Figure I shows a typical life history, in which the rate of growth declines with age ... theory (see, e.g., Charnov and Berrigan l99la;Appendix to this article) but our.
V o l . 1 3 9 ,N o . 6
The American Naturalist
June 1992
PATTERNS OF SURVIVAL, GROWTH, AND MATURATION IN SNAKES AND LIZARDS RrcnnnnSmNs* ANDERIcL. CnlnNovt *Zoology Department, University of Sydney, New South Wales 2006, Australia; tBiology Department, University of Utah, Salt Lake City' Utah 84112 ; AcceptedJune 6' I99l SubmittedMarch 19, 1990;RevisedMay 28, 1991
Abstract._We review published data to determine whether squamatereptiles show a specific seriesofquantitative relationshipsamonglife-history characteristics,as predicted by mathemati cal models and observedin other vertebrateand invertebrate groups. We focus on growth rates, adult survival rates, and agesat sexualmaturation. In general, snakesand lizards show patterns similar to those expected. The body size at maturation is a relatively constant proportion of maximum size, and adult survival rate is proportional to age at maturity. The von Bertalanffy growth constant (K) is positively correlatedwith the adult instantaneousmortality rate (M) such ihat the ratio of the two variables is generally close to 1.0. Phylogenetically based analyses show that these results are not artifacts due to phylogenetic conservatism. The constants of proportionality linking age at maturity to rates of mortality are higher than those of endothermic vertebrates but lower than those of previously studied invertebrates. Although snakes differ from lizards in mean values ofseveral life-history traits, the relationshipsamong thesevariables are usually similar in the two suborders. These analyses show that squamatereptiles exhibit interspecific and intraspecific patterns of growth, survival rate, and maturation that are of the same qualitative (and, often, quantitative) form as those seen in other types of organisms in which growth continues after maturity.
Although many speciesof animals (including a diverse array of birds, mammals, cephalopods,and telrestrial arthropods) cease growing after they reach sexual maturity, this pattern is the exception rather than the rule. Most other vertebrates and invertebratesbegin reproducing before they attain their maximum body size' Prior to maturation, energy is allocated to maintenanceand growth, whereasafter maturation it is also allocated to reproduction. The pattern of growth is commonly describedby equations such as the von Bertalanffy or logistic (see, e.g., Andrews 1982).Figure I shows a typical life history, in which the rate of growth declines with age and the animal eventually approachessome asymptotic length if it survives for enough time. These consistent general features suggest that certain consistentrelationshipsmay be expectedbetweengrowth patterns, survival rates, and ages at maturity in diverse animal taxa. This article analyzespublished data on squamatereptiles to compare some of their life-history attributes to those of previously studied speciesof other taxa. Many years ago, Bevefton and Holt (1959)and Beverton (1963)showed the existenceof two patterns that link growth, maturation, and adult mortality rates in fishes,at least within certain taxonomic boundaries(e.g., within the Gadidae Am. Nat. 1992.Vol. 139,pp. t257-1269. All rights reserved. @ 1992by The University of Chicago.0003-0147/9?3906-0007$02.00.
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THE AMERICAN NATURALIST
(* /) E t a o, c o J
h = (*(-dK')
hatching
CV(maturation)
Age (x) Frc. l.-Growth in length accordingto the von Bertalanffy equation. Age (x) is measured from a hypothetical zero length, even though the equation is usually fitted beginning at hatching. The symbol /- representsthe asymptotic size, which for other indeterminategrowers has been shown to be about 5Valargerthan the maximum-sizedindividual seenin a large sample (Taylor 1962;Pauly 1981).The symbol /" representsthe length at maturation, age o; thus, /"//- is the relative size at the onset ofmaturity (Charnov 1990&).Body massis usually a power function oflength, with the exponentapproximately3.0 (Ricker 1975;Pauly 1981).
or the Clupeidae).The two patterns are as follows. First, within each taxonomic group the adult instantaneousmortality rute (M) and the von Bertalanffy growth coefficient (K) are positively related to each other such that the ratio K/M tends to be relatively constant. However, this KIM ratio may differ greatly among groups. The second pattern is that the body length at maturity (/") is positively correlated with the von Bertalanffy asymptotic body length (/-), so that the relative length at maturity (/.//-) tends to be a constant value within a group, and this value tends to increase as the group's KIM ratio increases.It was later pointed out that a third pattern holds if the two just mentioned are true (Charnov and Berrigan 1991a,l99lb). From the von Bertalanffy equation of figure l, we have l.ll*:l-e-K"
(1)
where a is the age at sexual maturity. If a group of species share a common Ql- value, they must share a common K'ct value; but if their KIM ratio is also constant,then the product M.otwill itself be a constant.Thus, specieswith the sameKIM and l.ll* ratios will have adult instantaneousmortality rates that are inversely proportional to the ages at maturity. It was shown that for a wide variety of fishes M.a falls between 1 and 3 with an average near 2. A plot of log"M versus log"ctwas linear with the expected slope of - I (Charnov and Berrigan l99la, l99lb). Studies patterned on the work of Beverton and Holt showed that the same
REPTILE LIFE HISTORY
1259
- 0.56, threepatternsheld within the shrimpfamily Pandalidae(KlM - 0.37,1,11* M.a - 2.2), in a samplethat included27 populationsof five speciesand spanned the northern latitudes from California to the subarctic (Charnov 1979, 1989, 1990b).Ebert (1975)showed that the KIM ratio was approximately constant (close to 1.0) for a sample of 18 populations(including over a dozen species)of sea urchins that spannedboth tropical and Temperate to North Temperate waters. From thesestudieson fishes,shrimp,and seaurchins,it would appearthat (within certain taxonomic boundaries)there exist life-history generalizationsin terms of the valuesassumedby the dimensionlessnumbers(loll*, M'a, and KIM) that link survival rate, growth, and maturation. Life-history evolution models have been developedto account for these patterns (Charnov 1989, l990a,'Charnov and Berrigan l99la, I99lb;and seethe Appendix to this article). In the present article we simply wish to ask whether the patterns described above also hold for the squamatereptiles (snakesand lizards), another group of animalsin which growth continues after maturity. Our searchis motivated by the theory (see,e.g., Charnov and Berrigan l99la;Appendix to this article) but our major interest is to ask whether the life-history patterns of these lizards and snakeslook like those of the fishes, shrimp, and sea urchins that have been studiedpreviously. METHODS
We gathereddata on annual adult survival rates and agesat female maturation for 16 speciesof snakes(12 colubrids, four viperids) from the review of Parker and Plummer(1987,table 5) and for 20 speciesof lizards(14iguanids,three teiids, two lacertids, and one xantusiid) from severalreviews (Andrews 1982,app. l; Dunham et al. 1988,appendix; Shine and Schwarzkopf,in press, table I and referencestherein). It is important to note that there is a strong phylogenetic and geographicalbias in the speciesstudied (mostly North American iguanid lizards and colubrid snakes),and hence any extrapolation of our results to squamatesin generalmust be made with caution. We included data on separatepopulations of two wide-ranginglizard species(Sceloporusgraciosus and Sceloporusundulatus) and one snake (Croralus viridis) to incorporate subspeciflcvariation in the data set but did not include available data on several other lizard species, to avoid of a few taxa (see,e.g., Cluttoncompoundingthe problem of overrepresentation mortality rates were calculated instantaneous 1984). Average Harvey Brock and (S) to the relationship S : e-M. rate according survival annual adult from We also noted the sizeat sexual maturity and the maximum female body length (/.). Studies of other speciesin which growth continues after maturity show that /. is about SVosmaller than the von Bertalanffy /-, at least for large samples (Taylor 1962;ParlJy1981).For our purposes,the ratio /.//- is sufficiently close to I,ll*to be used as the relative size at the onset of maturity; thus, we treat /- as equivalent to /-. From this ratio and the age at maturity, we can use equation (1) to estimateK. We have not fitted equationsto growth data for the various species but have used this simple techniqueto estimateK. Of course, greaterprecision is possible if more growth data are available to estimate K and l-.
TABLE PuslrsHro Dlu Slour-VrNr
oN Acp lt Mlrunrrv, LpNcrH lr MlruurroN
1
MnlN ANNult Aout-t Sunvrvlr Rlrr, lNo FErulrE AND AT Mexruuu Srze rN SNlres llto Lrzlnls Felvtlrp Bony LnNcrn (mm)
Snakes: Ag kistrodon contortrix Crotalus viridrs (Utah) Crotalus viridis (British Columbia) Vipera berus Vipera aspis Elaphe quadrivirgata Pituophis melanoleucus Masticophis taeniatus Coluber constrictor Opheodrysaestivus Diadophis punctatus Carphophis vermis Nerodia sipedon Thamnophissirtalis Rhabdophis tigrinus Heterodon nasicus Heterodon platyrhinos Lizards: Talcydromus talcydromoide s Lacerta vivipara Cnemidophorussexlineatus Cnemidophorus tigris Cnemidophorusuniparens Xantusia vigilis Basiliscus basiliscus Cyclura carinata Crotaphytus collaris Crotaphytus wislizeni Uta stansburiana Urosarus ornatus Sceloporuspoinsetti Sceloporusjarrovi Sceloporus undulatus (Kansas) Sceloporusundulatus (New Mexico) Scelop or us undulat us (U tah) Sceloporus undulatus (Colorado) Sceloporusundulatus (Texas) Scelop or us undulatus (Ohio) Sceloporusundulatus (South Carolina) Sceloporusundulatus (New Mexico) Sceloporusundulatus (Arizona) Sceloporusscalaris Sceloporusvirgatus Scelop orus gr acio sus (U tah) Sceloporus gracio sus (Utah) Phrynosoma douglasi
AGE AT
ADULT
Mlrup.rrv (yr)
Sunvrvlr RlrB
At Maturity
At Maximum Size
.7 .75 .85 .77 .78 .6 .8 .8 .71 .49 .74 .65 .35 .5 .41 .63 .47
420 564 650 450 463 549 740 740 580 350 235 250 470 504 548 350 560
750 693 950 570 540 941 I,030 l,030 980 550 340 290 970 815 861 700 725
.24 .2 .16 .48 .08 .71
45 49 68 70 58 39 135 t92 78
62 55 88 90 77 50 194 292 lt2 135 52 53 128 90 67 73 80 80 67 82 7l 77 69 63 65 67 70 94
f
3 7 J
5 2 J J J
J J
2 2 2 2 2 I 1.5 2 1.84 .83 3 1.67 6.5 .83 1.83 .79 .83 1.38 .65 I I
2 1.7 I 1.7 I I .9 .74 1.83 1.83 1.95 2
.JJ
.9 .48 .5 .t2 .3 .43 .36 .27 .34 .48 .37 .tl .44 .49 .2 .13 .J
.47 .67
r03 4l 4l 87 73 47 53 60 58 47 66
))
54 60 4l 47 48.6 53 60
Norn.-These data were used to calculate the results described in the text and are derived from articles listed in the reviews of Parker and Plummer (1987)for sriakesand Andrews (1982),Dunham et al. (1988),and Shine and Schwarzkopf (l99l) for lizards.
REPTILE LIFE HISTORY
t26l
Our choice of the von Bertalanffy equation to characterize squamategrowth patterns was made primarily to facilitate direct comparison between our results and those of previous analyseson other types of animals(seeEbert 1975; Charnov 1979,1989, 1990b;Charnov and Berrigan l99la, l99lb). Reviews of growth trajectories in lizards and snakeshave generallyfound that the von Bertalanffy curve fits the data well, although in some cases the logistic-by-length or logistic-byweight equationsmay perform even better (see, e.g., Schoenerand Schoener 1978;Andrews 1982).For the purposes of the broad synthesis attempted in this article, the fit of the von Bertalanffy equation is sufficiently close that it will introduce only minor error relative to that coming from the numerous other simplifying assumptionswe have been forced to make. For parameter estimation we used functional regression(measurementerror assumedto be equal for both the .r and y variables)rather than simple linear regression(which assumesthat all the measurementerror is in the y direction; see Ricker 1973, 1975). The data on maturation, survival, and body size are detailed by speciesin table 1. Using each population or speciesas an independentdata point in analysessuch as these may introduce considerableerror becauseof the effects of phylogenetic of data points (see,e.g., Cluttonconservatism,which leadsto nonindependence Brock and Harvey 1984). In order to determine whether this potential source of error was significant, we repeated all of our correlation analyses using the phylogenetic method of Pagel and Harvey (1989).This technique works as follows. The values for each population or speciesare superimposedon a phylogenetic hypothesisfor the group, and the program calculatesevolutionary changes in one variable so that they may be compared to concurrent changesin another variable. If there is a significantfunctional relationship between the two variables, they should tend to changein a correlated fashion. This technique helps to overcome the problem of a potentially spurious correlation between two variables due to common inheritance rather than independent adaptation. Phylogenetic hypothesesfor the taxa were taken from Dowling et al. (1983) and Estes and Pregill (1988),and referencestherein.
RESULTS
Mortality and Age at Maturity The annual adult survival rate was positively correlated with the age at maturity, bothforlizards (r : 0.74,n : 28,P < .001)and snakes(r : 0.68,n : 17, P < .003). Visual inspection shows the relationship to be highly nonlinear, with snakesand lizards apparently falling on the same curvilinear regressionline (fig. 2a). If the reptiles are like the other previously studied types of animals with continued growth after maturity (such as fishes and shrimp), we expect that a plot of log,M versus log"crwill be linear with a slope of - 1. Figure 2b plots these data. As predicted, the relationship is significant and approximately linear (r : 0.86,n : 45,P < .001).The calculatedslopefor simplelinear regression(appropriate if measurementerror is much greater for mortality rates than for ages at maturity, as seemsprobable)is -1.12, approximatelyI SE greaterthan -1.0.
1262
THE AMERICAN NATURALIST
a
(t, L
6 o o
.= L
f (5
o @&Do
t. &ota ot'o t 6
(tt
o o)
ooo
.1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 Survival Rate
> 1.75 E 1.5
fr r.zs 6 .7s O
o)
b
o o
OC
o(
tob
E
.
: { .
- -o- io ri'rr-o. l o
Jo - . zos -.5
: a
- 2.5 - 2 - 1 . 5 - 1
-.5
0
.5
1
loge M Frc. 2.-a, Relationshipbetween annual adult survival rate and age at female maturation for 17 populations of snakes (16 species)and 28 populations of lizards (20 species).Softd circles, data points for lizards; open circles, data points for snakes.D, Regressionsoflog"M (instantaneousadult mortality rate) againstlog,c (ageat maturity, in years), for snakes(open circles) andltzards (solid circles). See text for statistical results and methods of calculation.
The calculated slope of the functional regressionfor these samedata (appropriate if mortality rates and age at maturation are measuredwith equal error) is - 1.3, 3 SE greater than the predicted value of - 1.0. Visual inspection suggeststhat a slope of - 1.0 would also fit the data quite well (fig. 2a). Analysis of covariance of the linear regression showed no significant difference between lizards and snakesin either the slopes(F : 0.91, df : 1,41,P : .35) or intercepts(F : 0.73, df : 1,42,P : .40) of the relationshipbetweenlog"M and log"cr. Thus, the instantaneousadult mortality rate among squamatesis inversely proportional to the age at maturity, just as it is amongfishesand shrimp. It is encour-
REPTILE LIFE HISTORY
r263
agingto seethis result, given the difficulty of accurately measuringsurvival rates in the field. The constants of proportionality (M'a product) are lower for the reptiles (mean : L.33, SD : 0.57) than for fishes or shrimp, which have M'a around 2. Birds and mammals also have M'o. near constant values, but these nonaquaticendothermshave M'o. around 0.4-0.6, much lower than the reptiles, fishes, or shrimp (Charnov and Berrigan 1990, l99lb). The correlation between adult survival rate and age at maturity among squamates is not an artifact of phylogenetic conservatism. An analysis of concurrent evolutionary changesin the two variables (Pagel and Harvey 1989)showed that changesin annual survival rate were significantly correlated with changesin the age at maturity among the 45 squamatepopulations studied (r : 0.35, n : 23, P : .05) and that changesinlog"M were highly correlated with changesin log,ct ( r : 0 . 6 6 ,n : 2 4 , P < . 0 0 1 ) . Relative Size at Maturity (lnll*) The ratio of size at maturity to maximum adult body size(l,ll*) in the squamates studied generally ranged between 0.50 and 0.90, with an overall mean of 0.71 (table 1; fig. 3a). The mean value of /"//- was higher in lizards (mean : 0.74, SD = 0.06)than in snakes(mean : 0.68,SD : 0.116;7: 2.51,,df : 43, P < .02). The reason for this difference is clarified by further analysis. There was a significant tendency for larger speciesto mature at a slightly smaller proportion of their maximum body size (r : 0.34, n : 45, P < .02), and phylogeneticanalysis confirmed that evolutionary increasesin maximum body size were accompanied by decreasesin the relative size at maturity (r : 0.83, n : 26, P < .001).This allometry was previously described by Andrews (1982) in her extensive review and analysis of reptilian growth. It is probably becauseof this allometric effect that snakes(which are much larger than lizards, on the average: t : 14.66,df : 43, P
