IntroductionStage Class ModelsLeslie ModelLefkovitch ModelComparisonTheoretical ProjectionsCalculating the RatesGi Survival and Stage AdvancementPi Survival RateLoggerhead Population MatrixStable Stage DistributionResultsConclusionIntroductionStage Class ModelsTheoretical ProjectionsResultsConclusionHome PageTitle PageJJ IIJ IPage 1 of 19Go BackFull ScreenCloseQuitImplications For Loggerhead Sea Turtle ConservationThrough A Stage-Based Population ModelAlex Varner and Ben MarshallNovember 11, 2009AbstractIn order to have an adequate program for the protection of various threatenedspecies, there must be a thorough understanding of population dynamics. Manymanagement groups are unaware of such an important need. Those that are un-informed have incorrect perceptions about conservation methods and how theyaffect the species they are dealing with. Our goal is to identify the most crit-ical parameters for understanding the general population of the loggerhead seaturtles (C aretta caretta). Using a Lefkovitch stage class matrix model, we canrefine our practices to more accurately project the sensitive areas in which popula-tions are affected. Through the comprehension of these important findings, bettermanagement practices can be designed to further encourage turtle populations toflourish.IntroductionStage Class ModelsTheoretical ProjectionsResultsConclusionHome PageTitle PageJJ IIJ IPage 2 of 19Go BackFull ScreenCloseQuit1. IntroductionThe human population’s increasing numbers threaten many species each day. Our con-sumption of resources and daily practices affect the habitats and routines of all classesof animals. Many have dedicated their lives to the study and practice of conservationfor these endangered groups. Various laws, programs, and agencies incur the practicesof conservation to strengthen almost extinct populations. These institutions have aprofound impact on the natural world and its ability to withstand the carelessness ofeveryday human life.On the other hand, many of the aforementioned methods (which are well intended)yield insufficient protection practices. The reason for this is a lack of understandingregarding the implications of certain efforts. For example, many rely on certain pro-grams’ ease of implementation such as accessibility to certain age groups or life stagesof the species. Past programs for conserving turtle populations focused on the eggs andnests as the culmination of their efforts. The nests are easily monitored and protected.But it seems efforts that pertain solely to egg protection will not ultimately secure theentire species. Hence, the poor understanding of populations as a whole inhibits theirgoals.The Leslie and Lefkovitch matrix models give us a way to quantitatively understandthe population data given to us. Using these models, we will explore various stimuliwhich affect the growth and maturation of the loggerhead sea turtle population. Wewill then be able to utilize the various results yielded by these stimuli and developpossibilities for future management of the species in question.IntroductionStage Class ModelsTheoretical ProjectionsResultsConclusionHome PageTitle PageJJ IIJ IPage 3 of 19Go BackFull ScreenCloseQuit2. Stage Class Models2.1. Leslie ModelThe matrices that we will utilize in determining population dynamics are the Lesliematrix and the Lefkovitch matrix. These matrices are modeled for each stage of lifethat corresponds to the species studied (which in this case is the loggerhead sea turtle).The first of these is the Leslie population model. Its classes are divided into reproductivecycles (which is usually one year), and it is actually the more general model in that itdoesn’t take into account the variables associated with a species survival. The systemhas the form ofAnt= nt+1where ntgives the population of individuals in a particular life stage t and nt+1is thepopulation of the next stage..a11a12... a1sa21a22... a2s. . ... .as1as2... assn1n2.nst=n1n2.nst+1The s in this system denotes the number of particular age classes. The Leslie modelequally partitions the entire population according to age. The matrix A is what is knownas the population projection matrix which incorporates the intrinsic survival ratesof any given age for any time period. It contains three distinct types of rates: fecundityor birth rate(Fi), survival in a stage (Pi) and growth (Gi). This matrix then projectsthe rates of a given age onto the individuals, leading us to an understanding of our newpopulation.IntroductionStage Class ModelsTheoretical ProjectionsResultsConclusionHome PageTitle PageJJ IIJ IPage 4 of 19Go BackFull ScreenCloseQuit2.2. Lefkovitch ModelThe Lefkovitch model does not correlate its classes to any particular age group. Instead,it was devised under the assumption that its classes have identical rates for fecundity,mortality and growth. This model can be used to project itself onto the populationvector of any given species. Our modelNt= N0ertcontains the eigenvalue λm= erwhere r equals the natural rate of the increase ina population. Ntis equated to the original population N0multiplied by λm. Thepopulation will remain at a stable size if λm= 1; thus when r = 0 or the rate ofincrease is zero, the population remains stable.Nt= N0λt= N0(er)t= N0(e0)t= N0(1)= N0If an environment remains constant, then the population of individuals in all stageswill reach a stable point. There exists a right eigenvector wmthat multiplies the generalmatrix A (from the Leslie model) to create that unchanging distribution.Awm= λmwm.The matrices considered would reach the equilibrium point wmwith each stage increas-ing by λm. The reproductive rate of a given stage is stated in the left eigenvalue v’such thatv’A = v’λm.These projection yield the expected amount of reproduction in all stages (fecundity).IntroductionStage Class ModelsTheoretical ProjectionsResultsConclusionHome PageTitle PageJJ IIJ IPage 5 of 19Go BackFull ScreenCloseQuit2.3. ComparisonThe two models obviously have differences in the way they project a population. TheLeslie model is based strictly on age; the Lefkovitch model has classes that differ inlength (or the duration of each class) and the amount of individuals in each class.Hence, the Lefkovitch model seems like a more accurate choice for our goal. Thismodel is less rigid which is valuable since it parallels the dynamics of populations.3. Theoretical