be considered consistent with the brood reduc- tion hypothesis because, as the brood reduction hypoth- esis would predict, lesser amounts of investment should be placed into the offspring that has the least chance of survival (Clark and Wilson 1981). Egg size in many species, such as the Common Grackle (Quiscula guiscu- lug), increase in size with laying order (Howe 1978). Many of the studies that have accepted the brood reduction hypothesis as an adequate explanation for hatching asynchrony in the study species have done so mostly on circumstantial evidence. Most often, re- searchers have accepted the brood reduction hypothesis because the last-hatched nestling either grew slower or died more frequently than its siblings (e.g. Mishaga 1974, Nisbet and Nisbet 1975, Proctor 1975, Zach 1982, Evans and McMahon 1987). There has yet to be any investigation into several aspects of the brood reduc- tion hypothesis, and, to date, there has been no inves- tigation that has examined all four levels of the brood reduction hypothesis. Lacking are studies on the pre- dictability of food resources, the effects of different food years on nestling growth and development according to hatch position, the amount of food apportioned to nestlings according to hatch position and the effect of hatching asynchrony on parental behavior and inves 16 investment. This chapter reports on experiments conducted from 1986 to 1989 on the tree swallow (Iagnygingtg bigglgz) designed to build upon the results of the observational study of Zach (1982). Zach (1982) found that the last-hatched nestling died more frequently, grew slower and reached lower asymptotic weights than their older nestmates. He cautiously concluded that brood reduction in the tree swallow was adaptive be- cause those broods hatching more asynchronously fledged the most nestlings. However, the adaptive significance of hatching asynchrony and brood reduction for tree swallows is called into question since brood reduction occurred in Zach's study when food did not appear to be limiting. In addition, Zach could not factor out the effects of brood size on brood productivity; those broods hatching most asynchronously were from the largest clutches in the population, therefore, the high productivity associated with increased hatching asyn- chrony could be due solely to brood size differences. The study reported here consists of adjusting broods, shortly after hatching, to simulate hatching synchrony (hereafter as SYNCHRONOUS), and two degrees of hatching asynchrony. One asynchronous hatching treatment contained one nestling a day younger than 17 other asynchronous treatment contained one nestling one day younger and a second nestling two days younger than their older siblings (hereafter as DOUBLE ASYNCHRONOUS). I adjusted all broods to five nestlings to exclude brood size effects and followed parental investment, feeding behaviors and nestling growth and development according to hatching position, on plots during a four year study in which two years provided parents with more food than the other two years. I attempted to determine: (1) if the mechanisms of brood reduction occur; (2) whether brood reduction, if it occurs, could be viewed as adaptive; and (3) if other reproductive patterns compliment brood reduction. I also address whether the prerequisites for brood reduc- tion exist in the tree swallow. II. MATERIALS AND METHODS Study Animal. The tree swallow is a monogamously breeding bird (but see Quinney 1983a) that nests in cavities and nestboxes. Tree swallows raise one brood per year (see Hussell 1983a for a case of double brood- ing). The most common clutch sizes are 5 and 6 (range 3-8) which are hatched over a two to four day period (Zach 1982). Only the female incubates the eggs. Incubation requires on average 14 days (Kuerzi 1941). sexes brood main; and C study foragq obs.). aroun: begin: durin Sine: firs: banr Of 31 “Eek 18 The nestling period generally lasts 19-23 days. Both sexes feed and defend the nestlings. Only the female broods the non-thermoregulating young. Insects, mainly small dipterans such as nematocerans (Hussell and Quinney 1987) and occasionally tabanids (this study), are their main food source. Parents usually forage within 100 m of the nest (Holroyd 1972; pers. obs.). Tree swallows arrive on the breeding grounds around the first of April of each year. Egg laying begins around mid-May and clutches start hatching during the first week of June. During 1986, I began my studies on May 1 and continued until the end of the first week of July. In 1987 through 1989, my studies began around June lst and ended around the first week of July. However, I spent two-days during the second week of May each of these years checking nests to determine initial clutch sizes. Study Sites. This study was conducted in the western portion of the Upper Peninsula of Michigan in north-central Dickinson County (Figure 1). The first year of my study, 1986, was conducted at a plot re- ferred to as Floodwood. In 1987, I moved my study approximately 15 km to the east to a site referred to as Aimones Power Hill. Several smaller sites near Aimones were also used in 1987 to increase the number ofne trave Hill. of} with Pose tOta In site hes Hew- Ext r331 19 of nests. In 1988, to reduce the amount of time spent traveling, I excluded the sites around Aimones Power Hill. A total of 127 cedar nest boxes (inside dimension of 3 1/2 x 6 in.) existed in 1986 at Floodwood arranged in a 30-meter grid arrangement. The site is approxi- mately 35 ha with several small ponds located within the nestbox grid. The area is open with scattered stands of aspen. The Aimones Power Hill site is also very open with scattered stands of young aspen. In 1987, Aimones Power Hill and the surrounding smaller sites had a total of 40 nestboxes scattered over a 5 mile stretch. In 1988, I added 87 nestboxes to the Aimones Power Hill site to bring this area to 100 nestboxes. These 100 nestboxes were also arranged in a 30 meter grid and were used exclusively for the study in 1988 and 1989. Natural Weight Hierarchies. To determine the extent of intra-brood weight differences established in nature by tree swallows, I visited nests every 4 hours beginning at 0800 during the hatching period of a brood. I recorded which nestlings were present, the condition of their down (wet or fluffy) and marked their toes using a nontoxic marker for later identifi- cation. In 1986, I determined that nestlings with 20 FIGURE 1. Location of the study site (indicated by the star) in the Upper Peninsula of Michigan. fist “€34. 21 wet down had hatched within 2 hours of the visit, those with fluffy down later than 2 hours from the nest visit. In 1988 and 1989, to determine the extent of naturally occurring weight hierarchies, I weighed all nestlings on the first noon visit after the entire clutch had hatched for those broods that had a 100% hatchability. Experimental Manipulations. I constructed three different hatching treatments: SYNCHRONOUS, SINGLE ASYNCHRONOUS, and DOUBLE ASYNCHRONOUS. A11 broods contained five nestlings. Within each hatching treat- ment, I shall refer to nestlings by their hatch posi- tion; the oldest chicks will be referred to as 'A' chicks; those a day younger than 'A' chicks as the 'B' chicks, and those two days younger than the 'A' chicks as the 'C' chicks. Hatching treatments were established by swapping nestlings between nests in the late morning (between 0900 and 1200 EST). During the transfer, nestlings were wrapped in polyester filling to reduce heat loss. Transfers were completed in all cases within 10 minutes. All nestlings were swapped before the age of 5 days posthatch; 83% were swapped before 2 days posthatch. I selected nests parented only by ASY (after menta 1986 Year nine: adjus '00:] Year: 22 I selected nests parented only by ASY (after second year) females using plumage characteristics (Hussell 1983b). First-year female breeders have been shown to be less productive than older, experienced breeding females (DeSteven 1978). In addition, I only selected nests whose original clutch size was 4, 5 or 6 eggs. Fifty-three nests were selected for the experi- mental manipulations during the four year study. In 1986, 1987 and 1989, twelve nests were monitored each year and in 1988, 17 nests were monitored. A total of nineteen, twenty and fourteen of these nests were adjusted for 'SYNCHRONOUS', 'SINGLE ASYNCHRONOUS' and 'DOUBLE ASYNCHRONOUS' nests, respectively, for all four years. Food Abundance. To measure insect abundances, I followed the method of Hussell and Quinney (1987). Briefly, this method entails trapping insects using a passive tow net device and obtaining an insect biomass index for the day after accounting for the effects of daily wind speeds. Johnson (1965) determined that the biomass of insects trapped in tow nests increases exponentially for windspeeds below 8 km and linearly with wind speeds above 8km. Insect biomass indices (IBI) are expressed as mg of biomass per 100 km of wind passing through the net. tea 3 ct St! cs: 0 f he 23 The passive insect trapping device is a suspended cone net that swings freely in the wind on a vertical pole 1.5 meters above the ground so that it constantly faces the wind. The nets were constructed of 1mm vinyl mesh using the same dimensions as Hussell and Quinney's nets. The opening of each net was 30.5 cm in diameter with a cone length of 61 cm. Insects that are blown or fly toward the rear of the tow net are trapped a col- lecting cone that leads to jars filled with 70% etha- nol. In 1988, I obtained two tow nets from David J. T. Hussell to compare the efficiency of his nets with mine. His nets differed from mine in the design of the rear collecting trap. My wind nets are similar to Johnson's (1965) original design where the net opens straight into the jar; Hussell and Quinney's nets contain a small cylindrical trap that opens to the jar of ethanol. I compared the daily insect biomass of my nets with his and found Hussell and Quinney's nets to be almost twice as efficient as mine (y = 0.0 + 1.60x, R2=0.520, df=51, P < 0.001, where y= insect biomass for my nets and x = insect biomass for Hussell's nets). However, IBI measures reported throughout are from my nets. I will take into account these differences in net efficiencies when I compare my results later with the efficiency of Hussell and Quinney's nets. The insect traps were functional from app: tot Juli one in‘ in 6‘! m n‘ 24 approxiately 0700 to 2000 EST during each day and from the day that the first hatchling at the plot appeared to the last day of the study (approximately June 5 to July 3 of each year). Of my version of wind net traps, one was erected during 1986, two each in 1987, 1988 and 1989. Two Hussell nets were erected in each of 1988 and 1989. IBI measures are expressed as the average for two nets for 1987-1989. Daily IBI measures were obtained as follows. Insects were keyed to Order (dipterans were keyed to three further subgroups, nematocerans, tabanids and other dipterans) and placed according to body length into eight size categories. The number of individuals in each of the size-taxa groups was multiplied by the average dry weight value for each size-taxa (Beaver, unpubl.) and these were summed for each daily net sample to obtain a total insect biomass. I compared these estimated total dry weight values by regressing 50 actual dry weights against the corresponding esti- mated dry weights and found that these estimated values needed to be corrected by multiplying the estimated values by 2.21 (P < 0.001). Wind speed measures were collected at the study sites three to ten times per day. Following the proce- dure of Hussell and Quinney (1987), windspeeds at the study site were used to adjust hourly wind speeds taken atK the: net c HOWE? remov+ Figure Speed 25 at K. I. Sawyer Airforce Base approximately 45 km from the study site following this regression equation: y = 1.16 + 0.435 x where 'y' = the wind speeds at Aimones Power Hill and 'x' = the windspeeds at K. I. Sawyer AFB (R2=0.723, df=149, P < 0.001). Wind speeds below 8 km/hr were corrected by cubing each hourly windspeed and dividing it by 64 (see Hussell and Quinney 1987). The IBIs were obtained by dividing the average dry insect biomass for the nets by the average amount of wind per day during net operation and then multiplying this value by 100. However, this procedure of Russell's did not entirely remove the effects of wind speed from IBI measures (see Figure 2). I adjusted IBIs from the effects of wind speed using linear regression (Steele and Torrie, 1980, p.251). IBIs reported are those adjusted to remove the effects of wind speed. After finding in 1987 that tree swallows fed tabanids to their nestlings during the afternoons of hot days, I constructed a Manitoba trap after Thor- steinson gt 31; (1965). The Manitoba trap was placed in the center of the plot in 1988 and 1989. Manitoba traps attract insects, mostly tabanids and other large predaceous dipterans, to a spherical black object that is suspended from the apex of a triangular trap. The 26 4 , , 3 - ' y=l.269-0.025x P < 0.001 _ 0 LIME” (mg/100 km wind) -4 l l 0 50 100 150 Windspeeds (km/hr) FIGURE 2 . The relationship between the natural logarithm of daily IBI measures (in mg insect/100km of wind) and daily windspeeds at the plots. bla: flie dipt Clea tic mcx (Ea iri 27 black ball emits radiative heat that attracts the flies. After circling the black object, many of these dipterans come to rest on the inside of the three, clear plastic panels. The insects invariably then walk against gravity toward the apex of the three plastic panels where they enter a one-way funnel into a glass jar. The insects usually die within a few hours. The Manitoba traps were operational during the same periods as the Hussell nets. All insects were collected at the end of the day. I used the number of insects caught in the trap and their estimated dry weights as two addi- tional insect abundance indices. Egg Weights. In 1986, I weighed eggs in the morning (630-900 EST) a few hours after they were laid. Each egg was numbered for identification with India ink. I used a 5.0 gram Pesola with an accuracy of i 0.05 grams. One hundred and seventy-four eggs were weighed from 34 clutches laid in 4, 5 and 6 egg clutch- es. Nestling Growth and Development. I recorded nestling growth and development every other day, when weather permitted, in the evening hours (approximately 1600 - 2000 EST). After hatching, I marked the nes- tlings on their toes with a nontoxic marker. Nestlings were identified by their toe marking until age 3 days post DPH A F; ——i_ nest inCrc lowii tail: grow lant; the 1 re9r. cubi't 28 posthatch (hatching is considered 0 days posthatch - DPH) after which a plastic colored leg band was used. A Fish and Wildlife Band was placed on a leg after the nestling reached 15 DPH. I recorded several measurements on each nestling. I obtained a body mass for each individual using a 50 gram Pesola accurate to i 0.1 g. I also recorded the length of several body parts using a dial caliper accurate to i 0.01 mm. These measures were: (a) the length of the right tarsometatarsus (hereafter as tarsus), from its proximal protru- sion at the joint with the tibiotarsus to its distal end at the joint with the halix; (b) the length of right ulna; (c) the length of the right wing chord, from the outer bend of the ulna to the tip of the ninth primary; and, (d) the length of ninth primary on the right wing. The growth of the tarsus, ulna and body weight increase were subjected to growth curve analysis fol- lowing Ricklefs (1967). Briefly, this procedure en- tails transforming growth data using one of three growth curve equations: logistic, Gompertz or vonBerta- lanffy. I used the logistic curve because it provided the best fit based upon examining the average linear regression coefficients of the transformed data. Growth curve transformation produces two statistics: a growth pri we: sul 29 curve constant, which is the slope of the curve trans- formed to a line; and the age that the growth curve inflects, which is the age of most rapid growth (hereafter as the inflection point). For subsequent analyses, I used only those nestlings that fledged and whose growth rate constant and inflection point dif- fered from 0.0 at a 95% confidence or greater. I used the heaviest weight, which occurs three to five days prior to fledging, for each nestling as the asymptotic weight value for curve fitting. This value had to be subsequently deleted from the curve fitting routine because of its high leverage on curve fitting estimates (Beaver, unpubl.). Growth of the wing chord was analyzed by fitting a straight line by log transformation. Thus, only the rate of wing chord growth was analyzed. Growth of the outer ninth primary was analyzed by calculating the slope of its linear growth using linear regression. I used the x-intercept from the calculated line as the age of primary eruption. During each growth measure visit, I also recorded whether the abdominal yolk sac was still present and if the eyes were opened. Because growth events were recorded every other day, the accuracy of these devel- opmental events is :2 days. Growth curve fitting requires an asymptotic value 30 which is difficult to estimate. Because of this, I also compared the rate of growth for the linear phases of body weight increase between, and including, the ages of 3-10 DPH, for all nestlings. Those nestlings that had three of more growth measures and where the slope of the straight line differs from a slope of 0.0 with a 95% confidence were entered in subsequent analyzes. Those nestlings whose growth measures failed to produce a straight line differing from a slope of 0.0 were considered to grow abnormally and were not included in the growth analyses. For those nestlings that fledged, I also used the heaviest weight and the age that this weight was attained as independent measures of a nes- tling's health prior to fledging. Feeding Behavior. From 1987 through 1989, I selected approximately half of the nests in the experi- mental design for food collection experiments to deter- mine the pattern of food provisioning to nestlings. I followed the neck collaring technique of Hussell (1972) with some modifications. Rather than using pipe clean- ers, I used flexible wire to constrict the passage of food moving down a nestling's esophagus. Care was taken to make sure that the constriction device was not affecting a nestling's behavior and that the trachea was not blocked. Food boluses were usually lodged st: ne. 16 31 striction device. A small percentage of food boluses (11.3%) were, however, ejected into the nest by some nestlings. Nests were inspected for ejected food boluses during each visit. Nestling feeding was monitored between 0900 and 1600 EST after the youngest nestling was at least 2 DPH and ceased once the oldest nestling reached 16 DPH. I allowed parents to feed their nestlings for 20 minute periods. At the conclusion of this 20 minute period, I visited the nest and examined each nestling for food boluses. I recorded which nestling received food and assigned a number to a food bolus which was collected and placed in a vial of 70% ethanol for later examina- tion. To replace the collected food bolus, I gave the nestling an equal sized waxworm. Insects in the food boluses were keyed to the same size-taxa categories used for the insect traps. I monitored 3 nests at one time; all nests were at similar ages. In most cases, I was able to select one nest from each hatching treat- ment. I did not follow a set of nests for longer than two, one-hour periods per day. Parental Care. In 1988 and 1989, I monitored parental investment by recording body mass changes over the nestling period. I weighed adults every other day in DE 'e'E ‘e‘fi B: I'! ME ar ri re be no (N 32 in the evening (1900-2100 EST) when weather permitted. I used a passive trapping device of Magnusson (1984) to trap the adults. Within one day of the first egg hatching, I measured the body mass of the adults and used the maximum percentage of weight change between the first day of hatching and the last evening weight (in most cases, 120PH or later in the nestling period) to calculate a percentage adult weight change for the nestling period. I also used the difference between the weight at hatching and the lightest adult evening weight as a measure of the maximum evening weight loss. Because I also collected body weights of parents during other times of the day, I took the difference between the evening weight at hatching and the lightest weight recorded during any part of the day to estimate the maximum percentage weight lost by parents. Statistical Procedures. For all statistical analyzes, I used an alpha level of 0.05 as the crite- rion for determining the level of significance for rejecting null hypotheses. Results of tests falling between alpha levels of 0.10 and 0.05 are cautiously entertained as significant. When results of tests are non-significant, observed trends are discussed. I used the statistical software package SYSTAT (Wilkinson 1990a) for all statistical analyses and SYG Bef tes In 33 SYGRAPH (Wilkinson 1990b) for graphical presentations. Before data were entered into any parametric tests, I tested for these assumptions of parametric tests (Sokal and Rohlf 1981): (1) normality, using the PPLOT routine of SYSTAT; and (2) homogeneity of variances using Bartlett's test. If data conformed to the assumptions of parametric tests, analysis of variances or covari- ances were conducted with the means and standard errors reported. Correlations were conducted to ascertain the amount of association of variables; all correlation coefficients reported are Pearson correlation coeffi- cients unless specified otherwise. If data were not normal, data were first transformed and assumptions for parametric tests reexamined. Failing any attempts to normalize the data, data were subjected to nonparamet- ric tests or are reported using descriptive statistics. III. RESULTS Natural Hatch Spreads. Figure 3 shows the normal hatching spread of clutches between 4 and 6 eggs. The hatching spread here represents the number of calendar days that hatching occurred. Only those clutches that: (1) had a 100% hatchability; (2) were incubated by ASY females; and (3) did not hatch during two critical cold spells (see below), are included here. Two and one ha: not ch: no ne pe 13' It 34 half times as many clutches of 4 eggs hatched synchro- nously (all eggs hatched on the same day) than asyn- chronously. As clutch size increased to five eggs, the modal hatching spread increased to two days, although nearly half of the clutches hatched over a one day period. Clutch sizes of six hatched more asynchronous- ly, with one nest hatching over a four day period. Interestingly, the amount of variation in hatching spreads increased with increasing clutch sizes. These data also show that hatching spreads were more synchro- nous than those reported by Zach (1982). To determine the extent of weight hierarchies established at the site by tree swallows, I also weighed all nestlings in a brood on the first noon after an entire brood had hatched. From these weights, I calculated the coefficient of variation for each brood and compared the average coefficient of variation for clutch sizes 4 through 6. Figure 4 shows that variations in the weights of broods soon after hatching increase dramatically with increasing clutch size; the coefficient of variation is twice as great in 6 egg clutches as in 4 egg clutches. Effects of experimental manipulation. I examined whether the original clutch size that females laid affected the outcome of the number of nestlings fledged .—.Z:Av.e .I.e‘ I In!!! 35 10 COUNT CLUTCH SIZE-4 _ N=7 ‘ _ COUNT CLUTCH SIZE-5 N-l4 ‘ COUNT l l CLUTCH SIZE=6 N=ll ‘ [—11 2. 3. 4. Hatching spread (in days) FIGURE 3 . Hatch spreads, by calendar days, for clutch through 6. sizes 4 DI Gre clu the flc we in 33‘ 36 or their growth rates. Perrins (1965) has found in the Great Tit (Bangs major), that parents laying larger clutches are able to raise larger broods. I compared the clutch size against: (1) the number of nestlings fledged; and (2) the slope of the linear phase of body weight increase for nestlings. I found a small but insignificant correlation between original clutch size and the number of young fledged (Pearson r= 0.134, X2 approx. = 0.891, P=0.345). I also found a small but insignificant correlation between the original clutch size and the slope of the linear phase of body weight increase (Pearson r= 0.042, X2 approx. = 0.382, P=0.537). I also compared the growth rates of those nes- tlings subjected to food bolus collections to those nestlings that were not subjected to food bolus collec- tions. I was able to introduce hatching treatment and year of study as covariates in this particular analysis using both effects as coded variables. These results, given in Table 1, show that there was no difference in growth rates between nests that were subjected to the bolus experiment compared to those that were excluded from this experiment. $523.23 :0 ZOE.<:_<> ...C .......~....~CU 23:2 MEAN COEFF. OF VARIATION OF WEIGHTS 0.25 0.20 0.15 0.10 0.05 ' 0.00 The coefficient of variation of weights of broods the first noon (12:00 EST) after natural hatching. 37 h. )— CLUTCH SIZE FIGURE 4. on st: to: '9} I. n: m 38 Egg weights. Figure 5 shows the mean and one standard error of egg weights by egg laying sequence for clutch sizes 4 through 6. Within clutches of 4 and 5 eggs, there was no linear relationship of egg weight with laying order. There was, however, a significant linear increase in egg weight with laying order in 6 egg clutches, described by the relationship: y = 1.39 + 0.143x where 'y' is the egg weight in grams and 'x' is the egg number in the laying order (R2= 0.66, df=59, P=0.044). I also performed a Wilcoxon sign-ranks test to compare the weights of the first and last-laid eggs in 4,5 and 6 egg clutches. I all cases, the last egg laid was significantly heavier than the first-laid egg using a one-tailed probability test (4 egg clutches, P = 0.056; 5 egg clutches, P = 0.036; 6 egg clutches, P = 0.014). Insect Abundances. Tow nets were operational for 27, 21, 28 and 30 days, for 1986 through 1989, respec- tively. Tow net data for 7 days in 1987 were not available. The average number of hours per day they were operational were 9.69, 10.52, 12.51 and 11.30 hours for these same years. A total of 1803 insects were collected in all of the tow nets. Weather during the study was unusual. Two cold periods occurred during this study, one in 1986 and the 39 2.0 I I I I I I 1.9 _ Clutch size - 6 ~ . } 1.7 - 7 EGG WEIGHT (3) L l l l 1 1.6 1 2.0 I I I I I 1.9 __ Clutch size - 5 — i - I I I i - 1.6 1 ‘ EGG WEIGHT (I) p.— ..— .— 2.0 I 1 1 I 1‘9 _ Clutch size =- 4 -I EGG WEIGHT (8) H—I .— P" 16 l l EGG FIGURE 5 . Mean egg weights (1 1 S.E.) by laying sequence. Shown are egg weights for clutch sizes of 4 through 6. 40 Table 1. Analysis of covariance examining the effects of the bolus collection experiments on the linear nestling growth rate. I compared the linear growth rate between broods in the bolus experiment (exper.) with those that were excluded from this experiment (control). Hatching treatment (tmt) and year were used as a covariate to control for these effects. SOURCE SS DF MS F-RATIO P Exp. v. cont. 0.011 1 0.011 0.069 0.794 Tmts 0.757 1 0.757 4.754 0.031 Tmt*exper. 0.384 1 0.384 2.407 0.123 Year 1.771 1 1.771 11.116 0.001 Year*exper. 0.007 1 0.007 0.046 0.831 Error 24.853 156 0.159 other in 1989. In 1986, the cold period lasted between June 13th and June 15th; the cold period of 1989 lasted from June 7th to June 13th. In addition, a severe drought occurred during the entire 1988 season. Figure 6 shows the pattern of daily IBI measures for each of the four years. The range of these IBI measures are from 0.0 mg/100km wind per day to 23 mg/100 km wind per day attained in 1987. The average IBI measures, for each year, are given in Figure 7. These data show that 1986 and 1987 had 5 times the insect abundances than in 1988 and 1989. The week long severe weather that occurred in 1989 at the study probably contributed toward lower average insect abundances. Good weather following the cold spell of 1986 and the small ponds at Floodwood probably resulted 41 FIGURE 6. Daily IBI measures (mg of insect/100km of wind) for each year of the study. Days that information is not avail- able is designated with an asterisk ('*'). 42 w mmDUHm WH: 3: 2C<22>< l AVERAGE IBI (MG/100 KM WIND) 20 15 10 48 n——~+ l l——l 1 l—I—l [—15—] H J l l 1986 1987 1988 1989 Year FIGURE 7 BF Hussell‘s Plots LP SL Size class in mm 11+ ”-11 I [-13 9-11 1-9 5-7 3-5 Size class in mm 09‘ a." t ‘O9~ Q‘P‘ ‘QQ‘ «0‘ ‘9 9° 0 ‘9 0“ 0° ‘09 0‘ | l l I | I I I I I l - o' {a c' :3 a; To 6 u a 7. 6 :3 S- in O s 6° “4’9 Q‘.‘ 99" 0" “fie 9\ ‘0 e" 9 s 0‘ O ~e‘ ~9° 0 60 4. 0" $0 I I l | I I I I I l _ - — 6 1'0 ' e to so is e 70 are )‘e or In at- 3'. Percentage of insects in each size-tan category FIGURE 8. Size-taxa distribution of insects (in percent of the total) captured by my tow nets for the entire four-year study. 50 size category, 1-3 mm (65%). Insects smaller than 1 mm were excluded from the above counts because they do not show up in food boluses of the tree swallow (Quinney 1983a, Hussell and Quinney 1987, this study). The size-taxa distribution of insects trapped in Hussell's two nets are shown in Figure 9. Hussell and Quinney's nets captured slightly more nematocerans that mine. A correlation of the numbers of insects in each taxa between tow nets of differing construction did exist (Spearman rho = 0.922), suggesting that both tow net constructions performed similarly in sampling the insect fauna. The Manitoba traps, operational for 24 days in 1988 and 25 days in 1989, trapped 2308 insects. Sixty- seven percent were tabanids and 31% were classified as other dipterans (Figure 10). The Manitoba traps were not operational for 4 days and 3 days, for 1988 and 1989 respectively, due to extremely strong winds. Daily Manitoba trap collections are given in Figures 11 and 12. The daily dry weights for 1988 (median= 1.12 grams) was significantly greater than for 1989 (median=0.074 grams, Mann Whitney U test, X2=7.053, df=1, P < 0.01) but the numbers of insects caught in these traps was not significantly different between years (Mann-Whitney U test, X2 = 0.595, df=1, P = 0.441). The low daily dry weights for the first two s 9 s’ e 99‘ 6". 9‘0 J" 6‘ 9 $° 9 ‘ 9° 9 \ ’39 06 ‘99 vé «at «23 e9 0‘ 11+ 13-11 8 £3 11-13 .9. 9-11 3 1 9 d — 0 5—1 I 0 2g is I III I 14 I. II I I. r {a 3'. So ; T 3'. {a c' {o In To 5 {a a} 95 1' s’ s 009 «‘6 ¢9 0° .é‘ 9‘ ‘g 9" e s 0° 0 'c’ ’9‘ 0 ‘3' .ge 0" $6 17+ 8 13-17 I a "-13 I .5 941 | 3 19 as fl 0 $4 I I o .5 rs I I l m 143 III-I'll IIIIIIII IIIIIIIII 6 13 i *64,‘; i ii :3 i 56 :3 5 Percentage of insects in each size-taxa category FIGURE 9 . Size-taxa distribution of insects (in percent total) captured in Hussell and Quinney's version the tow nets for the 1988 and 1989 seasons. of of Size class in mm Size class in mm e 9 O o $9 $0 4* J¢ ‘0‘ 9‘ “IO ‘° 6“ 00° vgo $¢‘ «2’ 4" e9 o‘ I 7+ IBI-17 I "-13 I | 9-11 | 14 | 91 I 34 | I -3 I I. a J. : I: I. J. I, IO 3 30 r I: r 1 ‘¢ ‘ 9 e (,0 $9 95 ‘e x Q 69 §> é» 69 I 1+ '3‘" _ "-13 l — m 9-11 I .- I 7-9 l I I 5-1 I — I 3-5 I n | 1-3 I | O I. g )1. I I. I. J. I6 I; fl )0 or III 1. 3. Percentage of insects in each size-taxa category FIGURE 10. Size-taxa distribution of insects (in percent of total) captured my the Manitoba traps for the 1988 and 1989 season. 53 FIGURE 11. Daily dry weights of insects captured in the Manitoba traps for 1988 and 1989. HH mmDUHh @53— e2. n2. «2. 3.. one one one hue efle eae nae nae 3e nae :e 3e 2e e_e 2e 3e 2e 2e 2e 2e _ _ a J '54 one one use eue nae vne nae nae .«e one 2e 2e 2e e_e 2e 2e 2e 2e Se 2e Se 3e pee eee 3e n e n (3) “Islam 41a cinema—ac (3) 11:18pm Asa \OIOVMNr-nc 55 FIGURE 12. The daily numbers of insects captured in the Manitoba traps for 1988 and 1989. NH flmDOHh MH 0.50 in both cases). Fledging success and nestling death. Fledging success by year was 85% (51/60), 77% (46/60), 70% (60/85) and 57% (34/60) for 1986, 1987, 1988 and 1989, In 58 respectively. This difference was highly significant (G = 12.71, df=3, P <0.01). During this four-year study, parents of SYNCHRONOUS broods fledged a greater propor- tion of their nestlings, followed by DOUBLE ASYNCHRO- NOUS and then SINGLE ASYNCHRONOUS broods (Figure 13). One SYNCHRONOUS brood was predated and was not used for fledging success calculations. Combining hatching treatments, nestlings hatching first (i.e. 'A' nes- tlings) fledged with a greater than 80% success rate, followed by 'B' chicks fledging at a lower than 50% rate and then 'C' chicks at a 25% rate. Fledging success was more pronounced between hatch positions (G = 34.54, df=2, P << 0.001) than across pooled hatching treatments (G=5.3, df=2, P <0.05). In both asynchro- nous brood types, fledging success decreased with decreasing hatch position. The greatest fledging suc- cess was by 'A' chicks in DOUBLE ASYNCHRONOUS broods. Fledging success was significantly greater in the first two years of the study (81%) compared to the latter two years of the study (65%) (G = 10.08, df=1, P < 0.005). During the two years of MORE FOOD abundance (Figure 14), fledging success increased, although not significantly, with more synchrony (G= 1.30, df=2, P < 0.10). During the LESS FOOD years, fledging success increased with greater hatching asynchrony (G=0.72, df=2, P < 0.10). All incidences of entire brood Proportion of nestlings fledging 59 m , HATCHING TREATMENTS m HATCH POSITIONS Incl Single Double A I C I- I. u . u h n . I I A A I A I C m illllO Mmlmll Double Asylum-en HATCHING TREATMENTS AND HATCH POSITIONS FIGURE 13. Fledging success of nestlings for the four-year study by hatching treatment and hatch position. 6O starvation occurred during the LESS FOOD years. Entire brood starvation rate increased with increasing syn- chrony. Of SYNCHRONOUS broods, two nests (2/10 = 20%) experienced entire nest starvation during LESS FOOD years, and of SINGLE ASYNCHRONOUS broods, only one of these nests, (1/9 = 11%), experienced entire nest starvation. No DOUBLE ASYNCHRONOUS broods experienced entire brood starvation during the four year study. Additionally, the incidence of partial brood loss, which I defined as any broods fledging between 1 and 4 young, increased with greater asynchrony when food was more limited; partial brood loss occurred in 40%, 64% and 71% Of the SYNCHRONOUS, SINGLE and DOUBLE ASYNCHRO- NOUS nests, respectively. However, partial brood loss was low in SYNCHRONOUS broods when there was more food, occurring in 25% of these nests, and was high in asyn- chronous broods, occurring in 77% and 57% of the SINGLE and DOUBLE ASYNCHRONOUS broods, respectively. I also determined the incidence of brood reduction by calculating the survival of late-hatching nestlings relative to the 'A' chicks (survival 'B' or 'C' chick/survival 'A' chick). For MORE FOOD years, 'B' chicks in SINGLE ASYNCHRONOUS nests fledged at a 57% rate compared to 'A' chicks. In DOUBLE ASYNCHRONOUS broods, relative survival of 'B' and 'C' chicks was 77% and 63%, respectively. In FLEDGING SUCCESS FLEDGIN G SUCCESS 61 1.0 I I I MORE FOOD 0.8 0.6 0.4 0.2 0.0 SYNCH SINGLE DOUBLE 1.0 1 l I LESS FOOD SYNCH SINGLE DOUBLE HATCHING TREATMENTS FIGURE 14. Nestling fledging success by food year type, hatching treatment and hatch position. Food year types are MORE FOOD and LESS FOOD. 62 LESS FOOD years, the relative survival of 'B' chicks was 63% in SINGLE ASYNCHRONOUS broods, and 71% and 42%, for 'B' and 'C' chicks, survival of 'B' and 'C' chicks was 77% and 63%, respectively. In the LESS FOOD years, relative survival of 'B' chicks was 63% in SINGLE ASYN- CHRONOUS broods, and 71% and 42%, for 'B' and 'C' chicks, respectively, in DOUBLE ASYNCHRONOUS nests. Brood reduction, by the death of the 'C' chick, was most prominent in DOUBLE ASYNCHRONOUS broods when food was less abundant. Therefore, brood reduction in DOUBLE ASYNCHRONOUS broods increased the fledging success of these broods when food was less abundant compared to the other two hatching treatments. The age that nestlings died, by hatch position and hatching treatment, is given in Figure 15. There is no significant difference between the age of nes- tling deaths in any of the hatching treatments (Krus- kal-Wallis, H=1.871, df=2, P=0.392). However, in DOUBLE ASYNCHRONOUS nests, the age of nestling death was significantly different between hatch positions (Kruskal-Wallis, H=8.88, df=2, P = 0.012); with 'C' chicks dying at a significantly younger age than 'B' chicks, which in turn, died earlier than the 'A' chicks. Nestling deaths occurred significantly earlier 63 FIGURE 15. Age of nestling deaths by hatching treatment and hatch position. Hatch position legend is located on the lower left corner of each plot. NUMBER a—Nueuaque NUMBER OWNW-FMGQN‘O NUMBER o—Nuauo‘qeee I -I Nil I I I I I j SYNCHRONOUS MHMMN-H W SINGLE ASYNCHRONOUS anMI-W I I I I I I r j I I DOUBLE ASYNCHRONOUS lflUMN-NM I AGE OF NESTLING DEATH FIGURE 15 Z CHICKB I CHICKA I CHICKC Q CHICKB I CHICKA 65 in LESS FOOD years than in MORE FOOD years (Mann-Whit- ney, U=810.5, df=1, P < 0.001). There was no differ- ence between hatching treatments in the age of nestling deaths during the MORE FOOD years (Kruskal-Wallis, H= 2.653, df=2, P=O.265) or during the LESS FOOD years (Kruskal-Wallis, H=2.349, df=2, P=0.309). However, nestling deaths occurred at a significantly earlier age in LESS FOOD years compared to MORE FOOD years with increasing hatching asynchrony; at a slightly signifi- cant earlier age in SYNCHRONOUS broods (Mann-Whitney, U=55.0, df=1, P=0.056), to a significantly earlier age in SINGLE ASYNCHRONOUS broods (Mann-Whitney, U=121.5, df=1, P=0.031) to a very significantly earlier age in DOUBLE ASYNCHRONOUS broods (Mann-Whitney, U=550.0, df=1, P=0.008). Nestling Growth and Development. Nestling growth curves for body weight increase, tarsus, ulna, wing chord and ninth primary growth, are given in Figures 16-20. The growth curve for body weight increase illustrates the four phases of tree swallow weight growth. The early phase of growth is a rapid, exponen- tial trajectory which levels off to the second phase of growth which is linear. The third phase is character- ized by growth rate cessation, where a peak in body mass is reached several days before fledging. Common of cavity nesting birds is the fourth phase of growth, 66 weight recession, which occurs just prior fledging. Ricklefs (1968) has attributed this weight recession in hirundines to water loss due to feather growth and maturation. Growth of tarsus and ulna follow a similar logistic growth curve, growth of the wing chord models an exponential trajectory and the growth of the ninth primary approximates a linear relationship. Analysis of linear body weight growth, age of yolk depletion and eye opening are performed on all nestlings surviving long enough to obtain measures. All of these variables had heteroscadastic variances which could not be re- moved using transformation and one-way nonparametric analyses were performed. The analysis of body weight growth, tarsus, ulna, wing cord, primary and maximum weight are performed on those nestlings that fledged. These data adhered to the assumptions for the analysis of variance. I present growth data under four differ- ent subheadings: (1) growth of all nestlings; (2) growth of nestlings that fledged; (3) dynamics of nestling weights; and (4) affects of food abundance on nestling growth. 1. growth of all nestlings, Nestling linear of growth rates for weight were significantly greater in MORE FOOD years than in LESS FOOD years (Mann-Whitney, U= 3083.0, df=1, P = 0.022). Nestlings in LESS FOOD years grew 10% slower than nestlings of MORE 67 FIGURE 16. Mean body weight measures (3 1 S.E. ) of all nestlings by age (days post-hatch, DPH) and hatching treatment. 68 I l I U DOUBLE l 25 I I I I I I I I ' III I I ..’/l I I I I l_ I II I ///,//// II / III II /,’I // I ,, ,/ I I II I II III IIII IIII' II I I I I / III L_ ’l/// /// II I] II III III/II I II I III/I III I I I I III ’ I I I IIII IIII I III/I I I . I // IIII I I/II III I SINGLE I SYNCH / / ///////’.’/ / / / I’ll I’ ////// ///// / /// WIWWm/fl/Mlllm/wwmlwmw " 'IIIIJIIMIWIIIIWMIII”[III/WI” 20*- F-l v—Il (3) Infirem In 0 W O I]. 12. 13. 14. 15. 16. l1. l8. AGE FIGURE 16 69 FIGURE 17. Mean tarsus measures (: 1 S.E. ) of all nestlings age (days post-hatch, DPH) and hatching treatment. by 7O I 7 I I I 1 ’m __ m 2515 —'.'—'> 055 ‘Qmm ”Cl-I l l N OQOOB v—iv—‘v-d (111 I11) snsml ll. 12. l3. 14. 15. l6. l7. IS. 10 AGE FIGURE 17 71 FIGURE 18. Mean ulna length measures (i 1 S.E. ) of all nestlings by age (days post-hatch, DPH) and hatching treatment. 72 I I I E] DOUBLE § SINGLE 30 - SYNCH <=> ICD CV (IIIIII) BUM] ”III/”11”,] ‘3'. ll. 12. 13. 14. 15. 16. 17. 1Q AGE FIGURE 18 73 FIGURE 19. Mean wing chord measures (3 1 S.E. ) of all nestlings by age (days post-hatch, DPH) and hatching treatment. 74 WIM/I/I/Io'fo‘. 80 m _._]I-T-I ran—IE 4302 05> ”Qt/am —[:III L I I l I I o c: o o o c o o [\Wlnfl'MNv—t (mm) ploqo 8mm 11. 12. 13. 14. 15. 16. I7. 18. 10 AGE FIGURE 19 75 FIGURE 20. Mean length of ninth primary (i 1 S.E. ) for all nestlings treatment. by age (days post-hatch, DPH) and hatching 76 Zflfl%fl%fl%fl%fl%fifl%fl%fl%fl%fl%fi W Mflflfl%fl%fl%fl%fl%fl%&$ W 40 W *- % U _:30 05E _Qmm DI. I I I , o O O o M N '— (unn) Kmmpd [IllIIN 12. 13. 14. 15. 16. l7. 18. ll. 10. AGE FIGURE 20 A FOC 8Y5 twc bro bet Wal FOO VGI'I inc LESS P=0. almc diff tior fitt hatc as u tlin CHRo “GUS diff earl. trea. 77 FOOD years. During MORE FOOD (Figure 21), nestlings in SYNCHRONOUS broods grew faster than nestlings in the two asynchronous broods; nestlings in asynchronous broods had similar growth rates. However, differences between hatching treatments were significant (Kruskal- Wallis, H=15.47, df=2, P < 0.001). During the LESS FOOD years, growth rates between hatching treatments were not significant (Kruskal-Wallis, H=1.645, df=2, P=0.439). The linear weight growth rates increased with increasing hatch position (Figure 22) in both MORE and LESS food years (Kruskal-Wallis, H=7.422, df=2, P=0.024). In the years of LESS FOOD, 'C' chicks grew almost half as fast as all of the 'A' chicks; this difference was not as great for these same hatch posi- tions during the MORE FOOD years. I also compared the number of nestlings not fitting the linear model by hatching treatment and hatch position. I considered nonlinear nestling growth as unhealthy growth. More than a quarter of the nes- tlings grew nonlinearly in the SINGLE and DOUBLE ASYN- CHRONOUS nests. Only 13% of the nestlings in synchro- nous broods grew nonlinearly during this period. The differences in proportions of nestlings growing nonlin- early was significantly different between hatching treatments (G=14.37, df=2, P < 0.01) but not between 78 FIGURE 21. Density plots of the linear phase of body weight growth for all nestlings by food year type and hatch- ing treatment. 79 LESS FOOD MORE FOOD 00:24 SYNCH I mum I: dun 20:30.:th 8:24 -5 1]. Mn H C r.... N .l y. In M u u m fl 0.30). Interest- ingly, those nestlings growing nonlinearly where not more likely to die than fledge (G=0.56 df=1, P > 0.30). The pattern of the age of yolk depletion between hatching treatments and food year types is interesting (Figures 23 and 24). Yolk depletion occurred signifi- cantly later during MORE FOOD years compared to LESS FOOD years (Mann-Whitney, U=1149.0, df=1, P < 0.001). In the MORE FOOD years, the age of yolk depletion increases with increasing asynchrony with differences between hatching treatments significantly different (Kruskal-Wallis, H=25.69, df=2, P < 0.001). In the LESS FOOD years, the opposite trend is observed with differences between hatching treatments also signifi- cant (Kruskal-Wallis, H=6.592, df=2, P =0.032). Yolk depletion occurred earlier with decreasing hatch posi- tion in the LESS FOOD years (Kruskal-Wallis, H=3.639, df=2, P=0.162). There were no differences in age of yolk depletion by hatch position in MORE FOOD years. The eyes opened significantly later during the LESS FOOD years (Figure 25) compared to the MORE FOOD years (Mann-Whitney, U=1852, df=1, P < 0.001). Eye opening occurred later in DOUBLE ASYNCHRONOUS broods compared to other hatching treatments in the MORE FOOD years. The difference in the age of eye opening be- 83 FIGURE 23. Density plots of the age of yolk depletion for all nestlings by food year type and hatching treatment. I10 5 IT. WIIIII; SYNCH - d u u u M a: an. 22.593: II SYNCH «van 1: 111 209—32011 SINGLE SINGLE 00021. I 7 '6 “S -4 "3 '2 "-1 mum“ 53 en. 22:22: _ uuuuu 1: 111 203301011 II 0002‘. ‘5‘311 FLILIPIEII m 1 m m B -s u u m U 1.. O D E ]II4|L u u m 1 0.50). In DOUBLE ASYNCHRONOUS broods, the 'B' chicks were the fourth heaviest nestling 47% and 53% of the time during the MORE and LESS FOOD years, respectively; the differ- ence between food year types was also not significant (G=0.37, df=1, P>0.50). The 'C' chicks were also the lightest chicks 82% and 67% of the time, in MORE and LESS FOOD years, these differences were not significant between food year types (G=0.37, df=1, P > 0.50). To determine if SYNCHRONOUS broods developed weight hierarchies as great as those in asynchronous broods, I calculated the coefficient of variation of body weights for all nestlings in a nest during each growth measure visit. The average coefficient of variation, by hatching treatment, is given in Figure 32. The variation of body weights in a brood increases with increasing hatching asynchrony. The mean coeffi- cient of variation for body weights was on average twice as great in DOUBLE ASYNCHRONOUS as in SYNCHRONOUS broods. 111 0.2 - - 0.1 - J J AVERAGE COEFFICIENT OF VARIATION 0.0 l l 1 SYNCH SINGLE DOUBLE HATCHING TREATMENT FIGURE 32 . The average coefficient of variation of nestling weights by hatching treatment (1 1 S.E.). 112 FIGURE 33. The mean percent of nestling body weight (: 1 S.E.) deviating from the "normal" body weight with respect to the day of brood reduction. Weights are for nes- tlings that fledged and only those broods fledging 4 young are included. Periods represent 2-days. 113 I I I I I I I L Synchronous I o «I 3 0 ..fi 4.) O 1:: 4 I I I I I I I 00 3 ,_ Single Asynchronous _ .8 2 I J H a 1 - a 0‘ ’ > o «- _ d.) -o -1 — — E -2 r ~ on -3 I ~ Ofi Q) _4 1 l L 1 I 1 1 3 —4 -3 -2 -1 o 1 2 3 4 c... O 0 00 g“ 4 I’ I r I I I I '8 3 _ Double Asynchronous I 0 o 2 " -I H O I 9" o .. Davs before and after death FIGURE 33 114 The nestling body mass deviations from "normal" on days preceding and following each brood reduction event are given in Figure 33. To construct this figure, I calculated the average nestling body mass for each age for nestlings in broods that fledged 5 young and considered this a nestling's "normal" mass. Then for all broods that fledged 4 nestlings, I took the differ- ence between this "normal" mass and the body mass of the nestlings in the broods and divided this value by the "normal" mass for that nestling. This produced a value expressing the percentage of weight deviating from the "normal" weight for its age for each nestling. I then plotted the averages of these mass deviations from "normal" for the four nestlings in each brood that fledged using two day intervals preceding and following the loss of the 5th nestling. For SYNCHRONOUS broods, nestling weight dipped below the "normal" weight of that nestling for its age by 1% in the three day-inter- val previous to brood reduction (day of brood reduction = 0). Weights of the surviving nestlings remained below the "normal" weight for as many as 6 days after brood reduction. In SINGLE ASYNCHRONOUS broods, 'weights of surviving nestlings decreased between the 3rd day-interval to the lst day-interval before brood (reduction. Their weights returned to the "normal" for that age on the day of the nestling death and remained 115 close to "normal" for as long as this comparison could be done. Interestingly, for DOUBLE ASYNCHRONOUS broods, nestling weights reached a low value on the 3rd interval previous to brood reduction and rebounded quickly back to the "normal” weight on the day that brood reduction occurred. Also of interest is that the average nestling weight reduction for all nests does not surpass 2% in any of the treatments, a possible critical growth reduction limit. Perhaps a tradeoff might exist between jeopardizing the potential survi- vor's health, and hence their chances of fledging at a substantial body weight, and the survival of the nes- tling singled out for eventual starvation. Figure 34 shows the same comparison for nestling weight changes, with respect to the first brood reduc- tion, but for broods that fledge three nestlings. Unfortunately, no SYNCHRONOUS broods fledged three young. Figure 34 shows that weights remained below "normal" for surviving nestlings throughout the entire phase of periods examined except for 4 days post-brood reduction in DOUBLE ASYNCHRONOUS broods. Weights below the average did occur in both hatching treatments prior to brood reduction. Nestling weights also dipped below the 2% weight loss value three times, once for SINGLE ASYNCHRONOUS broods just prior to brood reduction and 116 FIGURE 34. The mean percent of nestling body weight (1 1 S.E.) deviating from the "normal" body weight with respect to the day of brood reduction. Weights are for nes- tlings that fledged and those broods fledging 3 young are included. Periods represent 2-days. Percentage of weight deviating from the mean OHNNtb 117 p- I U r I I I I Single Asynchronous J I I I I f I T _ Double Asynchronous _ .— -I I L l L L J l -4 -3 -2 -l 0 l 2 3 4 2-day periods before and after death FIGURE 34 118 twice in DOUBLE ASYNCHRONOUS broods; once before and once after brood reduction. LEBEIELEQQIMDMMEQQQWI also tried to determine whether daily IBI measures affected the rate of weight growth during the linear phase of body weight and the maximum nestling weight attained. I calculated the average daily IBI value during the linear phase of growth for each nestling. The correlation between daily IBI measures and the rate of linear body weight increase was not significant (P=0.318). However, I detected a significant correla- tion (r=0.333, df= 195, P < 0.001) between the maximum nestling weight and the daily average IBI that occurred from hatching of the nestling to the day that maximum weight occurred. There was also a significant positive correlation between the linear nestling growth rate and the average daily insect dry weights in the Manitoba traps (r=0.215, df=195, P < 0.01). The age of maximum weight attained by nestlings that fledged did not correlate strongly (r=0.007, df=195, P > 0.10) with daily IBI measures. Feeding Behavior. I monitored 474, 20-minute feeding bouts to the nests from 1987 to 1989. During this period, a total of 736 food boluses were delivered containing a total of 14,859 insects. The size-taxa 119 distribution for these boluses are given in Figure 35. Note that the scale for nematocerans differs from the other Orders. Eighty-six percent (12,749) of the insects were composed of dipterans. Of the dipterans, 67% (9990) were nematocerans. Other important diet items, in percent of the total number of insects, included homopterans (8%), hemipterans (1%), and ephe- meropterans (2.5%). The most common size category preyed upon by tree swallows is 3-5mm (74%) followed by the 5-7mm category (12%). Thus tree swallows select insects of sizes less than those of insects trapped in Manitoba traps but larger than those most frequently found in the tow nets. Tabanids accounted for only 1.5% of the total number of insects delivered to the nest. However, they accounted for 5% of the total dry weight of the insects delivered to the nest. Generally, one tabanid sufficed to make one bolus. Tabanids made up 1.3%, 2.6% and 0.3% of the food items delivered during the 1987, 1988 and 1989 breeding seasons, respectively. These propor- tions by year were significantly different (G=124.9, df=2, P < 0.001). The higher percentage of tabanids in food boluses during 1988 is probably due to the very dry and hot conditions during that season. During MORE FOOD years, the amount of food par- ents delivered to the nest, per 20 minute feeding 120 s e 4? J9 0 e9 ‘9 0‘ 5°“ ‘0‘ 0‘ 9‘ ‘9 4" «$5 e9 o‘ n+ 13-11 £3 I a "-13 | - l .5 941 I | I O O _ £3 7 9 l I I I 9 ya I I l I o as 1-3 I I II f..z..‘.I;.....f..ié.‘.r;zzi.. s? s o s 6° ‘69' ‘6‘9 s§$ 19 e. ‘. 0‘ $0 11+ l3-l1 E5 1' £3 11-13 I I I .53 9-11 | I II a a F, I I. I .2 " 5-1 ll IIIIIIIIIIII I I) 15; 3-5 IIIIIIIIIIIIII IIIIIIIIIII IIIIII' l-3 I IIII 6 a .5 8 a. a J i 3 I i h I’ a . s s n 8 i i I’ a u Percentage of insects in each size-taxa category FIGURE 35 . Size-taxa distribution of insects (in percent of total) in food boluses for the 1987, 1988 and 1989 seasons. 121 session, when five nestlings were alive, increased with increasing hatching synchrony, with SYNCHRONOUS, SINGLE and DOUBLE ASYNCHRONOUS parents delivering 29.0 mg, 25.0 mg and 11.0 mg of food per 20 minutes, respective- ly. However, during the LESS FOOD years, the amount of food brought to the nest when five nestlings were alive increased with increasing hatching asynchrony, with SYNCHRONOUS, SINGLE ASYNCHRONOUS and DOUBLE ASYNCHRO- NOUS parents delivering 31.0 mg, 42.0 mg and 46.0 mg of food per 20 minutes, respectively. Surprisingly, the amount of food per feeding session was double during LESS FOOD years compared to MORE FOOD years. During MORE FOOD, the number of feeds to each nest during a feeding bout, when five nestlings were alive, did not differ significantly between hatching treatments (G= 2.96, df=2, P > 0.10), with DOUBLE ASYNCHRONOUS, SINGLE ASYNCHRONOUS and SYNCHRONOUS nests receiving 1.05, 1.92 and 1.72 feeds per 20 minutes, respectively. When food was less plentiful, parents of SINGLE ASYN- CHRONOUS delivered fewer food boluses (1.73 boluses/20 minutes), followed by parents of DOUBLE ASYNCHRONOUS (1.96 boluses] 20 minutes) and then parents of SYNCHRO- NOUS broods (2.17 boluses/20 minutes). These differ- ences were also not significant (G=1.37, df=2, P > 0.50). The number of food boluses brought to the nest 122 was almost significantly greater during the LESS FOOD years compared to the MORE FOOD years (G=3.17, df=1, P < 0.10). Thus, when food was more limited, parents brought more food to the nest, both in the amount of food and the number of food boluses. The proportion of food delivered to each nestling by the nestling's hatch position, and for each year type, is given in Figure 36. To construct Figure 36, I used information on bolus samples from nests where all five nestlings were still alive in the nest (some feedings were monitored after nestlings died, these are excluded). In MORE FOOD years, the 'B' chick received more than 40% of the food delivered to the nest; each 'A' chick received about 15% of the food brought to the nest (note that 4x15 + 40 = 100%). In DOUBLE ASYNCHRO- NOUS broods, each 'A' chick received less than 10% of the food brought to the nest, the 'B' chick received slightly greater than 30% and the 'C' received about 40% of the food brought to the nest (also note that 3x10 + 30 + 40 =100%). Thus, the youngest nestlings during the MORE FOOD years received the most food brought to the nest. A strikingly opposite trend in food apportionment is observed during the LESS FOOD years. The 'B' chicks received slightly more food than each 'A' nestling in a SINGLE ASYNCHRONOUS brood, but the 'C' chick in the PROPORTION OF FOOD TO EACH HATCH POSITION 123 MORE FOOD LESS FOOD 50 I I 50 I I SINGLE ASYNCHRONOUS SINGLE ASYNCHRONOUS 40L - CHICK CHICK 50 fi I I so I I I DOUBLE ASYNCHRONOUS DOUBLE ASYNCHRONOUS FIGURE 36. The proportion of food delivered to each nestling according to hatch position and by food year type for SINGLE and DOUBLE ASYNCHRONOUS broods. 124 FIGURE 37. The proportion of food and proportion of feeds deliv- ered to each nestling according to its weight ranking by food year type for SYNCHRONOUS broods. 125 LESS FOOD MORE FOOD um 80* 60 40 20 um 80 «one. we oueueoouom um 80 80 good no sexton-ohm RANK RANK FIGURE 37 126 DOUBLE ASYNCHRONOUS broods received less than 5% of the food brought to the nest; the 'B' chick received the most at 26% and the 'A' chick received 23%. Clearly then, the 'C' chicks in DOUBLE ASYNCHRONOUS died from a lack of food during the LESS FOOD years. Within SYNCHRONOUS broods, I examined the number of feeds and the amount of food given to each nestling according to its weight ranking (Figure 38). During MORE FOOD, the proportion of feeds to each nestling by its weight rank did not differ from a random feeding of nestlings by ranking (G=2.99, df=4, P > 0.50). The amount of food given to each nestling by its weight ranking did, however, differ significantly from a random apportionment of food (G=235, df=4, P < 0.001) with the lightest nestling receiving the largest food boluses brought to the nest. This same pattern is observed when food was less abundant, with the number of feeds to each nestling by its weight ranking not differing significantly from a random feeding of nes- tlings (G=1.03, df=4, P > 0.90). The amount of food given to nestlings appears to increase with decreasing weight ranking when food is less abundant (G=68.0, df=4, P < 0.001). Thus, the largest nestlings received the largest food boluses. 127 Parental Care. I weighed females on the evening within one day of her clutch hatching and followed their weight change by attempting to capture females every other evening until the oldest nestlings reached 18 DPH. I conducted this intensive weighing procedure only during the 1988 and 1989 season, thus, I am not able to compare weight changes of females during the more plentiful food seasons. The percent difference between the weight of females at hatching to an evening during the later portion of the nestling period, is negative for those females raising SYNCHRONOUS broods. Females raising asynchronous broods gained weight during this period; the most gained by parents raising SINGLE ASYNCHRONOUS broods (Figure 38). I also calculated the maximum weight lost from the evening of hatching to any other time period (morning through evening) that I was able to obtain a body weight. These patterns show that DOUBLE ASYNCHRONOUS broods experienced the most weight loss during the nestling period, more so than the other two hatching treatments. I also tried to determine the effect of daily IBI measures on the daily body weights of females. I found a slightly significant correlation (r=0.111, df=250, 0.10 < P < 0.05) between the absolute weight of all females and daily IBI measures. One of the most drastic 128 FIGURE 38. The (a) median percentage weight loss (from hatching to late in the nestling period) of females raising broods, by hatching treatment; (b) the average of the most percentage weight lost by females for (i 1 S.E.)evening weighings from hatching date; and (c) the average of the maximum weight lost by females (i 1 S.E.) from hatching date. PERCENT WT LOSS MEDIAN PERCENT WT LOSS PERCENT WT LOSS 3.: O 25 20 15 10 25 20 15 10 129 I I 1 HATCHING TO END OF NESTLING PERIOD I l l SYNCH SINGLE DOUBLE I T I EVENING BODY WT MEASURES I I I 1 I L l L SYNCH SINGLE DOUBLE I I I ALL BODY WT MEASURES I J L SYNCH SINGLE DOUBLE HATCHING TREATMENTS FIGURE 38 130 changes in weight occurred during the cold spell of 1989. Prior to this cold spell, the evening median weight of females was 21.1 grams. The median of female evening weights dipped to 19.5 grams during the cold spell and then rose to 20.9 grams one week following the cold spell. The differences in the weights between the three periods was highly significant (Kruskal- Wallis, P < 0.001). One female, whose body weights were monitored (her nest was excluded from the study because she laid three eggs), was weighed at 23.2 grams on the day her clutch hatched (10 June). On the morn- ing of the 15th of June, she weighed 16.8 grams, slightly more than 3/4ths her weight five days previ- ous. By the 17th of June, she was captured again and weighed at 19.9 grams. I also calculated the percentage weight change of a female from her weight when her clutch hatched to all evening measures and averaged these percentage weight changes for 2 day intervals previous to, and following, the first death in the nest. Because of small sample sizes, I had to combine data from all three hatching treatments. Figure 39 shows that the percentage weight change since hatching date is lowest 9-10 days prior to brood reduction. The weights increase, then fall again reaching a new minimum on the day of brood reduction. Adults appear to gain weight and reach their previous 131 15 l I I I I 10 — .- ~ 0 a H 2 s - ~ 0 5.3. "a 0 " 1' — B ‘5 § '5 " d o On -10 - ‘ I _15 I l l l l -6 -4 -2 o 2 4 6 Days before and after brood reduction FIGURE 39. The percent weight change of females from their weights at hatching averaged with respect to the day of brood reduction. All hatching treatments and only those broods that fledged 4 young are included. 132 weight at hatching 3-4 days after brood reduction. The lowest weights recorded did not occur during the cold snap of 1989. IV. DISCUSSION A. GENERAL RESULTS OF STUDY RELEVANT TO THE BROOD REDUCTION HYPOTHESIS 1. Natural Degree of Hatching Asynchrony Several studies have reported that tree swallows hatch clutches asynchronously (Hussell and Quinney 1987, Quinney 1983b, Zach 1982, Paynter 1954). Zach reported a low number of nests hatching broods all on the same day (13.8%). I have found that hatching asynchrony is the most common form of hatching for large clutch sizes; hatching asynchrony increased with increasing clutch size. This study confirms that tree swallows hatch their clutches asynchronously. However, clutches appeared to hatch more synchronously than reported by Zach (1982). Nearly one-half of all 5 egg clutches hatched on the same day. Synchronous hatching also appeared to be the most common hatching pattern for 4 egg clutches. I also found that a considerable amount of varia- tion in hatching spreads occurred within a clutch size, and that the amount of variation in hatching spreads increased with increasing clutch size. Within 4 egg 133 clutches, hatching occurred within a one to two day range. For 6 egg clutches, one nest out of twelve hatched on the same day and one nest hatched over a four-day period with most hatching over a two or three day period. Bryant (1978) reported variation in hatch- ing spreads in the House Martin (leighgn grhigg), increased with increasing clutch size. He also found that the modal hatching spread increased with increas- ing clutch size. Despite the reduced degree of hatching asynchrony observed during my study compared to other studies, the natural degree of hatching asynchrony did, however, produce distinct weight hierarchies in the nest. These weight hierarchies, as reflected in the coefficient of variation of weights soon after hatching (Figure 4), increased with increasing degree of hatching asynchro- ny. Zach (1982) reported that weight hierarchies were established by hatching asynchrony with the heaviest nestling weighing twice that of the youngest nestling after all young had hatched. He found that weight hierarchies are continued well into the nestling period with pronounced asynchronous fledging (Zach 1982). I also found that weight hierarchies persisted in nests with the coefficient of variation of nestling weights throughout the nestling period increasing with increas- ing degree of hatching asynchrony. 134 I also found that egg weights increased with laying order (Figure 5), with the last laid egg weigh- ing more than the first laid egg in 4, 5 and 6 egg clutches. Tree swallows hatch eggs in the order than they are laid (Zach 1982). Thus, egg size variation in a clutch does not contribute toward nestling weight hierarchieinn asynchronous nests but rather egg weight variation tends to reduce them. Furthermore, in natu- ral synchronous nests, subtle weight differences caused by the timing of egg hatching may be quickly offset by differences in egg weights making egg weight variation an unlikely contributing factor to weight hierarchies for SYNCHRONOUS broods. 2. Food Supplies Food supplies during this study were more limited than at the two non-pond sites of Hussell and Quinney (1987). Food supplies during my 1986 and 1987 seasons (Figure 6-7) were near the seven-year average of food levels they reported for one study site (Backus Field) that lacked habitat favorable for high insect abun- dances. Thus, conditions during my entire four-year study were probably less than ideal for parents to raise five nestlings. Because the 1986 and 1987 insect abundances were similarly high and the insect abun— dances for 1988 and 1989 were similar but low, I 135 assumed that the first two years provided parents with more food than the latter two years. A comparison of insect fauna in tow net catches and insects in the food boluses suggest that tree swallow appear to feed on the most abundant type of insect available -- small dipterans. However, tree swallows are selective in their feeding, selecting dipterans larger than those most commonly found in the tow nets. This result is almost identical with the findings of Quinney and Ankney (1985) who found that tree swallows were selective in the size of the most abundant insect group at their site -- also small dipterans. Two explanations may exist to explain this. First, prey items smaller than 3mm may be difficult for tree swallows to efficiently locate. Second, the tow nets may not be sampling the insects that are available to tree swallows. Perhaps the insects of 3-7mm are the most abundant at heights above the tow nets. Holroyd's (1972) observations that 53% of the time parents for- aged above heights of 5 meters seems to support this hypothesis. 3. Effects of Experimental Manipulations I am able to conclude that the clutch size ad- justment I performed had no apparent affects on the number of fledglings produced or the growth rates of nestlings. Additionally, linear nestling growth rates 136 were not affected by the food collection procedures (Table 1). The establishment of synchronous hatching and two degrees of hatching asynchrony was not out of the range observed to occur naturally in 5 egg clutch- es. The natural weight hierarchies established in 4, 5 and 6 egg clutches (Figure 4) were very similar to the weight hierarchies maintained in SYNCHRONOUS, SINGLE ASYNCHRONOUS and DOUBLE ASYNCHRONOUS broods, respec- tively (Figure 32). For DOUBLE ASYNCHRONOUS broods, the average coefficient of variation of nestling weights maintained during the nestling period was 18%, the same value for the weights of nestlings soon after hatching in natural 6 egg clutches. Likewise, the coefficients of variation in nestlings weight during the nestling period in SINGLE ASYNCHRONOUS broods was 10%, very close to the 12% coefficient of variation of nestlings weights found soon after 5 egg clutches hatched. The coefficient of variation of nestling weights during the nestling period in SYNCHRONOUS broods was slightly higher, 7.5%, than the coefficient of variation (4.9%) found soon after 4 egg clutches hatched. Thus, the experiment of increasing hatching asynchrony (i.e. DOUBLE ASYNCHRONOUS) mimicked the effects that would have been found in naturally asynchronous 6 egg clutches, and SYNCHRONOUS broods 137 mimicked the degree of synchronous hatching of 4 egg clutches. Moreover, the manipulation of hatching patterns had the added advantage of excluding the effects of initial clutch size. One effect that I did not directly test for is whether parents raise genetic offspring better than foster offspring. Burtt (1977), Burtt and Tuttle (1988), Hussell (1988) and Beaver (unpub.), in nestling switching studies using tree swallows, found that parents raise foster offspring as well as genetic offspring. These results are consistent with other studies on other species which have shown that growth rates and fledging success is dependent upon the quality of the parent rather than on the genotype of the nestling (Ricklefs and Peters 1981). Although it has been shown that tree swallow parents imprint on nestlings using plumage characteristics prior to fledging, the switching experiment at hatching avoided parent's identifying their offspring and thus affecting the produc- tion of broods by hatching treatment. Moreover, if tree swallow parents are able to recognize their own offspring by plumage characteristics and if they stopped feeding foster offspring at this time, then deaths from not being fed would occur at a consistent age throughout the hatch— ing treatments and occur late in the nestling period when nestlings have feathers. Nestling deaths were 138 concentrated within the first 15 days of the nestling period, thus ruling out the effect of parent recognizing offspring effect on the results of this study. B. EXAMINING THE BROOD REDUCTION HYPOTHESIS 1. Objectives of Study According to the brood reduction hypothesis, hatching asynchrony could be adaptive if it produced a weight and age hierarchy in the nest that aided parents in reducing the brood in the event food becomes limit- ing. On the other hand, the lack of feeding hierarchies in synchronous broods during food shortages should cause the entire brood to starve. The purpose of this study was to determine if, in tree swallows : (a) conditions necessary for brood reduction occur; (b) the mechanisms of brood reduction are in place; (c) brood reduction, if it occurs, has any adaptive value; and (d) if other reproductive tactics exist to compli- ment a brood reduction strategy. 2. Prerequisites for Brood Reduction Lack predicted that brood reduction would be beneficial if (i) food is unpredictable; (ii) the nestling period is long; and (iii) food levels affect parental performance. I discuss each of these in turn. Brood reduction and hatching asynchrony should be beneficial to parents if parents cannot predict, at the 139 completion of ovulation, future food levels for the upcoming nestling period (Lack 1948, 1954). If parents could predict future food levels, then the most adap- tive behavior would be for parents to lay eggs that will hatch the maximum number of nestlings they could raise given the pending food levels. Brood reduction, therefore, should not be necessary. O'Connor (1978) suggested that unpredictability of food levels would be reflected in food levels that change randomly from day to day. Hussell and Quinney (1987) have measured daily insect abundances from the time of nest initiation to the end of the fledging period at their study sites for seven years. They found no correlation between the food levels occurring during egg laying and levels occurring during the nestling period; thus, prey of the tree swallow appears unpredictable at the time of egg laying. Moreover, in three out of the four years during my study, the variance of daily IBI measures occurred at randomly. This random insect abundance levels were probably tied to random daily weather events. Severe weather events affecting IBI were relatively common during this study. Two lengthy cold spells occurred, one in 1986 and the other in 1989, where temperatures dropped below 45 PO. Aerial insects during these 140 periods were non-existent. Severe weather events caus- ing high mortality rates in nestlings and adults have been reported several times (see review in Zach 1982). Thus, the unpredictability of daily food supply of the tree swallow tied to the unpredictability of daily weather events. Lack also suggested that birds with longer nes- tling periods should be at a greater risk of facing food limitations sometime during the nestling period. The average nestling period for tree swallows has been reported to be 18 days to 22 days (Low 1936, Bent 1942, Kuerzi 1941, Quinney gt al; 1986). I did not follow nests closely enough to determine the length of each nestling's stay in the nest because disturbing nes- tlings after 18 DPH causes pre-mature fledging (Quinney 1983b). The average nestling period for most ground nesting birds is 13.2 days (Lack 1948). For cavity nesting birds, the average nestling period is 30-50% longer. Ground nesting birds probably have shorter nestling periods because of heavy predation (Lack 1948, Nice 1954). However, the long nestling period of tree swallows may be necessary because they are aerial insectivores and they will require good flight feathers and functional flight capabilities when they leave the nest. The prerequisite of long nestling periods for 141 brood reduction to be favorable has not received much attention in the literature. It is quite possible, though, that this is not a necessary prerequisite. Birds that have short nestling periods could be even more apt to require brood reduction. For example, a one day food crash might not effect a slow growing species such as the tree swallow but may necessitate brood reduction in a faster growing species. Thus, the condition requiring brood reduction might be the length of food limitation relative to the length of the nes- tling period. Another, but yet neglected condition of the brood reduction hypothesis is that the reproductive perform- ance of parents must depend upon food levels. Quinney (1983b) and Quinney gt git (1986) have shown that clutch sizes of the tree swallow correlate with the insect abundances occurring during the egg laying period. Growth rates and the age of primary eruption of nestlings has also been found to correlate with the average insect abundances during the nestling period (Quinney 1983b, Quinney gt glt 1986). I have also found a correlation between daily insect abundance and the maximum weight that nestlings attained and the age of yolk depletion. Body growth rates and primary growth rates were also faster in years of more food. In 142 addition, age of developmental events occurred earlier and primaries erupted earlier when food was more abun- dant. Furthermore, I found a slightly significant correlation between the daily body mass of adults and the daily insect abundance. There was also a signifi- cant correlation between the dry weights of the insects caught in the Manitoba trap and linear nestling growth rate. The amount of food brought and the number of food boluses brought to the nest, per feeding session, was however, inconsistent with food abundances affecting parental performance. Parents brought more food and in more food boluses when food was less abundant compared to when food was more abundant. However, there are two lines of evidence to suggest that parental performance was curtailed at my study site because of low insect abundances. First, Wiggins (1990), in a study on the tree swallow in British Columbia, found that parents made between 4-5 trips to the nest per 20 minutes. Quinney (1986) also found that tree swallows at an insect rich site made 4-5 trips/20 minutes to the nest. Both figures are well above the 1-2 trips/20 minutes that I recorded during my study. Second, Quinney (1986) reported that broods received about an average of 760 mg of wet weight of insects in a twenty minute period. If insects are 90% water, then parents 143 delivered 3-4 times as much food as parents during my study. Thus, in comparison to other studies, the amount of food brought to the nest appears to be food dependent. Lack also stated that another condition for brood reduction is that parents should only occasionally be able to raise their entire brood. Brood reduction should be necessary a majority of the time. I found that tree swallow parents rarely raised all five nes- tlings. Nestling mortality during this study was variable; the highest was 43% in 1989 and lowest was 15% in 1986. These figures are within the ranges reported by researchers who conducted studies at other localities. Kuerzi (1941) reported a mortality rate of 18.5% and 27.5% in two different years of his study, the later of which he considered high. Quinney (1983) reported fledging success rates of 88% and Low (1933) reported variable fledging success rates, with mortali- ty varying between 19-53% of nestlings. However, parents should also be able to raise their entire brood in some years. If parents cannot, then natural selec- tion should favor laying smaller clutch sizes. The results of De Steven (1980), though, do suggest that there are some years where conditions are favorable for rearing large broods. She reported fledging success that was nearly 100% in five and six nestling broods. 144 Fledging success was even in excess of 90% in broods enlarged to 9 nestlings. Thus it appears that tree swallow parents require brood reduction because they rarely raise all nestlings in their broods, however, natural selection will not favor smaller clutch sizes because they may be able to raise a large sized brood during some years. In summary, the first condition for brood reduc- tion to occur, namely, unpredictable food resources, applies to the prey items of the tree swallow. The second condition of long nestling periods also applies but its necessity is questionable. Third, it has been shown elsewhere, and here, that food levels affect the reproductive performance of tree swallows. Only the amount of food brought to the nest was inconsistent with this third prerequisite for brood reduction, although, compared to other studies conducted under more favorable food conditions, parents appeared to be restricted in bringing more food to the nest because of the reduced food levels during my study. Lastly, I have argued that parents most often cannot raise their entire brood and most broods need to be reduced. Additionally, there is some evidence to suggest that parents can raise their entire broods during some years, thus selection will not favor smaller brood sizes over laying large broods and using brood reduction. 145 3. Mechanisms of Brood Reduction The brood reduction hypothesis states that brood reduction should occur when food is limited. The weight hierarchy within the brood should allow the largest nestling to acquire food until it is satiated; the next largest should win the next series of feeding bouts until it is satiated; and then so on, down the weight hierarchy (Ricklefs 1965). When food is in short supply, parents will need additional time between foraging trips to collect enough food to bring back to the nest. If this time is sufficiently long, then time will pass where the largest nestlings will become hungry before the last-hatched nestling gets fed. Thus, the last-hatched nestling eventual starves during a food limited period. A necessary condition for this mechanism is that hatching asynchrony should establish substantial competitive feeding hierarchies so that the last-hatched nestling gets fed only if its nestmates are satiated. Also according to the brood reduction hypothesis, natural selection should select against synchronous hatching because these broods lack weight and age hierarchies. Thus, partial brood loss is not an option and instead, the entire brood may starve when food is limited. I have found that, when food is limited, the 146 incidence of partial brood loss increases with increas- ing hatching asynchrony (Figure 14). Relative survival decreased with decreasing hatch position with the youngest nestlings' relative survival always less than 100%. Those nestlings that died in these nests were the youngest nestlings. Thus, when food was scarce, part of the brood died and those dying were the youngest chicks in the brood. Because the last-hatched nestling in DOUBLE ASYNCHRONOUS broods died, the first-hatched nestlings had a high fledging rate. This caused the DOUBLE ASYNCHRONOUS broods to have the highest fledging success of all hatching treatments when food was limit- ed. The feeding bout observations revealed that when food is limited, the last-hatched nestlings are not fed (Figure 36). The 'C' chick in DOUBLE ASYNCHRONOUS broods received less than 8% of the food brought to the nest during the LESS FOOD years. Thus, its death is due to starvation. This starvation was also quick, as reflected in the early deaths of later-hatched nes- tlings. Earlier ages of yolk depletion by 'C' chicks in DOUBLE ASYNCHRONOUS broods when food was scarce also suggests that these nestlings needed to draw upon food reserves more often than their older nestmates. Also consistent with the brood reduction hypothe- sis is my finding that entire brood loss increases with 147 increasing hatching synchrony. Entire brood starvation occurred only during the LESS FOOD years. Weight hierarchies did appear to result in SYNCHRONOUS broods but not to the degree that weight hierarchies existed in either of the asynchronous hatching treatments. Furthermore, the weight hierarchies did not create feeding hierarchies. Nestlings were fed at random, with respect to their weight ranking, when food was less abundant. Nestlings in DOUBLE ASYNCHRONOUS broods were also fed at random with 'B' chicks receiving as much food as the 'A' chicks. Thus it appears that entire brood starvation occurred in SYNCHRONOUS and SINGLE ASYNCHRONOUS broods because parents did not single out a nestling to starve. Possibly, the feeding hierarchy was not as well established in SINGLE ASYNCHRONOUS broods as they were in DOUBLE ASYNCHRONOUS broods to produce a quick starvation of one nestling. It is probable that the last-hatched nestling did not get fed because of its small size. Hatching asyn- chrony contributed toward the last-hatched nestling always being the smallest because it was found in this weight ranking the most often. In addition to the disparity of weight among nestlings, the older nes- tlings may have the added advantage of a day or two advance in development of eyes to help locate parents 148 and to increase their food intake. Moreover, this disparity in eyesight development was increased because the eyes of younger nestlings opened at a significantly later age. One of the more interesting findings of this study is that, when food was more plentiful, the last- hatched nestling received a majority of the food (Figure 36). It is possible that when food is abun- dant, parents might preferentially feed the younger nestling in an attempt to counteract the weight hierarchy established by hatching asynchrony. It is difficult to explain why these nestlings that were fed the most food eventually died. One possible explana- tion is that I monitored feedings for only one of the MORE FOOD years, 1987. The first two weeks of this year produced the highest food levels observed during the entire study. Food levels then decreased during the last few weeks of the season. Thus, I may have meas- ured the parent's attempts to offset the weight hierarchies by preferentially feeding the last-hatched nestling, but food levels soon afterward may have become so scarce that brood reduction may have been re quired. This food year for some parents may have been a low food year for those raising nestlings toward the end of the nestling period. There have been several studies that have shown 149 that nestling begging interactions differ according to food levels. Proctor (1975) and Evans and McMahon (1987) have shown that the intensity of sibling compe- tition increases with decreasing food levels. Mock gt a1; (1987) have suggested that nestlings, by monitoring their own nourishment level, can ”detect" low insect abundances. When food is in short supply, then inter- sibling competition is fierce which would lead to brood reduction. On the other hand, when food is adequate, then all nestlings are fed. This mechanism allows nestlings to be adequately fed when food is more plen- tiful to counteract the weight hierarchy established by hatching asynchrony, but when food is scarce, sibling competition for food can elicit brood reduction. Two of my results, however, appear to be incon- sistent with the brood reduction hypothesis. First, during the LESS FOOD years, partial brood loss did occur in SYNCHRONOUS broods when food was scarce. The slight weight hierarchies that developed in SYNCHRONOUS broods did not contribute toward a differential feeding of the broods when food was scarce. Thus the risk of raising a SYNCHRONOUS brood, entire brood loss, may at times be avoided, but how the partial brood loss oc- curred is uncertain. Second, during the MORE FOOD years, brood reduction did appear to occur in the 150 asynchronous broods almost to the same degree as it did in the LESS FOOD years. Partial brood loss occurred because 'B' and 'C' chicks died. Amundsen and Stokland (1988) suggest that the youngest nestlings in an asyn- chronous nest could die when food is plentiful if it gets buried by its larger siblings. This appears an unlikely cause of death in my study since these nes- tlings were fed more food than their older siblings. More research is needed to try to understand why these nestlings die when food does not appear to be limiting. In the tree swallow, therefore, most data sug- gests that hatching asynchrony facilitates brood reduc- tion when food is limited. The last-hatched nestlings of DOUBLE ASYNCHRONOUS broods receive less food when food is less abundant. In addition, SYNCHRONOUS broods experienced the most entire brood starvation, as pre- dicted by the brood reduction hypothesis. Entire brood starvation seemed to occur because parents fed nes- tlings at random. Starvation also occurred in SINGLE ASYNCHRONOUS broods because 'A' and 'B' chicks were fed with an equal frequency and equal amounts of food. However, partial brood loss rather than entire brood loss occurred in some SYNCHRONOUS broods. Thus the risks of SYNCHRONOUS hatching may be different from Lack's original hypothesis. Additionally, brood reduc- tion did appear to occur when food was more plentiful. 151 The reasons for these deaths is still unclear because these nestlings received the most food. More studies are needed on the begging behaviors of nestlings under different food conditions. 4. Reproductive Tactics Consistent with Brood Reduction I also examined whether other reproductive tac- tics of the tree swallow are consistent with brood reduction. Specifically, I determined if egg weights correlated with their laying sequence and whether survival-promoting tactics are employed previous to brood reduction. Survival-promoting tactics would be highly beneficial to parents if short-term food level fluctuations occur. I have found that the last-laid egg of a clutch is consistently heavier than the first-laid egg. As clutch sizes increase, the differences between the first and last egg also increase. My findings of egg weight variation in a clutch are, however, different from the findings of Zach (1982). He measured the width and length of eggs and calculated egg volumes and found that egg size decreased with laying order. It is quite possible, that both egg size and egg weights do change with laying order in the tree swallow; this would have the effect of changing egg density with laying order. If this is true, then tree swallow eggs 152 might be provisioned differently. Bryant (1978) has shown that the eggs in House Martin (pglighgn grbiga) clutch are provisioned differently with last-laid eggs containing more water. Clark and Wilson (1981) have argued that increas- ing egg size with laying order is inconsistent with the brood reduction hypothesis because the least amount of investment should be placed in the offspring with the least chance of fledging. Slagsvold g; a1; (1984) took this one step further and examined egg size patterns with laying order and found that many birds either increase or decrease egg size with laying order. He postulated that birds laying larger last eggs adopt a brood survival strategy; those laying a small final egg adopt a brood reductionist strategy. However, laying larger last-laid eggs may not be inconsistent with the brood reduction hypothesis (Magrath 1990). A larger last-laid egg may increase the fledging success of the last-hatched nestlings when food is plentiful and thus may compliment the brood reduction strategy (Howe 1978, Magrath 1990). Howe (1978) and DeSteven (1978) have also argued that weight variation at hatching due to egg size variation is oftentimes removed by unequal feeding of nestlings soon after hatching. It is also quite possible that egg size variation 153 with laying sequence may be selectively neutral with respect to a brood reduction strategy. Egg size may increase with laying order due to physiological tenden- cies during ovulation. Egg size variation may also be influenced by daily food abundances, and thus might occur because of an increase in daily food abundances during egg laying. Survival-promoting reproductive tactics do seem to occur prior to brood reduction. I estimated the condition of nestlings prior to and after brood reduc- tion in broods where 4 and 3 nestlings fledged. I compared the three different hatching treatments. Body weights of surviving nestlings were 1-2% below the normal weights prior to brood reduction. In SYNCHRONOUS broods, body weights of nestlings did not return to normal for several days after brood reduction. In SINGLE ASYNCHRONOUS broods, nestling weights returned to the normal weight on the day of brood reduction; in DOUBLE ASYNCHRONOUS broods, nestling weights returned to normal prior to brood reduction. Thus it appears that the surviving nestlings benefit most by a brood reduction sooner as hatching asynchrony increases. Weights of parents change prior to and after brood reduction. Parents seem to loose the most weight just prior to brood reduction. If weight loss reflects 154 parental investment (sensu Drent and Daan 1980), then parents tend to increase their expenditure to make up for low food levels. Brood reduction does, therefore, appear to be a last result. In summary, egg weights do increase with laying order. However, I argue that this does not necessarily conflict with the brood reduction hypothesis as sug- gested by some researchers. Survival promoting repro- ductive tactics do appear to occur in the tree swallow. I found that nestling weights are maintained below their average prior to brood reduction and parents also increase their investment. 5. The Adaptive Value of Brood Reduction The crux of the brood reduction hypothesis is that hatching asynchrony and brood reduction should be adaptive for parents. Williams (1966a) states that an adaptive trait should increase a parent's lifetime reproductive success compared to an alternative trait. Unfortunately, it is difficult to monitor the reproduc- tive productivity of vertebrate parents over their entire lifespan. Alternatively, ecologists have sought to examine an adaptation at its proximate level and attempt to measure the effects of the adaptation in any one of several short-term effects (in sensu Williams 1966b). I propose that hatching asynchrony and brood reduction is adaptive for tree swallows because it 155 increases lifetime production of offspring by either increasing annual productivity or increasing annual survival of parents. Below, I present four possible adaptive scenarios. a.m2nimwmnmdr_edueti2nm MMLL—s chonousnetgnimghenmmgm are Egg; frequent; During the LESS FOOD years, fledging success increased with increasing hatching asynchrony. This increased fledging success appears to result from brood reduction. The last-hatched nestling is starved allowing the first hatched nestling to fledge. More- over, a high percentage of SYNCHRONOUS nests experi- enced entire brood loss. These two mortality patterns allowed parents raising DOUBLE ASYNCHRONOUS broods to fledge the most young when food was in short supply. Thus, it appears that DOUBLE ASYNCHRONOUS broods are the most productive during years of scarce food. On the other hand, asynchronous hatching seems to be maladaptive when food is more plentiful. During the MORE FOOD years, fledging success decreased with in- creasing hatching asynchrony. Deaths in asynchronous broods appeared to be due to the weight or age hierarchy established by hatching asynchrony. Greater productivity of synchronous broods during more favora- ble food and greater productivity of asynchronous 156 broods when food is scarce is consistent with the findings of other studies that have manipulated broods to establish different hatching treatments under dif- ferent food conditions. Magrath's (1989) study on the Fieldfare (Igrggg pglarig) found that hatching asyn- chrony produced more nestlings that lived two weeks past fledging when food was limited. On plots where food was supplemented, broods adjusted for synchronous hatching produced more offspring surviving to two weeks postfledging. Skagen (1988), in a study on the Zebra Finch (Eoephila guttata), found that nestlings from asynchronous broods fledged at lower weights than fledglings from broods adjusted for synchronous hatch- ing. Amundsen and Stokland (1988) have argued that brood reduction during food plentiful conditions is maladaptive. Magrath (1989) has suggested that, if hatching asynchrony carries a cost when food is plentiful, then natural selection will favor hatching asynchrony and brood reduction over hatching synchrony when poor food years are most common. Lack (1954) suggested that for hatching asynchrony and brood reduction to be adaptive, parents must be subjected to more years of scarce food than plentiful food. I present a quantitative model of how the frequency of good and bad food years selects for hatching patterns in Chapter 4. 157 This frequent bad year adaptive scenario would also explain why there is a lot of variation in hatch- ing spreads within a clutch size. If good years oc- curred most frequently for a short time period, this would favor hatching synchrony and a hatching synchrony gene would be maintained in the population. Alterna- tively, a series of bad food years would help maintain an asynchronous hatching gene. Thus, this adaptive scenario could explain how a polymorphic population could exist and be a result of fluctuating natural selection. b. Hetching asynchrony increases geemee;ie mega figness, There have been several suggestions that natural selection may select for reduced variance in offspring number per year as well as the average in offspring production (Gillespie 1974, 1977). Clearly, SYNCHRONOUS broods are at a greater risk of having higher variances in offspring number than asynchronous broods. It has been suggested (e.g. Lacey e; ele 1980, Cooper and Kaplan 1982) that rather than comparing the arithmetic means of reproductive success of various traits, a researcher should instead compare the geomet- ric means of reproductive success. I calculated geo- metric means for the productivity of broods for all four years for each hatching treatment; these are shown 158 in Figure 40. This comparison shows that, for all four years, the geometric mean of fledging success for the DOUBLE ASYNCHRONOUS broods is 10% greater than the geometric means of fledging success for the other two hatching treatments. The importance of variation in reproductive success of different hatching patterns may be over- looked. Several studies have reported that broods adjusted for synchronous hatching are more productive than the normal asynchronously hatched clutch (see Amundsen and Stokland 1988 for review) but did not compare variances in their hatching treatments. Two studies presented data to allow variances to be com- pared. Bryant and Tatner (1990) found that, in the white-bellied swiftlet (Qelleeelie eeeeleQEQ), fledging success in synchronous broods was 1.19 nestlings per two nestling broods while fledging success in asynchro- nous broods was 0.86 nestlings/2 nestling broods. However, fledging success for synchronous broods was more variable than for asynchronous broods. Using data from their Table 4, I found that using a geometric mean reduced these fledging success differences by more than 10%. However, even with variances incorporated, syn- chronous broods were still more productive than asyn- chronous broods. Haydock and Ligon (1986) reported 159 FLEDGING SUCCESS (GEOMETRIC MEAN) no I SYNCH SINGLE DOUBLE HATCHING TREATMENTS FIGURE 40. Geometric means of fledging success for all four years, by hatching treatment. 160 that broods of the Chihuahuan Raven (geryee erypteleg; gee) adjusted for synchronous hatching also fledged more nestlings than asynchronous broods. Their data also show that the range of fledging success values for synchronous broods was more than double compared to fledging success values for asynchronous broods. Thus, in both studies, synchronous broods experienced a higher variance in reproductive success. A geometric mean fitness model has been used to explain why many birds lay fewer eggs than the most productive clutch in the population (Boyce and Perrins 1987). Boyce and Perrins (1987) have suggested that natural selection favors smaller clutch sizes than the most productive clutch size because parents laying large clutches experience high variance from year to year when good, moderate and bad food years occur. Their geometric mean fitness model adequately predicted the mean clutch size in the population when annual variance in reproductive success was introduced. In conclusion, the high variation in fledging success by broods hatched synchronously may lower a parent's fitness. More researchers should calculate a geometric mean for reproductive measures that influence fitness. c- L4H chin M51131! n M110 mammal; l1 traek the environmegt. Temme and Charnov (1987) have 161 suggested that hatching asynchrony and brood reduction can allow parents to temporally track a constantly changing environment and to reduce their brood when it becomes "evident" to parents that the current brood size cannot be successfully raised. Parents of syn- chronous broods do not have the option of quickly reducing the brood because no feeding hierarchy exists in the brood. I have found that prior to brood reduction, nestling weights are decreased below an average weight for their age. It appears that a maximum of a 2% nestling weight loss from the average occurs, after which brood reduction is then carried out. Hatching asynchrony may be adaptive because it may allow parents to reduce the brood quickly once a certain limit is reached after survival-promoting tactics, such as maintaining nestling weights below the average, are used. If, however, food levels return to ample levels, then parents might find enough food to raise the entire brood. The switch between survival-promoting and brood reduction tactics would benefit parents that prey on food levels that change on a daily basis. This is certainly applicable for tree swallows. If survival-promoting tactics prior to brood reduction are favored by natural selection, then 162 mechanisms that allows parents to monitor how close nes- tlings are to a critical weight loss from the average. Hussell (1988) has suggested that parents adaptively monitor the hunger level of the brood using the brood's overall begging intensity. I propose that parents might be able to use hunger levels to determine how close the brood is to a critical lower weight reduction. Once the brood reaches this hunger level, brood reduction is initiated. In summary, it appear that asynchronous hatching might allow tree swallow parents to track an environ- ment that is changing daily and allows them to initiate brood reduction once a certain brood hunger level is reached. I suggest that parents might be able to moni- tor the how close nestlings are to a critical weight reduction by monitoring the average hunger level of the brood. gr Hatching asynchrgny reduces perenrei inveer- men; ghee feeg ie iimited. Parents that invest the least amount of energy into their offspring can expect to live longer lives and hence produce more offspring in their lifetime (Williams 1966a, Drent and Daan 1980). I have found some evidence to suggest that parents raising asynchronous broods during food scarce years invest less in the offspring that they raise. Over the course of the nestlings period, DOUBLE 163 ASYNCHRONOUS parents invested slightly less energy into nestlings that eventually died. Their chicks, espe- cially their 'C' chicks, died sooner than nestlings in either of the two nests. Furthermore, parents of asynchronous broods gained weight during the nestling period while parents raising SYNCHRONOUS broods lost weight. Having a heavy weight at the end of the nes- tling period may be more important for tree swallows than for other passerines because tree swallows begin their southward migration one to two weeks after the nestlings have fledged (Butler 1988). Asynchronous parents during LESS FOOD years also were able to bring more food to the nest. There have been few studies that have investigat- ed parental investment with respect to hatching asyn- chrony. Gibbons (1987) found that Jackdaw (geryge menegie) parents of asynchronous broods invested less in reproduction compared to broods adjusted for syn- chronous hatching because nestlings in asynchronous broods died earlier. Fujioka (1985b) found that, in the Cattle Egret (Bubuiegs ihié), parents raising asynchronous broods made fewer trips to the nest than parents raising even-aged broods. This reduced paren- tal investment in asynchronous nests was attributed to reduced nestling demands. Broods adjusted for 164 synchronous hatching exhibited more frequent sibling aggression. Thus, hatching asynchrony reduces sibling aggression that is spurred by a lack of a feeding hierarchy established by hatching asynchrony. I did, however, obtain one result that is incon- sistent with the scenario that brood reduction reduces parental investment. I found that parents of DOUBLE ASYNCHRONOUS broods experienced the greatest reduction in their body weights compared to parents raising either of the two hatching treatments. Coming closer to a maximum weight loss suggests that these parents may have placed themselves at a greater risk of dying than the other two groups of parents (in sensu Drent and Daan 1980). In summary, I argue that hatching asynchrony and brood reduction can reduce parental investment. This would have the benefit of increasing a parent's chances of surviving to reproduce again. This in turn would increase the number of offspring a parent could produce in a lifetime. I explore the ramifications of introduc- ing effects of hatching asynchrony on parental survival in chapter 4. 165 IV. Conclusions I manipulated broods of the tree swallow to establish three different hatching patterns, hatching synchrony and two degrees of hatching asynchrony, to determine if the brood reduction hypothesis is an adequate explanation for hatching asynchrony in tree swallows. I measured the reproductive performable of parents raising these three broods during MORE and LESS food years. I found that brood reduction mechanisms do exist during years of less food. Nestlings in inferior hatch positions are not fed and they eventually starve. I also found that survival-promoting tactics occur prior to brood reduction in effect complimenting brood reduction. These same mechanic may be responsible for its adaptive value because parents might be able to track a temporally varying environment. Three other adaptive scenarios are also presented. I propose that hatching asynchrony and brood reduction are adaptive for parents if bad food years occur more frequently than good food years, that hatching asynchrony and brood reduction increase parental fitness because they reduce variation in reproductive success and finally that hatching asynchrony may reduce parental investment because nestlings die earlier in asynchronous broods. CHAPTER 3 A REVISION OF LACK'S BROOD REDUCTION HYPOTHESIS USING A GAME THEORY MODEL I. INTRODUCTION In many altricial birds, incubation commences prior to the laying of the last egg of the clutch (Clark and Wilson 1981). This behavior produces 'hatching asynchrony', which results in broods where some nestlings hatch a day or more later than others, so that nestlings differ in ages and weights. The most cited adaptive explanation for the occurrence of hatching asynchrony is the one proposed by David Lack (1947, 1948 and 1954) called the brood reduction hypothesis. According to Lack, hatching asynchrony could be adaptive if it produced a competitive feeding hierarchy within a brood. If food becomes scarce, the youngest nestlings starve because the oldest and strongest nestlings receive the food brought to the nest by their parents. Hatching asynchrony increases a parentis lifetime productivity because large clutch sizes can be quickly reduced when food is scarce. When food is plentiful, the entire large-sized brood is raised. On the other 166 167 hand, Lack assumed that if the same large-sized brood is hatched synchronously when food is scarce, every nestling will be effected by food shortages and all nestlings might starve. Lack thought that hatching asynchrony would be beneficial for parents which cannot predict, at the time of egg laying, food levels for the upcoming nestling period. Most support for the brood reduction hypothesis is indirect. It has been reported that the last-hatched nestling grows more slowly and dies more frequently than its siblings (e.g. Mishaga 1974, Bryant 1978, Zach 1982, Bechard 1983, and Greig-Smith 1985 and others); that the last-hatched nestling receives smaller amounts of food than its siblings (e.g Groves 1984, Horsfall 1984, Fujioka 1985b, and Forbes and Ankney 1987); that larger clutches experience more partial brood starvation (e.g. Howe 1976, Skagen 1988) and that hatching asynchrony tends to increase in degree among those birds nesting late in the season (e.g. Murphy and Fleischer 1986, Slagsvold 1986). In the latter case, the degree of hatching asynchrony is increased because it is thought that food becomes more unpredictable as the season progresses. There have been, however, several major criticisms of the brood reduction hypothesis. Several researchers (e.g. Clark and Wilson 1981, Slagsvold er 168 elr 1984) have argued that the common occurrence of increasing egg size with laying order among species hatching broods asynchronously is inconsistent with the brood reduction hypothesis. They argue that the least investment in egg size, not the most, should be placed in the nestling having the least chance of survival. The brood reduction hypothesis has also been criticized on the grounds that hatching asynchrony may not be required to facilitate brood reduction (Clark and Wilson 1981). Clark and Wilson's (1981) literature review showed that, at least for several species of birds, the number of young starving was often greater than the number of nestlings set at a competitive disadvantage with hatching asynchrony. In addition, partial brood starvation can occur as frequently in synchronously hatched broods as it does among asyn- chronously hatched broods (e.g. Howe 1978). Thus, factors other than hatching asynchrony may facilitate nestling starvation when food is scarce. Amundsen and Stokland (1988) have argued that hatching asynchrony can result in brood reduction even when food is plentiful. They reviewed several experimental studies and showed that when food is plentiful, naturally hatched asynchronous nests are, on average, less productive than nests that are adjusted to 169 simulate synchronous hatching. They concluded that the brood reduction hypothesis cannot adequately explanation the adaptive significance of hatching asynchrony if last-hatched nestlings die when food is plentiful. Another criticism of the brood reduction hypothesis has been that, because it has been presented only verbally, the hypothesis is difficult to apply to field data. The hypothesis could be made more testable if it was quantitative rather than qualitative (Magrath, 1990). A quantitative hypothesis would also clarify the assumptions. Finally, the brood reduction hypothesis has not been widely accepted because alternative hypotheses have not been ruled out as plausible explanations. The most notable of these hypotheses are the "peak-demand reduction hypothesis" (Hussell 1972), the "predation hypothesis" (Hussell 1972), the "nest-failure hypothesis" (Clark and Wilson 1981), the "sibling rivalry reduction hypothesis" (Hahn 1981), the "nest- crowding hypothesis" (Slagsvold 1982) and the insurance hypotheses (see Magrath, in press, for a review). Unfortunately, very few studies have attempted to rigorously test any of these hypotheses. The aim of this chapter is to present a quantitative model of Lack's original brood reduction hypothesis using the game theory techniques of Lewontin 170 (1961). I show that, even if hatching asynchrony causes occasional brood reduction when food is plentiful, hatching asynchrony can be adaptive because the lifetime productivity of parents will be increased compared to hatching synchrony. I conclude with a presentation of the assumptions and predictions of this brood reduction model. II. THE MODEL Lewontin (1961) was the first to suggest that the game theory technique of the social sciences could be a useful tool for evolutionary biologists. Lewontin developed several different types of models. Here, I shall follow the theoretic he labeled as 'states of nature' games. These games allow evolutionary biologists to compare two or more different phenotypes that exist in environments that are characterized by the alternation of some qualitative trait, such as wet and dry or good and bad seasons. Suppose years exist either as 'good' or 'bad' depending upon the level of food. Each type of year represents a different 'state of nature'. A good food year is one in which, if any nestling mortality occurs, it is not caused by a lack of available food in the environment. A bad food year, on the other hand, is one in which poor food levels in the environment cause 171 nestling mortality. Let there be two or more alternative strategies that 'play' against these states of nature. Allow one strategy to consist of synchronous hatching. The parents' payoff is the recruitment of the entire brood of size 'B' into the next generation during good years because no nestling is set at a competitive disadvantage. In keeping with the brood reduction hypothesis, in a bad year, let all nestlings be equally affected by reduced food levels. As a result, each nestling will have a reduced chance of surviving until its reproductive age (hereafter, simply as 'nestling survival') compared to its chances in a good year. Let the expected nestling survival of synchronous hatching be denoted as 's', a value that should always be less than 1.0. The payoff for hatching young synchronously in a bad food year then becomes 's*B'. Consider the alternative strategy to be represented by parents hatching one nestling a day after all of the rest. During a good year, these parents expect to recruit all of their first-hatched nestlings, which number 'B-1', into the next generation. However, suppose that the last-hatched nestling has a reduced probability of surviving until its reproductive age because of the competitive feeding hierarchy established by hatching asynchrony. Let the probability of the 172 last-hatched nestling surviving until its reproductive age be 'q'. The payoff for these parents in good years becomes 'B-1+q'. In a bad year, asynchronously hatched broods are reduced by starving the last-hatched nestling; the remaining nestlings, however, survive to reproductive age. Figure 41 shows the payoff matrix of these two hatching strategies in good and bad food years. Now, let us suppose that good food years occur randomly, and with a certain frequency, 'j'. From the payoff matrix in Figure 41, the expected number of nestlings from synchronously hatched broods surviving until their reproductive age, per year, is: E(Ps) = 1*8 + (1'1) * (8*3) (1) and for parents that are raising a brood in which one nestling hatches a day later than its siblings: E(Pa) = 1* (8'1 + C1) + (1-3') * (3'1)- (2) Hereafter, equation (2) will be simplified by allowing R = 'B - 1 + q'. Lack predicted that brood reduction and hatching asynchrony should increase lifetime productivity because parents can lay large clutches. Ricklefs (1977) has shown that nestling survival rates decrease exponentially as the brood size increases. Following 173 FIGURE 41. Payoff matrix for two alternative hatching strategies generated by the game theory model. 174 H¢ mmDUHh T m f H . m mvwm m mfl noon Lo @5391 ad No ed md Yo md Nd fio ad mmI mé 182 FIGURE 44 Productivity of hatching asynchrony and hatching synchrony versus brood size. Parameter values are 'B'=5, 'a'=0.2, 's'=0.7, 'q'=0.7 and 'c'=1.0. 183 m F «v mmaon mum 805 m m a _ 33:88.1 184 The HPR values for different 's' and 'q' values, when all other variables are held constant, are shown in Figure 45a. The model is consistent with the intuitive notion that hatching asynchrony is favored over hatching synchrony when 'q' is high, and when '8' is low. Also note that 's' has a greater effect than 'q' on HPR values because 's' affects an entire brood while 'q' affects only one nestling. However, as 'q' approaches zero, then parents of asynchronously hatched broods will essentially be pro- ducing 'B-1' offspring in good and bad food years. Figure 45b shows that in some instances, a synchronously hatched brood of size 'B-1' may be a better strategy to employ than either a synchronously hatched brood of size 'B' or an asynchronously hatched brood of size 'B'. I used the productivity ratio of synchronously hatched broods of size 'B-1' to asynchronously hatched broods of size 'B' to represent the reduced brood size edvan- tage (RBA). When 'q' is very low, it is more favorable for parents to begin with a small ('B-1'), synchronously hatched brood. When 'q' is near 1.0, however, a large ('B'), asynchronously hatched brood is more productive than a synchronously hatched brood of either 'B-1' or 'B', as represented by HPR values greater than 1.0 and RBA values less than 1.0. When 'q' values are 185 FIGURE 45 HPR values (A) as a function of 'q' and 's' with parameter values of 'B'=5, 'a'=0.2 and 'c'=1.0 (for 's' iterations, 'q'=0.7 and for 'q' iterations, 's'=0.7); and (B) as a function of 'q' for brood sizes of 'B' and 'B-1', where RBA denotes the reduced brood size advantage, see text for details; (C) as a func- tion of 'a' and 'c'. 185A HPR 1.0 (A) 1.7 — 1.6 - 1.5 - 1.4 - 1.3 - 1.2 ' 1.1 i- 0.10 020 030 0.40 0.50 0.50 0.70 0.00 0.90 1.00 'q' or '3' values 2 HPROIRBA 1. (B) 0.8 1 . 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 .0 HPR FIGURE 45 186 intermediate, the better strategy is for parents to lay large broods, hatched synchronously. Figure 45c shows the effect of the brood size dependent mortality constant, 'a', and the bad years effect constant, 'c', on HPR values. When the effects of 'c' are excluded (i.e. 'c'=1.0), and 'a' is increased (i.e. as a larger brood becomes more difficult to raise), HPR values increase as well. This is because, when 'a' is large, there is a large difference in the ability to raise an asynchronously hatched brood of size 'B' compared to raising the reduced brood of size 'B-1'; as a result, brood reduction is beneficial. Interestingly, when had years are severe (i.e. when 'c' > 1.0), hatching synchrony is favored over hatching asynchrony. This is because, as 'c' increases, nestlings raised in good years eventually make up a greater proportion of lifetime productivity; this proportion also increases with increasing values of 'c' (Table 8). Hatching synchrony is favored over hatching asynchrony because hatching synchrony is more productive during good food years. The values of 'Tj', as a function of 'q' and 's', are provided in Figure 46a. When 'q' is high and 's' is low, the frequency of good years may be very high and still favor hatching asynchrony over hatching synchrony. 187 Table 8. The expected yearly reproductive success of parents hatching nestlings synchronously and asynchronous in good and bad food years. The ratio presented represents the proportion of lifetime reproductive success that is gained during good food years calculated as (good food years)/(good + bad food years). SYNCHRONOUS BROODS ASYNCHRONOUS BROODS 'c' good bad ratio good bad ratio 1.0 1.839 1.472 0.5556 1.766 1.797 0.4956 1.2 1.839 1.205 0.6042 1.766 1.532 0.5355 1.4 1.839 0.986 0.6509 1.766 1.305 0.5750 1.6 1.839 0.808 0.6949 1.766 1.112 0.6136 1.8 1.839 0.661 0.7356 1.766 0.948 0.6507 * The parameter values are 'B'=5, 'a'=0.1, 'q'=0.8 and 's'=008'. For example, when '5' is 0.8 and 'q' is 0.8, then T- is 3 0.815 (when all other variables are held constant). All environments that have good years with a frequency of 0.815 or less will favor hatching asynchrony over hatching synchrony. 188 This graph also shows that Tj values immediately become zero after a large '8' value. In the model, when '3' becomes greater than '(B-1)/B', then hatching synchrony becomes more productive than hatching asynchrony during bad food years as well as during good food years. For Figure 46a, synchronous hatching becomes more productive than asynchronous hatching when the 's' value is more than 4/5 or 0.80. In such cases then, brood reduction via hatching asynchrony will not be favored over hatching synchrony, according to the brood reduction hypothesis. The value of T- as a function of the brood size 3, dependent mortality, 'a', and the bad years effect constant, 'c', is shown in Figure 46b. As 'a' increases, when the effects of 'c' are excluded, hatching asynchrony is increasingly favored in environments with frequent good food years. This is because the cost to asynchronously hatched broods during a good food year is comparably less than costs to synchronously hatched broods during a bad food year, and hence, good years can be frequent. However, when 'c' increases, the range of environment types favoring hatching asynchrony over hatching synchrony is reduced. The benefits of a brood reduction strategy during a bad food year becomes reduced because larger values of 'c' reflect lower proportions of nestlings produced during 189 FIGURE 46 Tj values (A) as a function of 'a' and 'c' (upper solid line, c=1.0; dotted line, c=1.5; bold line, c=2.0. (B) as a function of 'q' (increasing with increasing abscis— sa values) and 's' (descreasing with increasing abscissa values) with parameter values of 'B'=5, 'a'=0.2 and 'c'=1.0 (for 's' iterations, 'q'=0.7 and for 'q' itera- tions, 's'=0.7). T1 1 190 '0. 0.8 0.8 0.2 k ._.-.oo-o--¢ooo . 1 l l i T1 0.4 0.5 0.8 ’a' Value. 0.7 0.8 0.9 1.0 0.2' 0.3 l l l T l 0.4 0.5 0:0 'a' or ’q’ Values FIGURE 46 0.7 1.0 191 FIGURE 47 Expected productivities of hatching synchrony (A) and asynchrony (B). Given are good food year (...), bad food year ( ), and the mean (- - -) productivities between both year types. 193 Productivity 2 I 7 / / I ‘ \ \ \ \ / \ / / \ \ \ 15- ’ \\\ / \ / ................... \ \ / \ / \ \ / \ \ / \ \ \ 1 _ // \ ‘1 /f / /.- /f' .. /.-’ 0 l I 1 l I l 1 l I 1 1 055 o l l l l L l L I L l 2 3 4 5 6 7 a 9 10 11 12 13 Brood Size FIGURE 47 193 had food years compared to good food years. The expected productivities of hatching synchrony and asynchrony, in good years and bad years, as a function of brood size, are shown in Figures 47a and 47b, respectively. A comparison of these two figures shows that the number of young fledged is more variable between good and bad years for broods hatched synchronously compared to those hatched asynchronously. In other words, hatching asynchrony tends to yield a more stable number of young surviving until their reproductive age when two types of years occur. IV. DISCUSSION A. Introduction Amundsen and Stokland's (1988) review of several experimental studies on various species showed that, during good food years, survival rates of last-hatched nestlings of asynchronously hatched broods were lower than their siblings and nestlings in nests simulated for synchronous hatching. These researchers argued that if brood reduction occurs as a result of hatching asynchrony when food is plentiful, then the brood reduction hypothesis cannot be viewed as an adaptive explanation. I constructed this model to examine whether introducing a risk of the last-hatched nestling 194 dying as a result of asynchronous hatching, even when food is plentiful, is less favorable than hatching synchrony. I have shown that brood reduction and hatching asynchrony can be adaptive because hatching asynchrony can increase a parent's lifetime productivity over hatching synchrony. Allowing the last-hatched nestling to have lower survival rates compared to siblings and nestlings of synchronously hatched broods during plentiful food years, may at first seem counter-intuitive. However, there are several factors that may contribute toward the death of the last-hatched nestling when food levels are good. First, Amundsen and Stokland (1988) suggested that the last-hatched nestling, because of the feeding hierarchy established by hatching asynchrony, may become malnourished and starve. This is feasible if parents regulate their feeding rate to the begging intensity of the entire brood (von Haartman 1953, Hussell 1988). When only one or two nestlings of large broods beg, parents tend to devote time instead rather than feeding the begging nestlings. If the last-hatched nestling is consistently fed last, then its lone begging may not be effective to elicit a feed. Starvation ensues, therefore, because the food brought to the nest is limited rather than by food limitations in the environment. 195 Second, the last-hatched nestling may die during a good food year as a result of intense sibling rivalry established by hatching asynchrony. Mock (1984, 1987) and Fujioka (1985a), have shown that last-hatched nestling ardeids commonly die from physical attacks by their older and larger siblings. There is some evidence that last-hatched nestlings may die from physical attacks made by older siblings in other birds as well (Bryant and Tatner 1990). Third, parents raising asynchronously hatched broods may also experience difficulties feeding nestlings differing in development states. For example, if the youngest nestling must be forced fed, as are most altricial hatchlings (Ryden and Bengtsson 1980, Bengts- son and Ryden 1981, 1983), and the older nestlings are fed based on their begging activity, then parents may preferentially feed the older nestlings. Thus, during transitional developmental periods, older nestlings may grow faster at the expense of the younger nestling resulting in their starvation. Feeding asynchronously hatched broods may be less efficient then, than synchronously hatched broods when nestlings are at different ages (although, see Hahn 1981). Fourth, the last-hatched nestling may die more frequently than its siblings if parents preferentially 196 provide care for fledged nestlings after fledging (Clark and Wilson 1981). The last-hatched nestling may not receive enough care if it fledges a day later than its siblings or fledges at a premature age. Lastly, Slagsvold (1982, 1985, 1986) provided evidence showing that, in some species, the last-laid egg in less likely to hatch than first-laid eggs. He speculated that a lower hatchability is caused by inadequate incubation temperatures during hatching due to females being off the nest to forage for their first-hatched nestlings. Thus, costs of asynchronous hatching could even occur prior to the nestling period. Occasional brood reduction during good food years is a result of hatching asynchrony that needs further confirmation by field researchers. In particular, more studies are needed to understand the causes of death in last-hatched nestling. If asynchronously hatched nests are, however, more productive than synchronously hatched nests when food is good, then my present game theory model and its predictions do not apply. The frequency of good years would be selectively neutral to hatching asynchrony because hatching asynchrony would be favored over synchronous hatching in good and bad food years. 197 B. Model Specifications LW Many of the model's assumptions were made implicitly or explicitly by Lack or by researchers who have tested the hypothesis. Despite the large number of studies that have tested the brood reduction hypothesis (see review by Magrath, 1990), very few have attempted to examine whether Lack's assumptions hold. Here, I present arguments supporting the assumptions made in my model, show how some of the assumptions differ from those made by Lack, show where alternative assumptions can be made, and present ways that these assumptions may be tested. I also point out which assumptions need further confirmation by field researchers. A1. Annual food levels are either good or bad. I have assumed that yearly food levels can be classified into types. Recognizing only two types of years keeps the model simple, instructive and also follows from Lack's original hypothesis. Unfortunately, very few studies investigating the reproductive performance of birds have measured natural food levels over extended periods (e.g. Bryant 1978, Hussell and Quinney 1987), making it difficult to determine whether this assumption is realistic. _LJF‘L'_" 198 The simplest way to categorize whether a year is good or bad is to compute the sum of daily food levels and compare this annual total across years. However, short-term spurts or shortages of food, which may be hidden in a total annual food measure, may be more important in characterizing the nestling period as good or bad rather than a sum of daily food abundances. This may be important in species utilizing resources which are highly variable on a daily or even hourly basis (e.g. Bryant 1978 or Hussell and Quinney 1987) or in cases where there are critical periods affecting nestling survival (Hussell 1972). In addition, food levels can be difficult to measure, and, even when food is measurable, the data may be difficult to interpret because parents do not always feed on all items, or in proportion to the items in traps (Bryant 1975). One solution to the problem of classifying or measuring food levels is for researchers to examine mortality patterns, over several years, from asynchronously hatched nests and nests simulated for synchronous hatching. To be consistent with the present model, annual mortality patterns within each brood size should match the patterns predicted in Figure 41. Controlling food levels either by supplementing natural food (e.g. see Magrath 1989) or conducting experiments in the laboratory (e.g. see Skagen 1988) may 199 also solve the difficulties of measuring natural food levels. A2. Only two, heritable hatching strategies exist. Other degrees of hatching asynchrony are not possible alternative strategies within the present model. Clark and Wilson's (1981) review of the hatching asynchrony F literature showed that over 75% of altricial species hatch their clutches either synchronously or asynchronously with one nestling hatching a day later than the rest. If this review is representative of all a] altricial birds, then this model will apply to most altricial species. Implicit in the present model, as in all adaptive explanations, is the assumption that the adaptive trait has a heritability of 1.0 (Fisher 1930, Williams 1966b, Endler 1986). No studies have examined the heritability of hatching patterns. However, making the assumption that h2 = 1.0 keeps the model simple and the predictions more congruent. A3. Natural selection favors those parents employing hatching strategies that produce more offspring surviving to reproductive age than alternative hatching strategies. Lack assumed that natural selection favors reproductive tactics "corresponding with the greatest number of young for which the parents 200 can, on the average, find enough food". (Lack 1967, p. 22). To test this condition of the model, researchers should measure nestling survival to reproductive age. Unfortunately, most studies that have examined the brood reduction hypothesis have not followed nestlings past fledging (Magrath, 1990). The failure to record nestling mortality has been largely due to the difficulty in following nestlings that disperse from their natal grounds. Researchers have, instead, collected data on indirect measures of a nestling's chance of surviving to reproductive age, the most common being fledging mass (Magrath, 1990). Heavier nestlings at fledging have a greater chance of surviving until their reproductive age (Perrins 1965). However, this may not be a reliable measure for all species. If used, researchers should attempt to confirm its value for the study species by correlating fledgling return rates with fledging mass. The most convenient method to compare the reproductive value of alternative strategies is to manipulate nesting conditions and to establish alternative hatching pattern(s). This has been a popular method to test the brood reduction hypothesis (see Amundsen and Stokland 1988 for review). However, researchers should heed Magrath's (1990) advice and establish adequate controls for these experiments. I also assumed that hatching asynchrony has no 201 effect on parental survival. Williams (1966b) states that natural selection will favor traits that maximizes the lifetime production of offspring surviving until their reproductive age. I consider parental survival in the model presented in Chapter 4. A4. In had years, nestling mortality rates are greater in synchronously hatched broods than in asynchronously hatched broods. Lack's version of the brood reduction hypothesis assumes that, when food is scarce, the last-hatched nestling of an asynchronously hatched brood is starved, whereas for a synchronous brood, each nestling risks starvation which would result in an entire brood starving. Lack essentially assumed that feeding hierarchies, which would facilitate brood reduction, cannot be established in a synchronous brood. Clark and Wilson (1981) argued that Lack's assumptions for synchronously hatched broods rarely hold. They reported that in several synchronously hatched species, partial broods starved before entire broods starved. The game theory model that I have presented, though, can accommodate partial brood starvation in synchronous nests in bad years and still follow the spirit of the original brood reduction hypothesis. The variable '8', the survival rate for synchronously hatched broods, could represent the 202 proportion of an entire synchronous brood surviving until reproductive age rather than the equal probability that each nestling survives to reproductive age. Synchronous broods can thus be subjected to one of two forms of risk in this game theory model, entire brood starvation or partial brood starvation. For brood reduction to be favorable, risks associated with synchronous hatching in bad food years should be greater than losing the youngest nestling(s) to selective starvation in asynchronously hatched nests. Clark and Wilson (1981) also argued that, because weight hierarchies can result in broods that were initially adjusted for hatching synchrony, the mechanism set up for brood reduction, size hierarchies, can be established without hatching asynchrony. Several studies (see Magrath, 1990, for review) have since shown, however, that establishing weight hierarchies in broods adjusted for synchronous hatching is an inefficient way to facilitate brood reduction. In synchronously hatched broods where weight hierarchies have resulted, nestlings starved late in the nestling period; in asynchronously hatched broods, nestlings died soon after hatching. If parents of synchronously hatched broods invest energy and time into offspring that will eventually be starved, then they may unnecessarily reduce their own chances of surviving to breed again; a 203 condition that natural selection does not favor (in sensu, Williams 1966b). As. Parents cannot predict future food supplies. This model also assumes, as did Lack, that adults cannot forecast, at egg laying, food levels for the upcoming nestling period. If parents could make this assessment during egg laying, then they would adjust their clutch sizes to correspond to the maximum number of offspring they could raise during upcoming conditions. They would hatch their clutches synchronously because brood reduction would not be required. Many studies have not determined whether parents are able to predict future food levels (Magrath, in press). Qualitatively, however, the degree of predictability of food resources and the preponderance of asynchronous hatching seems to correlate well with latitude. Clark and Wilson (1981) showed that tropical species, which rely on scarce but predictable food (Ashmole 1965, Ricklefs 1980), hatch their clutches synchronously. On the other hand, food resources in temperate regions are much less predictable and birds hatch their clutches predominantly asynchronously (Clark and Wilson 1981). A6. Food levels are the sole ultimate factor affecting hatching patterns. I have assumed that no 204 factors other than food levels affect hatching patterns. Among these other factors are the dynamics of nestling growth (Hussell 1972) and the patterns of nest predation (Clark and Wilson 1981); factors suggested as important by alternative hypotheses. I have made this assumption to keep the model simple and testable; however, I believe that alternative hypotheses may also adequately explain the adaptive value of hatching asynchrony in altricial birds. Lfiredigtim Many of the predictions generated from this game theory model are similar to those made by Lack. Here, I present the predictions of this model, indicate how researchers may test these predictions, and show how to estimate values for the variables contained in this game theory model. P1. Hatching asynchrony and brood reduction are favored over synchronous hatching when 'q' is high, and 's' is low. I have shown that hatching asynchrony and brood reduction are favored when the survival of the last-hatched nestling to reproductive age, 'q', is high, and nestling survival in synchronously hatched broods, 's', is low. These two conditions will also produce a high Tj value. To determine if hatching asynchrony will be favored over hatching synchrony based upon the values of 205 's' and 'q', two methods can be employed if researchers only have fledging success data. First, a researcher may estimate values for 'q', or 's', and rely on these estimates to decide if hatching asynchrony is favored over synchronous hatching. This procedure may be necessary if a researcher has nestling mortality data for only one food condition. The value of 'q' and 's' can be estimated as follows. The fledging success of the last-hatched nestling in asynchronously hatched broods, Nlhn' will be a product of the survival rate due to hatching asynchrony and of brood size: N1hn = q * e-aB- (8) The survival rate of each first-hatched nestling will be a function only of brood size: thn = e’aB. (9) where Nlhn is the fledging success of the last-hatched nestlings of asynchronously hatched broods during good food years and thn is the fledging success of first- hatched nestlings of asynchronously hatched broods during good food years. Substituting (8) into (9) and rearranging gives: q = Nlhn/thn° (1°) An estimate of 's' can be obtained likewise. The survival rate of each nestling in synchronously hatched g (I ..__f,‘-.‘ 206 broods during a bad food year, Nsb' will be a product of the risk associated with raising a synchronously hatched brood and the survival rate due to brood size: N b = s * e"aB (11) s and the survival rate of each first hatched nestling in asynchronously hatched broods during a bad food year, Nab' is a function only of brood size: Nab = e‘a(B'1). (12) Substituting the left side of (11) into the brood size survival rate expression of (12) gives a conservative estimate of 's' after rearranging: S = NSb/Nab. (13) where Nsb is the fledging success of each nestling from broods simulated for synchronous hatching and Nab is the fledging success of each first-hatched nestling of asynchronously hatched broods. A second possible way to determine if hatching asynchrony is favored over synchronous hatching is to use fledging success of broods from good and bad food years to estimate Tj. Equations (5) and (6) may be rewritten as: w H s (I * F59) + (l-I) * Fsb (14) and w H a (j * Fag) + (l-j) * Fab (15) 1s! 207 where Fa is the fledging success of asynchronously 9 hatched broods in good food years, and F8 and Fsb are 9 the fledging success of synchronously hatched broods in good and bad food years, respectively. Tj is calculated, as before, by setting (14) equal to (15), and solving for 'j': T- = ----------------------- (16) For these to be adequate estimates, mortality patterns must follow the payoff matrix of Figure 41, initial brood sizes for all treatments must be the same, and the food year type must be determined. The latter of the two above approaches might yield more insightful results. Values of Tj, calculated from either (7) or (16), can be compared between closely related species hatching nestlings differently. Species having high Tj values, for example, should hatch nestlings asynchronously in more types of environments than closely related species having a low Tj value. Unfortunately, such a comparison of the hatching literature cannot be accomplished at this time. Only a handful of published studies can be analyzed using either of these two procedures because most studies that have tested the original brood reduction hypothesis have failed to report conditions or food levels during the if 208 study. I have analyzed the data from my earlier data analysis chapter and two experimental studies to show how each method may be used to determine if hatching asynchrony is favored over synchronous hatching. From my earlier Chapter 2, I found that the fledging success from asynchronous broods in the less food years was 3.3 nestlings and 4.1 nestlings in the more food years (from Figure 14). Fledging success in synchronous broods in the less food years was 3.0 nes— tlings and was 4.5 nestlings for the more food year. This gives a Tj value of 0.43. Thus, good years must not occur any more frequently than 0.43 for asynchronous hatching to produce more nestlings per brood than synchronously hatched broods. Amundsen and Stokland (1988), in a study conducted on the Shag (gheieereeerer eristoteiie) during a relatively good food year, found that the last-hatched nestling suffered a higher mortality rate than its siblings or than nestlings in synchronously hatched broods. They reported that 91% of first-hatched nestlings in asynchronously hatched broods fledged; the same fledging rate for nestlings in broods adjusted for hatching synchrony. Last—hatched nestlings in asynchronously hatched broods fledged 88% of the time. If fledging rate is correlated to the chance of the nestling surviving until its first reproductive year, as 209 it might be since fledging mass was similar for all fledglings, then the value of 'q' is estimated to be 0.97 (0.88/0.91), an extremely high value. Thus, hatching asynchrony and brood reduction may be favored over synchronous hatching, contrary to their claims. Magrath (1989) conducted an experimental study on the blackbird (Igrgge mergie). He manipulated food supplies and recorded the number of fledglings alive four weeks after fledging from simulated synchronous and natural asynchronously hatched broods. All parents began raising four nestlings. Using data from his Table 1, I estimated the following values: for asynchronous nests, F = 2.23 and Fab = 2.08; and for synchronous 39 nests, Fsg = 2.88 and Fsb = 1.38 Using (11) above, Tj is 0.52. This is a vlue that, according to Magrath (pers. comm.), is a reasonalble Tj value as these birds breed in environments that are often "poor". For hatching asynchrony and brood reduction to be favored over hatching synchrony, the frequency of good years in the breeding environment must be less than Tj. P2. If the frequency of good years, '5', is high, then selection should favor a large value of 'q' in asynchronously hatched broods. Selection may favor strategies that increase the survival rate of the last-hatched nestling, 'q', when good years are fre- 210 quent. There are several possible factors that may increase 'q'. First, Howe (1978) has suggested that laying a large final egg may increase the last-hatched nestling's chance of fledging when food is plentiful because this may reduce the weight hierarchy established by hatching asynchrony. There is some evidence to suggest that larger eggs give rise to larger hatchlings which grow more rapidly because they contain more nutrient reserves (Parsons 1970, Nisbet 1973, Schifferli 1973, and Williams 1980). Laying a large final egg to increase the survival rate of the last-hatched nestling counters Clark and Wilson's (1981) argument that the brood reduction hypothesis and a larger last-laid egg lead to conflicting effects. This game theory model predicts that brood reduction and hatching asynchrony may be favored over synchronous hatching if the last-laid egg is the largest of the clutch. Second, the last-hatched nestling can use special begging behaviors to counteract the feeding hierarchy established by hatching asynchrony to acquire its food during a good food year. For example, Bengtsson and Ryden (1981, 1983) have shown that the last-hatched nestling can increase its chances of being fed by gaining access to nest positions where parents prefer to feed or by displaying a high rate of spontaneous 211 begging. Parents engaged in feeding the brood notice this nestling first. The last-hatched nestling's chances of receiving food increases which in turn increases its chances of surviving. Alternatively, parents could preferentially feed the last-hatched nestling more often so that it catches up in its development to that of its siblings (Hussell 1972, Bryant 1978). Lastly, the last-hatched nestling can develop motor and sensory skills at an accelerated rate so it may compete more effectively against siblings. Khayutin er elr (1988), in a study of the Pied Flycatcher (Eieeggle hypeiegee), found that last-hatched nestlings can develop neurologically at an accelerated rate because they compete against older nestlings having more advanced sensory and motor skills. This accelerated development is possible, they speculate, because rates are not under tight genetic control. P3. If the frequency of good years, 'j', is low, then selection night favor a low 'q' value because intense feeding hierarchies will often be required in asynchronously hatched broods. The value of 'q' may have some effects on the ease of reducing an asynchro- nously hatched brood during a bad food year. These effects are not considered mathematically in the present 212 model. For example, the value of 'q' might reflect the feeding hierarchy intensity among nestlings in the brood. Intense feeding hierarchies, in asynchronously hatched broods, will lead to efficient brood reduction which should benefit parents during a bad food year; the last-hatched nestling will be easily outcompeted for food and it will die quickly. However, when this intense feeding hierarchy is present in asynchronously hatched broods during good food years, it might result in a low 'q' value. Thus, when good years are rare (i.e. 'j' is low ), a low 'q' value might be selected for because efficient brood reduction will often be necessary. If bad food years favor low 'q' values, and good years favor high 'q' values (see P2), then the value of 'q' probably represents to parents raising asynchronously hatched broods a balance between efficient brood reduction during bad food years and the risk of losing this nestling during good food years. Selection might favor an optimum 'q' value depending on the value of 'j' and how 'q' is related to efficient brood reduction. Factors that might influence 'q' values are summarized in Table 2. Interestingly, there have been some reports that the intensity of sibling rivalry within a nest increases with decreasing levels of food (Drummond and Garcia, q 213 1989). This may represent a beneficial strategy for these parents so that 'q' is high when a good food year occurs and efficient brood reduction can be carried out through intense feeding hierarchies during a bad food year. More studies are needed to determine whether this pattern is common and what types of parent-offspring interactions are involved. P4. Hatching asynchrony and brood reduction are favored over synchronous hatching when initiating large clutch sizes. This model predicts, as does Lack's original hypothesis, that large broods will benefit from hatching asynchrony. This is because large broods can be raised in good food years and reduced to a size that can be raised when food is scarce. This prediction holds, however, only if two conditions are met. First, the brood size dependent mortality constant, 'a', cannot be a small value. Small 'a' values reflect no differences between being able to successfully raise an initially large-sized brood, 'B', and a brood of size, 'B-1'. Thus parents cannot benefit from a reduced brood size when the value of 'a' is small. Second, a large brood is favored over a smaller brood only when 'q' is sufficiently large. If 'q' is very small, then parents will produce nearly 'B-1' 214 Table 9. Factors that might increase or decrease the value of 'q' . .rm80 large last-laid egg LHN increases neural development LHN adopts special begging behaviors infrequent sib rivalry selective feeding of LHN LHN = last-hatched nestling. number of young in both good and such cases then , parents should smaller brood of a size 'B-l'. ============= DECREASE ' q ' small last-laid egg low hatchability of last-laid egg premature fledging of LHN infrequent frequent sib rivalry feed largest nestlings first bad food years. In then invest in a This is especially important if larger brood sizes reduce parental survival. To test this prediction of the model, researchers need to conduct hatching pattern manipulations for different clutch sizes. This will allow searchers to calculate a value for 'a' using the linear regression techniques of Ricklefs (1977) and to determine whether large clutch sizes are more productive for asynchronous hatching than for synchronous hatching. P5. When had food years are severe, hatching synchrony is favored over asynchronous hatching. When 215 the severity of bad years is increased, (i.e. when 'c' is increased), nestlings produced during good food years comprise a greater proportion of a parent's lifetime productivity. As a result, synchronous hatching becomes more productive over a lifetime than asynchronous hatching. The value of 'c' is most easily estimated from nestling mortality data from synchronously hatched broods during a bad food year. Recall that, during a bad food year, the probability of each nestling surviving to reproductive age as a function of brood size, is: ME) = 8XP(-a*C*B) - (17) The natural logarithm of this expression gives: -a*c*B = ln[p(B)]. (18) Solving for 'c' produces this equation: c = ln[p(B)]l-a*B. (19) All that is needed to solve this equation is the value of 'a', which must be calculated during a good food year. An interesting implication of the prediction made here is that more variable food resources should favor hatching synchrony over hatching asynchrony. However, this prediction is inconsistent with trends for birds differing in their food habits. Insects, abundances which are tied to short-term weather patterns (Bryant 216 1975, Hussell and Quinney 1987), are thought to be more variable from year to year than seed and nectar supplies. Insectivorous birds are typically more asynchronous hatchers than nectar and seed eaters (Clark and Wilson 1981). P6. Hatching asynchrony and brood reduction may reduce annual variation in reproductive success further increasing lifetime productivity. The present model shows that hatching asynchrony and brood reduction allow parents to recruit a stable number of nestlings into the next generation each year compared to synchronous hatching. Several researchers (e.g. Gillespie 1974, 1977; Cooper and Kaplan 1982; Lacey e; 311 1983) have suggested that natural selection will favor a reduced variance in expected productivity even at the expense of a lower mean annual productivity. This is possible when there is a negative second derivative with respect to an independent factor related to fitness (in this case, brood size, 'B'). Fig. 4 shows that the change in the slope of the productivity curve declines with brood size, giving a negative second derivative. Thus, hatching asynchrony may be further favored over hatching synchrony because it reduces the variance in yearly reproductive success. There is some evidence to suggest that hatching asynchrony does produce less variation in reproductive 217 success between good and bad food years than synchronously hatched broods. Magrath (1989) reported that synchronously hatched broods experienced significant differences in fledging success between supplemented and food stressed treatments. On the other hand, fledging success was not significantly different between these same two food level treatments for broods hatched asynchronously. Haydock and Ligon (1986), in a study on the Chihuahuan Raven (Qgrvue eryprelegege), found that asynchronously hatched broods had a much lower variability in fledging success and fledging masses between good and bad food years than broods simulated for hatching synchrony. Similarly, Shaw's (1985) study of the Blue-eyed Shag (gheieereeerex eerieepe) revealed that total brood loss was much higher in simulated synchronously hatched broods than in asynchronously hatched broods. V. SUMMARY A recent literature review by Amundsen and Stokland (1988) showed that, when food was plentiful, the last-hatched nestling of asynchronously hatched broods died more frequently than its nestmates or nestlings in synchronously hatched broods. They argued that if the last-hatched nestling died as a consequence v ’ .r~m.11 218 of hatching asynchrony, then the brood reduction hypothesis does not adequately explain the adaptive significance of hatching asynchrony in altricial birds. Using a game theory approach, I allowed the last-hatched nestling to have a lower survival rate compared to its siblings and nestlings in synchronously hatched broods during good food years. I showed that hatching asynchrony and brood reduction can increase a parent's lifetime productivity if two general conditions are met. First, the risks of raising synchronously hatched broods must be greater than losing one nestling to selective starvation in an asynchronously hatched brood during a bad food year. Second, the risks of raising an asynchronously hatched brood during a good food year must be offset by the benefits of raising the same brood during a bad food year. Several predictions were generated using computer simulations. I showed that hatching asynchrony is favored over synchronous hatching when good food years are not very frequent, when the survival of last-hatched nestlings in asynchronously hatched broods during good food years is high, when the survival rate of nestlings raised in synchronously hatched broods during bad food years is low, or when bad food years are not characterized as severe. I also addressed other criticisms of the original 219 brood reduction hypothesis. I have argued that increasing egg size with laying order compliments, rather than contradicts, the brood reduction hypothesis, because it may increase the survival of the last-hatched nestlings during good food years. Also, when food is scarce, the occurrence of partial brood loss in synchronously hatched broods does not conflict with the brood reduction hypothesis because it has been shown that hatching asynchrony facilitates efficient brood reduction which may benefit parents. 220 CHAPTER 4 A MATHEMATICAL MODEL FOR HATCHING ASYNCHRONY AND BROOD REDUCTION I. INTRODUCTION In birds, the parent that incubates the eggs can control the hatch interval of a clutch (Lack 1947, Clark and Wilson 1981). When the hatch interval is less than one day, hatching is referred to as synchronous. On the other hand, if the clutch of eggs hatches over a period of more than one day, then hatching is said to be asynchronous. Hatching asynchrony is possible because the female lays her eggs in intervals, often one egg per day, so that when incubation is commenced in the middle of the egg laying period, eggs present at the start of incubation hatch at the same time. Eggs laid after incubation has been started hatch after the first eggs on successive days. The most evident result of hatching asynchrony is that nestlings in a brood differ in ages and weights. Hatching asynchrony was first recognized as a reproductive strategy employed by only a few birds, such as the raptors (Lack 1947). After more careful observation of hatching patterns, this list grew to L _..'Jn.1 -_‘ I 221 include birds in many groups, mostly nonpasserines (Lack 1954, 1968). More recently, Clark and Wilson (1981), in a extensive review of hatching asynchrony in birds, found that hatching asynchrony is more common than hatching synchrony. More than 80% of the birds including nearly all orders of altricial birds examined by Clark and Wilson, hatch clutches over more than 24 hour period. They found that most altricial birds hatch clutches over a two or three day period. There have been many attempts to explain the adaptive significance of hatching asynchrony. The most widely cited explanation is that of David Lack (1947, 1948, 1954, 1968), called the 'brood reduction hypothesis'. He suggested that hatching asynchrony establishes a competitive feeding hierarchy within the brood. When food becomes limited, the larger, older nestlings easily compete better than the last-hatched nestlings for food and the last-hatched nestling is starved. The reduced brood is more adequately nourished during food shortages and nestlings have a greater chance of fledging. Hatching asynchrony produces more nestlings than a same-sized brood hatched synchronously because it is assumed that no nestling can be efficiently singled-out for starvation and all nestlings in a brood are affected by the reduced food supply. 222 Consequently, the entire synchronous brood risks starvation when food is scarce. Lack predicted that brood reduction facilitated by hatching asynchrony would benefit parents lacking the ability to predict, at the start of incubation, the food levels during the upcoming nestling period. Some researchers (see Amundsen and Stokland 1988) have argued that competitive feeding hierarchies established by hatching asynchrony for the purposes of brood reduction is maladaptive. This criticism has arisen because it has been observed that the last- hatched nestling in asynchronously hatched nests sometimes starves when food is plentiful (cf. Amundsen and Stokland 1988). Amundsen and Stokland (1988) have claimed that if the last-hatched nestling dies when food is plentiful, then brood reduction should be viewed as a consequence of hatching asynchrony. They claim that other hypotheses, especially nonadaptive hypotheses, should be given more merit as explanations for the significance of hatching asynchrony. I addressed this criticism of the brood reduction hypothesis with an earlier model that allowed the last-hatched nestling to have a reduced survival to reproductive age because of its inferior position in the feeding hierarchy established by hatching asynchrony. I showed that hatching asynchrony and brood reduction can 223 increase the expected number of nestlings per clutch for parents when they initiate large clutches, when limited food years occur often, and when the cost to synchronous hatching is high during a limited food year. .rm64 My earlier model does not, however, address the adaptive significance of clutches hatched over more than a two day period. Thus, the significance of the hatching pattern of many birds can not be directly addressed by this model. Second, my earlier model also assumed that only two different types of food conditions could occur in nature: plentiful and limited food. Parents are most likely subjected to wide range of food years to occur during the nestling period with moderate food years being the most frequent food year type. Third, my earlier model was not in a form to rigorously examine tradeoffs between brood size and degree of hatching asynchrony that will yield the most offspring per brood. Lastly, in my earlier model, I assumed that there were no effects of hatching asynchrony on parental survival. The effect of hatching asynchrony has been largely ignored (although see Proctor 1975, Gibbons 1987 and Magrath 1988). Here, I present an extension of my earlier model. I examine the effects of a continuous distribution of food year s, where moderate food years are the most 224 frequent, on the degree of hatching asynchrony and brood size that produces the most offspring per year. In particular, I examine whether a continuous distribution of food years selects most for brood size or degree of hatching asynchrony. I also describe the conditions where parental survival can most affect the most productive form of hatching and brood size. I present the results of computer simulations of the model and discuss the predictions of the model. II. EXTENDED MATHEMATICAL MODEL FOR BROOD REDUCTION AND HATCHING ASYNCHRONY A. Introduction The following model presentation has three parts. First, I present the portion of the model that expresses food years as a continuum where moderate food years are the most frequent. I then consider how nestling survival to reproductive age (hereafter as nestling survival) is influenced by hatch position over the food year continuum for various hatching forms (i.e. any degree of asynchronous hatching or synchronous hatching) and for different brood sizes. I then present the third portion of the model that shows how annual adult mortality influences the number of offspring parents can produce in their lifetime. A list of the model's varia- bles is contained in Table 10. 225 B. Food Year Type Continuum Consider an environment where many different food years occur and each food year can be classified by yearly food levels with each food year designated as 'x'. Let the best food year have a value of x=0.0 and the worst food year x=1.0. The best food year should be one in which enough food exists so that parents may easily raise their entire brood. The worst food year, on the other hand, should be one in which food scarcity makes rearing all nestlings impossible and nestling deaths occur. Allow moderate food years to be repre- sented by values between these two extremes. If moderate food years are most frequent, then the frequency of each food year could be expressed using a normalized probability distribution: 2 freq (x) = ——————————— e ‘0.5[(X'U)/8d] (1) sd*sqrt(2*pi) where 'x' is the food year value, 'u' is the mean of all food year s, and 'sd' is the standard deviation for these food years. The objectives of this model are to understand the effects of 'u' and 'sd' on what form of hatching and brood size that yields the most productive brood. Table 10. 226 List of variables contained in model. m(B) m(N) L(B) MN) Food Year Type Variables food year type (represents the average amount of food per year) the mean of the food year distribution the standard deviation of the food year distribution Hatch Position and Brood Size Variables hatching form (N=0 hatching synchrony, N > 0 is asynchronous hatching) brood size optimal hatching form optimal brood size hatch position for latter-hatched nestlings (e.g. i=1 for nestlings hatching a day later than first-hatched nestlings) Nestling Survival Variables the combined survival of all latter-hatched nestlings survival difference between nestlings by hatch position survival rate of each first-hatched nestling survival of nestlings along food year continuum due to the number of first-hatched nestlings survival of nestlings along food year continuum (referred to as the 'slope function') brood size dependent mortality constant Adult Mortality Variables annual adult mortality due to brood size annual adult mortality due to hatching form lifespan of adult for m(B) lifespan of adult for m(N) Variables for Number of Offspring Surviving expected productivity (i.e. number of offspring produced to reproductive age) of parents if food years conform to a normal probability distribution number of offspring surviving to reproductive age as a function of hatching form number of offspring surviving to reproductive age as a function of brood size number of offspring produced in a lifetime that survive until their reproductive age. . “ ”'le ‘ .-) 227 C. Nestling Survival by Hatch Position Let us now consider nestling survival. Nestling survival should be affected by: (1) a nestling's hatch position; (2) the number of nestlings in a brood; and (3) the amount of food that exists during the breeding season. Let the degree of hatching asynchrony be denoted using integer values of 'N': where synchronous hatching is N=0; one nestling hatching a day after its siblings is N=1; and so on, to complete hatching asynchrony. Those nestlings hatching after the first- hatched nestlings shall be referred to collectively as 'latter-hatched nestlings' and will number 'N'. The first-hatched nestlings will be referred to as the '0' chicks, those hatching a day later as the '1' chicks, those hatching two days after the '0' chicks as the '2' chicks, and so on. The survival of all '0' nestlings in nests of all hatching forms should be 1.0 during the best food years because parents can easily feed these nestlings. Let the survival of '0' nestlings decrease so that their minimum survival will occur during a worst food year. Consider also that all '0' nestlings in a nest will represent a synchronously hatched brood of size 'B-N'. The brood reduction hypothesis predicts that, when food is scarce, entire brood starvation will increase 228 linearly with an increasing number of first-hatched nestlings (O'Connor 1978). Thus, the survival of '0' nestlings will decrease along the food year continuum as a function of the number of the '0' nestlings, which will always number 'B-N' for all hatching forms. It therefore follows that the survival of each first- hatched nestling in each nest will be: S(B,N) = (1 - beta * x). (2) The variable 'x' represents the food year. The variable ' ' is expressed as a function of the number of '0' nestlings and a nestling slope function: beta = (B-N) * z. (3) The nestling slope function '2' takes on values less than 1.0 and quantifies the degree to which nestling survival decreases with food years. Larger '2' values mean that nestling survival decreases rapidly across the food year continuum compared to small '2' values. The survival of latter-hatched nestlings along the food year continuum can be quantified using a similar linear expression. The survival of latter-hatched nestlings should be less than 1.0 during the best food year because of their inferior hatch position (see discussion of my previous model to see why this occurs). A '1' nestling in an N=1 asynchronous hatching nest should have a lower survival value than any '0' nestling 229 in a same-sized, synchronously hatched brood. Let the survival difference in their nestling survival values from '0' chicks and between each successive of the latter-hatched nestlings be 'k' ('k' should be between 0.0 and 1.0). The survival of latter-hatched nestlings should also decrease with increasing number of '0' chicks that they must compete against. In addition, the survival of latter-hatched nestlings should also decrease with decreasing food levels. Denoting the hatching position of latter-hatched nestlings with 'i' (e.g. i=1 is a '1' chick), the survival of e11 latter- hatched nestlings becomes: N Q(B,N) = sum [(1.0 — (B-N+i) * z * x) - (i * k)] (4) The expre;:ion (i*k) quantifies the amount the ith nestling's survival is decreased relative to a '0' nestling in a synchronously hatched brood. The number of nestlings produced each year surviving until reproductive age, as a function of hatch position, will be equal to the number of first-hatched nestlings present in the nest (i.e. 'B-N' number of nestlings), times the probability that each nestling survives to reproductive age, plus the number of latter-hatched nestlings surviving to reproductive age: R(B,N) = S*(B-N) + Q. (6) Following my earlier model, and Ricklefs (1977), 230 allow each nestling's survival in a nest to decrease exponentially with increasing brood size as such: E(B) = e('a*3). (7) The variable 'a' is the same as 'a' in my earlier model. It relates brood size and nestling survival. Large 'a' values reflect that the most productive brood size is small. Ricklefs (1977) has shown that 'a' takes on values less than 1.0 and, for the most part, is a species specific value (see Ricklefs 1977 for the use of this equation and Temme and Charnov 1987, for a similar modeling application). The expected proportion of a parent's annual productivity for a food year, P can be calculated as x' the product of all nestling survival values due to hatch position, [equation (6)], and nestling survival due to brood size, [equation (7)], times the frequency of the food year in question [equation (1)]: P = freq(x) * R * E (8) x The total annual expected productivity will be equal to the sum of all proportions of annual expected productivities for all food years. This can be written as the following integral: P(B,N) = integral {freq(x) * R * E} dx. (9) The maximum annual productivity parents can expect, as described in (8), can be determined by calculating the 231 partial derivatives of 'P' with respect to 'B' and 'N', and finding this maximum, or when: QB _ dB (10) I 211% u C E: The brood size and degree of hatching asynchrony that produces the maximum annual productivity values will be designated as B* and N*, respectively. D. Annual Parental Mortality Natural selection should favor those parents that employ the hatching strategy that produces, in a lifetime, the greatest number of offspring that survive until reproductive age (Williams 1966a, Stearns 1976, Endler 1986). Parents can increase their lifetime fecundity in two major ways: increase annual productivity or decrease annual adult mortality. Any decrease in an adult's annual mortality will increase an individual's lifespan. Charnov and Kreb's (1974) model of the effect of adult mortality and brood size on a parent's lifetime production of offspring assumed that adult mortality increased proportionately with brood size. Let us make the same assumption here and assume that annual adult mortality, 'm', increases proportionately with increasing brood size so that the lifespan of a parent becomes: 232 L(B) = 1/[m(B)*B]. (11) where L(B) is the lifespan of an individual as a function of brood size and 'B' is the original brood size. Now let us also consider adult mortality caused by a function of hatching form employed. Permit adult mortality to either increase or decrease proportionately with the degree of asynchronous hatching so that the parent's lifespan, as a function of brood size and degree of asynchronous hatching, can be represented by: L(BIN) = 1/[(m(B)*B + m(N)*(N+1))] (12) where m(N) is mortality caused by the degree of hatching asynchrony and 'N' is the degree of hatching employed (note: (N+1) was used because m(N) could not be directly multiplied by 'N' , N=0 would always produce no annual adult mortality). Adult mortality due to hatching form, m(N), can be any value between -1.0 and +1.0 (a positive value would reflect adult mortality increasing with increasing hatching asynchrony and a negative value would reflect that adult mortality decreases with increasing hatching asynchrony). The sum of the adult mortalities due to brood size and hatching asynchrony should not be larger than 1.0 ['m(B)*B + m(N)*(N+1) = 1.0' would represent a semelparous species]. The number of offspring produced in a parent's lifetime, will be equal to the number of offspring produced per year (equation 9) times the number of years the adult lives 233 and breeds: F(B,N) = L(B,N) * P(B,N) (13) where F(B,N) is the number of offspring produced in a parent's lifetime as a function of brood size and hatching form. III. RESULTS A. Introduction I ran computer simulations on the present mathematical model and addressed these two questions: (1) what is the effect of a continuous distribution of food years on the most productive hatching form and brood size when moderate years are most frequent? (2) what conditions do annual adult mortality influ- ence the hatching form and brood size that will pro- duce the most offspring in a lifetime? I used the annual productivity forms of the model, equation (8) through (10), to address the first question. In particular, I address whether the variables of this present model yielding the most productive brood favor a parent's adjustments in brood size or hatching form. The form of the model as equation (13) is used to address the second question qualitatively. B. Food Year Type Distribution on Nestling Survival Figure 48 shows the effect of food years on nestling survival, by hatch position ('i') and hatching form ('N'). I produced this figure using a standard l -s ““1 234 deviation for year distribution, 'sd', of 0.25, a mean of the food year distribution, 'u', of 0.50, a nestling survival difference by hatch position, 'k', of 0.15, and a brood size dependent mortality constant, 'a', of 0.05. The survival slope function, '2', was set at 0.25. All nestlings are from a brood size of five. Here we see that an increase in the number of '0' nestlings .. -.. 1.1.7167] decreases nestling survival as annual food levels decrease. This was the original intention of introducing a nestling slope function that was a W function of brood size (see equation (3)). Note also that the survival of the very last-hatched nestling in an asynchronous brood is always less than the survival of first-hatched nestlings in a synchronously hatched brood. In addition, this figure also shows that, with the current values for all variables, nestlings in synchronous nests never survive in food years of 0.8 or worse. When the nestling slope function is larger than the 0.25 used here, then the slope of all nestling survival values along the food continuum will become steeper; when it is smaller than 0.25, then the nestling survival values will become more horizontal across the food year continuum. The expected proportion of annual productivities along the food year distribution (equation (8)) for 235 Figure 48. Nestling survival values by hatch position for three different hatching forms along the food year continuum. Solid line is for nestlings in an N=0 nest, dashed lines for nestlings in a N=1 nest and dotted lines for nestlings in N=2 nest. 236 l l l l °°. ‘0. ‘2 “l c o c a 01mm [mums SUIIISON 1.0 0.8 0.6 0.4 0.2 Food year type (x) FIGURE 48 237 Figure 49. The expected proportion of brood productivity for each food year for three different nestling slope function, '2', values. a) for 'z'=0.05; b) for 'z'=0.15; and c) for 'z'=0.50. 238 I I I I I I I /'4 /. /.' /. l,' /‘ /.' ,. ./ " I.' / . / ,‘ —- / ' / '. , . '— 2 x, u ,x .n z , , ' / / /, .' // / / / ’ / /,’ / / / ‘— / / / / / / / I I I I I \ \ \ \ \ — \ \ \ \ \ \ \ \ \\ \\ \ \\ \ \ C \ II \ \\ ‘ \ Z \. . \ . ... \\ ‘. \ s \\ ~‘ \ \ \\\'. \. \\‘. \‘| \. \\.‘ \- \\'. I I I I I I I ’5 0d£1 1205 poo; u; Kimnonpoxd jO uquodOJd pomedxg 1.0 0.8 0.6 0.4 0.2 0.0 Food year type (x) FIGURE 49 "3 II l-\ ...D 239 V I I I I I L 0d£1 1201C poo; III AIIAIionpOJd jO uopxodom pomedxg 0.0 Food year type (x) FIGURE 49 4 ’5 240 fl 4. mum {a 1 I J 1 1 N d _. 2 2 2 3 2 3 3 3 MOM / / / / '- / . / '/ .'/ f/ / '/ .7 / l'l / / I I / // l -_ r / // 11 I/ I . l/,/ 0d£1 1201C poo; III Kmmonpoxd JO uopxodoxd poisedxg 1.0 0.8 0.6 0.4 0.2 0.0 Food year type (x) FIGURE 49 241 three different nestling slope function values, '2': 0.05, 0.15 and 0.50, are given in Figures 49a-c, respectively. These figures show all five different hatching forms (N=0 through N=4) for a brood size of five. I used the same values for these variables as I did to construct Figure 48. The most productive forms of hatching for a range of food years (which I call N and which should not be confused with N*) are also max' given in these figures at the top. Inset in each figure is the value of the productivity integral for each hatching form (the value of equation (9) for each 'N'). Note that in just about every case, the greatest proportion of the expected annual productivity comes from moderate food years because these food years are the most frequent. Figure 49a shows how a small nestling slope function, '2' affects the expected proportion of annual productivity for a brood size of five. Note that when the nestling slope function, '2', is small (0.05), synchronous hatching is the most productive form of hatching in most of the food years; N =0 for food max years 0.0 through 0.81. For food years worse than 0.81, Nmax=1' Any other degree of hatching asynchrony (i.e. for N > 1) will never be the most productive form of hatching in any food year. Since synchronous hatching is the most productive in most of the food years, then 242 natural selection will select for it over any form of asynchronous hatching because parents can expect to raise the most offspring per year given the food year distribution. The expected annual productivity for all hatching forms (inset) shows that annual productivity decreases with increasing degree of hatching asynchrony. When the nestling slope function, '2', is increased (Figure 49b) for a brood size of five, synchronous hatching is still the most productive form of hatching when food years are toward the best food year (i.e. N =0). As the food year becomes one max where less food exists in the environment, the most favored hatching form is a greater degree of hatching asynchrony. For the very worst food year, complete hatching asynchrony (i.e. Nmax=4) is the most productive form of hatching. This figure shows that N*=2 is the most productive form of hatching when moderate food levels exist during breeding (inset). Very large nestling slope functions, '2', selects heavily against synchronous hatching because a high proportion of broods starve in most food years (Figure 49c). Entire brood starvation decreases with increasing hatching asynchrony because there are fewer '0' nestlings in the brood. When '2' is very large, then the expected annual brood productivity increases with 243 Table 11. The B* and N* values for iterations of model's 'k' (survival difference between latter-hatched nestlings), 'z' (nestling survival across food type continuum), 'a' (brood size dependent mortality constant) and 'u' (mean of food year type distribution) variables. Values used to construct this table are: a = 0.05, z= 0.25, k=0.10, u=0.50, and sd=0.25. 'z' B* N* 'u' B* N* 'sd' B* N* 0.02 9 0 0.25 7 2 0.0500 2 1 0.06 9 1 0.30 7 2 0.1000 3 2 0.10 9 2 0.35 6 2 0.1500 3 2 0.14 7 2 0.40 6 2 0.2000 5 3 0.18 6 2 0.45 5 2 0.2500 6 4 0.22 5 2 0.50 5 2 0.3000 6 4 0.26 5 2 0.55 5 2 0.3500 6 4 0.30 5 2 0.60 5 2 0.4000 6 4 0.34 4 2 0.65 4 2 0.4500 6 4 0.38 4 2 0.70 4 2 0.5000 6 4 244 Table 11, continued. 'k' 3* N* 'a' 5* N* 0.020 7 6 0.00500 7 4 0.040 6 4 0.01000 6 3 0.060 6 4 0.02000 6 3 0.080 5 3 0.03000 5 2 0.100 5 2 0.04000 5 2 0.120 5 2 0.05000 5 2 0.140 5 2 0.10000 4 1 0.160 5 2 0.20000 3 1 0.180 5 2 0.30000 2 0 0.200 4 1 0.40000 2 0 245 increasing hatching asynchrony (inset). Here, a high degree of asynchronous hatching, N*=3, is the most productive form of hatching a brood of five nestlings. Thus far, we have examined the model by keeping brood size constant. Equation (10) gives us the means to examine which brood size and hatching form that will yield the most productive brood. Table 14 shows the results of iterating 'z' over a large range of values and determining the most productive form of hatching, N*, and brood size, B*. I used the same values as I did to construct 49 to construct this table. When the nestling slope function ,'z', is small, large synchronous broods are the most productive brood size and hatching form. As '2' increases, the most productive form of hatching is greater asynchronous hatching. Larger '2' values also favor initializing smaller brood sizes. Notice that 'z' affects brood size adjustments more so than degree of hatching asynchrony to produce the most productive brood. The mean in the food year distribution, 'u', affects B* values but not N* values. When the mean of the food year distribution is shifted to the left, large broods are favored (Table 11). This is because a large brood can be raised in good food years and hatching synchrony is the most productive form of hatching in these food years. Likewise, a shift in the food year distribution to the right favors a smaller brood sizes 246 hatched completely asynchronously because poor food years selects against large broods. A shift in the mean of the food year distribution does not affect the degree of hatching asynchrony that yields the most productive brood because changes in 'u' do not affect the shape productivity curve along the food year type distribution (i.e. 'u' does not affect the shape of the curves that we saw in Figures 49a-c). A change in the spread of the food year distribution, 'sd', affects the values of both B* or N* (Table 11). As 'sd' increases, parents can expect a higher frequency of more diverse year types to occur. This favors hatching asynchrony because parents can employ brood reduction if the food year is on the bad food year side. In addition, they can also raise a major portion of the brood if the food year is on the good food year side. A larger spread in the food year distribution (i.e. larger 'sd') also favors larger brood sizes because more good food years occur more frequently and good food years favor large brood sizes. When the survival difference between nestlings in successive hatch positions is small (i.e. when 'k' is small), the most productive brood is from a hatching form that approaches complete hatching asynchrony (Table 11). This is logical because when 'k' is small, the costs of 247 asynchronous hatching when food is plentiful is low. These costs outweigh the costs of initiating a synchronous brood because all nestlings in these broods die when food is scarce. Likewise, when 'k' is large, costs to asynchronous hatching is high so that synchronous hatching is the most productive form of hatching. Notice that 'k' influences mostly N* rather than 8* values. For the range of 'k' iterated, N* went from complete hatching asynchrony to N=1 hatching asynchrony. Over this same range of 'k' values, 3* changed by only 3 nestlings. Table 11 also shows the brood sizes, B*, and hatching form, N*, that yields the most productive brood for different values of the variable 'a', the brood size dependent mortality constant. When 'a' is a small value, then the most productive brood is a large brood hatched asynchronously. As 'a' increases in value (i.e. as the same-sized, large brood is more difficult to raise), then the most productive brood is smaller. These results of productivity on brood size were intended (see equation (7)). However, an increase in 'a' also decreases the degree of hatching asynchrony that yields the most productive brood. This is because as 'a' decreases, broods are easier to raise in most food years but may require brood reduction if the food year turns out to be a bad food year. This is an identical result of my 248 previous model. C. Annual Parental Mortality Figure 50a shows a productivity landscape produced from equation (9) for different brood sizes and hatching forms. Note that, with the conditions specified, the most productive form of hatching and brood size is N* = 2 and B* = 8. To aid in visualizing where the maximum productivity occurs along the brood size and hatching form axes, I also included a contour plot of the productivity landscape. This contour plot is located on the x-y facet of this figure. Figure 50b shows an adult annual mortality plane where adult mortality decreases slightly with an increasing degree of hatching asynchrony (m(N)=0.05) and increases slightly more with increasing brood size (m(N)=0.10). Plotted on bottom of the page on the x-y facet (Figure 50c) is a contour of adult lifetime production of offspring, F(B,N), as calculated from the quotient of the productivity landscape of Figure 50a and adult mortality of Figure 50b (I used equation (13) to produced Figure 50c). Let us now examine, qualitatively, how the land- scapes in Figure 50a and 50b can influence the position of the brood size and hatching form that yields the most productive brood when an individual's lifetime is consid- ered. There will be two different 249 Figure 50. A productivity landscape as a function of brood size and hatching form. Also included is adult mortality plane described as a function of brood size and hatch- ing form (z-axis is component of fitness). See text for details. 250 251 conditions that will most affect a parent's lifetime production of offspring. First, as we can see from Figures 50a and 50b, natural selection will change the most productive brood size and hatching form from those calculated from annual productivities (equation (10)) when the slope of the adult mortality plane differs from 0.0. For example, Figures 50a and 50b show that a slight increase in adult annual mortality as a function of the degree of hatching asynchrony increases the most productive form of hatching from N*=2 (as we see in Figure 50a) to N* = 4. The change in the most productive brood size when adult mortality increases with brood size is from B*=8 to B*=5. If adult mortality decreases with increasing hatching asynchrony, then the most productive hatching form will be smaller than the N* calculated from the annual pro- ductivity form of the model (equation (9)). The second condition that will effect the number of offspring a parent produces in a lifetime will be the shape of the productivity landscape. Lande and Arnold (1983) have shown that the intensity of selection depends upon the concavity of a fitness function along a character gradient. When the productivity landscape (Figure 50a) lacks a lot of curvature, small changes in annual adult mortality will cause a large shift in B* and N* values calculated from annual productivity 252 (equation (9)). Thus, even when adult mortality as a function of brood size of hatching form is very small, it can still have a large effect if the annual productivity plane is relatively flat. There are several variables in the annual productivity form of the model that effect the curvature of the productivity landscape. I plotted three different values for each variable in the productivity equation (equation (9)) on the brood size and hatching form facets of the productivity landscape (Figures 51 through 53). I chose values from Table 14 that produced hatching synchrony, an intermediate degree of hatching asynchrony and complete asynchronous hatching so that a full range of values for each variable would be represented. The largest value of the three is plotted as a dotted line, the intermediate value as the dashed line and the smallest value of the variable is plotted using a solid line. In particular, I ask what values of the model's variables will produce a flat productivity landscape. Figure 51 contains those variables influencing the food year distribution portion of the model. We can see that the standard deviation of the food year distribution, 'sd', has the same degree of curvature along the hatching form facet, 'N', for all three 253 Figure 51. The effect of different 'sd' and 'u' values on the curvature of the productivity landscape along the 'N' and 'B' facets. 254 3: [1‘ 3o . 50+ . I; 3.. . I'. FIGURE 51 255 Figure 52. The effect of different 'k' and '2' values on the curvature of the productivity landscape along the 'N' and 'B' facets. 256 FIGURE 52 257 Figure 53. The effect of different 'a' values on the curvature of the productivity landscape along the 'N' and 'B' facets. 258 variables (sd = 0.05, solid line; sd = 0.25, dashed line; sd= 0.50, dotted line). However, these three values differ in the degree of curvatures along the brood size facet, 'B'. Larger values of 'sd' produce a slightly flatter productivity landscape. Thus, when adult mortality, as a function of brood size, m(B), is changed slightly, natural selection will favor a larger change in the brood size that yields the most offspring per year, compared to when 'sd' is small. On the other hand, different values of the mean of the food distribution, 'u', produces similar degrees of curvature in the annual productivity landscape. Thus changes in adult annual mortality will have the same effect in the magnitude of the shifts in B* and N* from the annual productivity form of the model to the lifetime form of the model. Figure 52 shows the effect of the slope function, 'z', and differential survival by hatch position, 'k', on the curvature of the annual productivity landscape. We can see that large values of 'z' produce a flatter productivity landscape, both along the brood size and hatching form facets, than do small values of '2'. Thus, any small changes in annual adult mortality can change either N* or B* more so when 'z' is large. Three values for the survival difference between hatch positions, 'k', are also shown here in Figure 53. We 259 can see that when 'k' is small, the 'N' facet of the productivity landscape lacks the most curvature. Different values of 'k' do not produce different degrees of curvatures along the 'B' facet of the annual productivity landscape. Lastly, Figure 53 shows the effects of 'a', the brood size dependent mortality constant, on the curvature of the annual productivity landscape. We can see that a large value of 'a' produces a flatter annual productivity landscape than small 'a' values along the hatching form facet. On the other hand, the three values of 'a' depicted here do not influence the shape of the annual productivity landscape along the brood size facet. IV. DISCUSSION A. Introduction My earlier model compared the expected annual productivities of parents raising synchronous broods and asynchronous broods where one nestling was one day younger than its siblings. I allowed upcoming food years to be unpredictably good or bad. I found that by allowing the last-hatched nestling in an asynchronously hatched nest to have a lower survival rate compared to first-hatched nestlings when food was good, natural 260 selection could still favor asynchronous hatching over synchronous hatching. Asynchronous hatching was more productive than synchronous hatching when good food years were infrequent, when costs to synchronous hatching was high in bad food years and when parents initiated large clutches. It is probably more realistic that birds are subjected to a wide variety of food years where some types are more frequent than others. Thus, my earlier model may be considering only the extreme in food years that could occur. In addition, my earlier model also did not consider degrees of hatching asynchrony other than broods where one nestling hatches a day later than the rest of the brood. Lastly, my previous model assumed that hatching asynchrony did not affect parental survival. The objectives of this present model were to modify this earlier model by considering all possible hatching forms within a brood size and also consider nestling survival along a continuous distribution of food years where moderate food years are the most frequent. I used this model to address two questions: (1) what is the effect of a continuous distribution of food years on the most productive hatching form and brood size when moderate food years are most frequent? (2) how does annual adult mortality influence the 261 hatching form and brood size that will produce the most offspring in a lifetime? I will discuss the predictions of this model in relation to these two questions. I also address how this model may be combined with other hypotheses that present reasons for the adaptive significance of hatching asynchrony. 7'! B. Food Year Distribution on the Most Productive Hatching Form and Brood Size I have found that when nestling survival decreases rapidly across a continuum of food years that parents could potentially breed in, then adjustments in brood size are favored over adjustments in the degree of hatching asynchrony. A large decline in nestling survival across the food year continuum favors smaller brood sizes over larger ones. I have also found that a shift in the mean of the food year distribution also favors an adjustment of brood size over adjustments in the degree of hatching asynchrony. When good food years are most frequent, large broods are easily raised when food is good and brood reduction is not required often. The costs of raising broods during good food years outweigh the benefits accrued by parents during infrequent bad food years. In addition, if there is a large spread in the 262 food year distribution (i.e. when 'sd is large), some form of hatching asynchrony will yield the most productive brood. I have also shown that changes in 'k', survival difference due to hatch position, favors adjustments in brood size and degree of hatching asynchrony. When 'k' is small, then large asynchronous broods yield the most productive brood. As 'k' increases, costs to asynchronous hatching increases making more synchronous broods the most productive brood. F In my previous model, I found that, as the brood FI size dependent mortality constant, 'a', is increased, hatching asynchrony was more productive than hatching synchrony. This present model generates a different prediction. When 'a' is increased, synchronous hatching is favored. This present model emphasizes the need for researchers to carry out studies for more than one year and to measure food abundance. Studies conducted for one or two years which find that the model degree of hatching asynchrony is not the most productive form of hatching cannot claim that brood reduction is maladaptive. Studies must examine long term consequences of reproductive traits on fitness. Furthermore, this model also extends Lack's brood reduction hypothesis by treating a continuum of food 263 year distributions. I have shown that even during moderate food year types, some form of hatching asynchrony and brood reduction can be more productive than synchronous hatching. Lack (1947, 1948, 1956, 1968) never addressed whether hatching asynchrony or hatching synchrony would be more productive for 5‘ moderate food year types. Thus, this model treats all food year types and shows how hatching asynchrony and brood reduction can be adaptive. L C. Adult Mortality on the Most Productive FI Hatching Form and Brood Size I have introduced into the present model the effects of adult annual mortality both as a function of brood size and hatching form employed. I assumed that annual adult mortality increased proportionately with increasing brood size and either increased or decreased proportionately with the degree of hatching asynchrony. I have shown that if adult annual mortality decreases with increasing hatching asynchrony, then natural selection will favor more asynchronous hatching, compared to when adult mortality is not considered. On the other hand, an increase in adult mortality with increasing hatching asynchrony will favor more hatching synchrony. A larger change in. adult mortality as a function of brood size or hatching 264 form will select for larger changes in brood or hatching form that was predicted from when just annual productivity is considered. This model also shows that small curvatures of the annual productivity landscape and small changes in adult annual mortality along a hatching form or brood size gradient can influence large shifts in the brood size and hatching form yielding the most offspring per year. This is interesting because some researchers have claimed that if parental survival is changed little by a character gradient, it must have very little influence on the selection of that character (e.g. DeSteven 1980, Bell 1984, Boyce and Perrins 1987). I have shown, however, that small changes in adult mortality with brood size or hatching form may change the brood size and hatching form that produces the most productive brood. I explored the model and examined conditions of the variables that produced the least concave productivity landscape. I found that the productivity landscape is relatively flat along the brood size gradient when the standard deviation in the food year continuum, 'sd', is large, and when the nestling slope function, '2' is large. The productivity landscape is relatively flat along the hatching form gradient when: (1) the difference in nestling survival by hatch position, 'k', is small; (2) 265 the nestling slope function, 'z', is large; and when (3) the brood size dependent mortality constant, 'a', is large. D. Implications of the Model to Field Research The predictions of this present model have several implications toward results of field experiments that are common in the examination in the role of hatching asynchrony. Many researchers (see Amundsen and Stokland 1988 for a review) have manipulated broods to simulate hatching synchrony and a degree of hatching asynchrony greater than that employed naturally by a species. This present model shows that during some breeding seasons, hatching synchrony might yield the most productive brood, and that during other breeding seasons, an increased degree of hatching asynchrony might yield the most productive brood. Thus, researchers should use caution in declaring the degree of hatching asynchrony in a population as maladaptive if these broods are not the most productive in the experimental design. It is entirely possible for unnatural degrees of hatching asynchrony to be the most productive form of hatching. Additionally, this model also underscores the need to measure food abundances and to conduct studies over many years. This model also considers new types of measures for 266 researchers to report and examine carefully to determine the adaptive value of hatching asynchrony in their study species. First, researchers should carefully examine the difference in survival values between hatch positions. When large differences in nestling survival exist between hatch positions, then hatching asynchrony will not be the most productive brood in all food years. Second, this model also emphasizes the need to understand more about the effects of hatching asynchrony over a wide range of food conditions. In addition, it is also desirable to determine what food conditions might represent the most frequent food year available to parents. Third, re- searchers need to examine adult annual mortality and do so in relationship with the other variables presented in this model. This model is the first model to incorporate both annual reproductive success and adult mortality affects on the hatching form and brood size that will yield the most productive brood size. This model underscores the importance of examining all both fitness components and to analyze the shape of the fitness components with respect to hatching form and brood size. Finally, this model is in a form that can allow researchers to begin comparing different species to determine if brood reduction can explain the common occurrence of hatching asynchrony that is observed in 267 altricial birds. E. Relationship of the Present Brood Reduction Model to Alternative Hypotheses Presently, a myriad of adaptive hypotheses exist that attempt to explain the adaptive significance of hatching asynchrony (see Magrath, 1990, for review). However, only two hypotheses have been introduced as a quantitative model; these are the peak load reduction hypothesis (Mock and Schwagmyer 1990) and the nest- failure hypothesis (Clark and Wilson, 1981). There has been a general agreement among researchers (see Magrath 1990) that all adaptive hypotheses explaining the significance of hatching asynchrony are not mutually exclusive. In fact, it is highly probable that selection by more than one factor may play a role in favoring the specific degree of hatching asynchrony in any bird species. For example, the nest-failure hypothesis and the brood reduction hypothesis (in the present model's form) could both explain the significance of hatching asynchrony in any given species. The nest-failure hypothesis states that hatching asynchrony is favored in species where the per diem nest-failure rate due to predation (see Magrath, 1989 for another possible cause of nest-failure) is greater during the incubation period than during the 268 nestling period (see also Hussell 1983, for another form of this model). Hatching asynchrony could be one mechanism that adjusts the amount of exposure an offspring experiences as either an egg or a nestling. The nest-failure reduction model examines this also as a function of brood size. Combining both models mathematically could be F” accomplished relatively easily. The adaptive landscape produced by the present continuous brood reduction model (see Figure 4a for example), for example, could be constrained using Lagrange multipliers on the ”I partial derivatives dP/dB and dP/dN. Thus, predation could produce a brood size and degree of hatching asynchrony that could be further selected upon to produce the most productive brood. Such an approach could prove fruitful since there is currently no unified approach to the problem of hatching asynchrony. Quantifying other verbal adaptive hypotheses could also help researchers understand the relationships between all of these adaptive hypothesis. V. CONCLUSIONS This present model was constructed to determine the effects of a continuum of food years where moderate food years are the most frequent would have on the hatching form and brood size that would produce the most productive brood. I also introduced effects of 269 parental survival, as a function of brood size and hatching form, into this model. I found that hatching asynchrony is favored over more synchronous hatching when: (1) the costs to asynchronous hatching, reduced survival of latter-hatched nestlings in good food years, is low; (2) when the nesting slope function F‘ along the food year continuum is high; and (3) when the i mean in the food year distribution is not toward the best food year side of the food year continuum. I also L found that adult mortality can influence the brood size and hatching form that produces the most productive brood type in a parent's lifetime. Adult mortality has its greatest influence on the hatching form and brood size that yields the most productive brood when: (1) adult mortality along a brood size or hatching form continuum is large; and (2) when the annual productivity landscape is relatively flat. Furthermore, this model is in a form that can be used to combine other models that exist to explain the adaptive significance of hatching asynchrony. 270 LITERATURE CITED Anderson, D. 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