Tópicos importantes da deﬁnição de População:

(1)

Dinâmica Populacional de Plantas

Disciplina BIE 0320

Ecologia de Populações e Comunidades Vegetais

2015

(2)

Tópicos importantes da deﬁnição de População:

-‐ Mesma espécie -‐ Mesmo local

-‐ Mesmo tempo (?)

(3)

Estrutura Populacional Quais aspectos?

-‐ Distribuição de idades

-‐ Distribuição de tamanhos -‐ Distribuição de estágios -‐ Razão sexual

-‐ Estrutura genéQca

-‐ Distribuição espacial

(4)

Dinâmica Populacional Taxas vitais

-‐ Nascimento -‐ Mortalidade -‐ Imigração -‐ Emigração

+ Crescimento

(5)

1 -‐ Deﬁnir e demarcar área

Permanent plot -‐ Swiss Na7onal Park

Como se faz na práQca?

Para populações de herbáceas parece rela7vamente simples

Permanent plots in Switzerland-‐ University of Lausanne

Mas nem sempre...

(6)

Como se faz na práQca?

1 -‐ Deﬁnir e demarcar área

Projeto Diagnós7co, Manejo e Uso de Floresta Secundária no Nordeste Paraense

DNIT -‐ Mata Santa Tereza-‐ PB

Em ﬂorestas

(7)

Giacomini Wetland Restora7on Project

2 -‐ Contar indivíduos e monitorar ao longo do tempo

Como se faz na práQca?

Nesse caso, sem marcar e acompanhar cada indivíduo

(8)

2 -‐ Contar indivíduos e monitorar ao longo do tempo

Como se faz na práQca?

Nesse caso, marcando e acompanhando cada indivíduo

 









Geonoma scho4ana (Portela, 2008)

(9)

Como se faz na práQca?

Camcore projects Projeto Litoral Norte -‐ Labtrop Projeto Litoral Norte -‐ Labtrop

ugt-‐online.de

ecoma7k.de

(10)

Diferentes formas de estudar dinâmica

1 -‐ Inferir dinâmica a parQr de estrutura

0 50 100 150 200 250

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Classes de tamanho

No. de indivíduos

Ideia geral: Diferença entre classes = probabilidade de transição

Premissa perigosa: Estrutura atual representa a estrutura estável

(11)

0 50 100 150 200 250

1 2 3 45 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Classes de tam anho

No. de indivíduos

no passado, como abate seletivo e pisoteio, impediu que algumas gerações de jovens atingissem o porte adulto, provocando defasagem na classe etflria das populações.

A Égura 2 mostra a distribuição das classes de 2 cm de diâmetro para Xylopia aromatica. A forma é de um “J” invertido com progressão geométrica decrescente no sentido do maior diâmetro. Este padrão indica que estfl havendo reposição das classes etflrias subseqüentes dos indivíduos da espécie. Admitindo que houve interferência antrópica na flrea,X. aromatica exibe, pela maior proporção de indivíduos jovens, tendência de crescimento.

Figura 2: Classes de diâmetro deXylopia aromatica. Classes Éxas de 2 cm. 4-3,1 a 5,0 cm;

6-5,1 a 7,0 cm; . . .; 14-13,1 a 15,0 cm; e, 16-15,1 a 17,0 cm.

A Égura 3 mostra que para Pterodon emarginatus hfl um grande número de indivíduos jovens a que se segue uma diminuição nas classes de 10 a 14 cm. Pos- sivelmente, este fato possa estar relacionado a alguma interferência no recrutamento de novas plântulas em um dado momento. No entanto, a forma predominante da curva indica que hfl tendência de regeneração e possibilidade de crescimento da população. As classes de indivíduos acima de 25 cm incluem adultos que devem ter sido poupados de extração seletiva evidenciada pela presença de troncos cortados rentes ao solo na flrea.

ParaVochysia tucanorum, a Égura 4 exibe distribuição irregular das classes iniciais, intermediflrias e superiores com vflrias interrupções, indicando épocas sem reposição. FrutiÉcação inconstante, baixa capacidade germinativa, competição in- ter/intra especíÉca ou mesmo abate podem ser as causas. No cerrado, a taxa de ataque de insetos e parasitas aos frutos é alta (RIZZINI, 1971), e espécies que não frutiÉcam regularmente poderiam estar mantendo estratégia contra a predação e o parasitismo.

60

Figura 5: Classes de diâmetro de Ocotea pulchella. Classes Éxas de 2 cm. 4-3,1 a 5,0 cm;

6-5,1 a 7,0 cm; 8-7,1 a 9,0 cm; . . .; 42-41,1 a 43,0 cm; e, 44-43,1 a 45,0 cm.

Figura 6: Classes de diâmetro de Anadenanthera falcata. Classes Éxas de 2 cm. 4-3,1 a 5,0 cm; 6-5,1 a 7,0 cm; 8-7,1 a 9,0 cm; . . . ; 84-73,1 a 85,0 cm; e, 86-85,1 a 87,0 cm.

Virola sebifera, pela anfllise da Égura 7, apresenta boa capacidade de regenera- ção na flrea, porém com diÉculdades no estabelecimento dos indivíduos de maior diâmetro na população. A presença de um indivíduo de 30 cm de diâmetro indica que, em tese, este nível de crescimento pode ser atingido por outros indivíduos da população. Na falta destes, a hipótese é que os mecanismos de seleção natural são mais rígidos com os adultos do que com os jovens nesta flrea. Ou, em se tratando de abate, este indivíduo teria sido poupado, e os indivíduos jovens podem vir a exibir tal crescimento.

Para Miconia rubiginosa a distribuição das classes de diâmetro (Fig.8) mostra haver predominância de indivíduos jovens. Cerca de 2/3 de todas as flrvores amostra- das estão concentradas nas duas classes iniciais, enquanto que o restante encontra- se distribuído em sete classes. A alta proporção de indivíduos jovens indica bom recrutamento de plântulas e crescimento da população. Entretanto, mecanismos de

62 Interpretação convencional:

População em crescimento ("J inverQdo")

População em declínio

Si lv a & S oar es 1 99 9

(12)

Porém...

Condit e t al . ( 19 98 )

502

The American Naturalist

Figure 3:Size distribution and demographic parameters forCe- Figure 4: Size distribution and demographic parameters for cropia insignis. All symbols are identical to those in figure 1. Zanthoxylum belizense. All symbols are identical to those in UnlikeTrichiliaand Tetragastris,many individuals grew by two figure 1. As with Cecropia, many individuals of Zanthoxylum or even three size classes in this species. The top panel shows grew by two or more size classes. The top panel shows growth growth and survival probabilities for each 50-mm dbh bracket and survival probabilities for each 50-mm dbh bracket (10–49, (10–49, 50–99 mm, etc.). The bottom panel shows number of 50–99 mm, etc.). The bottom panel shows number of individu- individuals in each 50-mm dbh class divided by the total num- als in each 50-mm dbh class divided by the total number of in- ber of individuals of that species. dividuals of that species.

viduals). However, the result can also be viewed in the

slope

L

against observed

L

and simulated

!

against ob- light of the third prediction from equation (4): growth

served

!. Predictions were good (fig. 5).

was 0 in the terminal size class (by definition), so growth declined sharply from the subterminal to the terminal class. In

Zanthoxylum,

this decline was the greatest, and

Correlates of Size Distribution

the number of individuals in the terminal size class was

very high relative to prior classes. As predicted by theory, population growth correlated negatively with the slope of the size distribution (fig. 6).

In the lower panels of figures 1–4, size distributions

based on life-table simulations are given along with ob- Species toward the right-hand side of each graph in fig- ure 6 had flatter size distributions (less negative

L), with

served size distributions. The simulated output closely

(13)

Condit e t al . ( 19 98 )

Assim como espécies com distribuições de tamanho diferentes podem apresentar crescimento e sobrevivência similares

Estruturas de tamanhos não são boas preditoras de dinâmica!

506

The American Naturalist

Figure 8: Size distribution and demographic parameters for Figure 9: Size distribution and demographic parameters for Heisteria concinna. All symbols are identical to those in figure Guarea sp. All symbols are identical to those in figure 1. Top 1. Top panel gives growth and survival probabilities for each panel gives growth and survival probabilities for each 50-mm 50-mm dbh bracket (10–49, 50–99 mm, etc.). Bottom panel dbh bracket (10–49, 50–99 mm, etc.). Bottom panel shows shows number of individuals in each 50-mm dbh class divided number of individuals in each 50-mm dbh class divided by the by the total number of individuals of that species. total number of individuals of that species.

was subtracted. Each of these correlation links left a sub- although survival and size distribution did work in

treelets. Species with low survival rates are declining in stantial amount of unexplained variance, and this ex- plains why some of the associations were not significant.

abundance in the BCI plot. We believe this is a result

specific to Barro Colorado Island: pioneer species have For example, although high survival was significantly re- lated to population change (this study) and to growth been in steady decline since the plot began (Hubbell and

Foster 1990, 1992; Condit et al. 1996b). This is possibly rate (Condit et al. 1996a), growth rate was not signifi- cantly associated with population change.

because areas adjacent to the plot were cleared in the

nineteenth century and have since reforested. Invasive Regardless of these details, we can say that we found no unequivocal shortcuts for predicting population species were undoubtedly extremely abundant just out-

side the plot during this recovery and pumped large changes. Static and short-term data on a population are not sufficient for predicting longer-term dynamics, at numbers of seeds into the old forest; now they are gradu-

ally being lost (Hubbell and Foster 1990, 1992). least in this forest.

The seven species with flat size distributions that qual- The trend for pioneer species to be declining appar-

ently underlies the weak correlation observed between ify as Newbery and Gartlan’s group 5 are an especially interesting set. All include immense trees—the largest in size distribution and population change in canopy spe-

cies. Pioneers, which had decreasing populations, tend to the plot—but very few juveniles. These characteristics have been the focus of much attention in Africa with dis- have high growth (Condit et al. 1996a) and, thus, flatter

size distributions. Thus, there was a weak association be- cussion revolving around whether such dominant canopy species are replacing themselves. Here is a summary of tween population change and size distributions in canopy

species, but it disappeared when the effect of growth rate what we know about the group at BCI: all are early suc-

(14)

Não foi encontrada ^(*) uma relação inversa entre inclinação e taxa de crescimento ( λ ) para plantas lenhosas em BCI (216 spp.)

Valores negaQvos indicam maior decaimento -‐ "J inverQdo"

Condit e t al . ( 19 98 )

(*) Exceto

para

arvoretas

(15)

Diferentes formas de estudar dinâmica

2 -‐ Descrição das mudanças ao longo do tempo

Cerne, Lavras, v. 15, n. 1, p. 58-66, jan./mar . 2009 63 Estrutura temporal de sete populações em três fragmentos...

Figura 2 – Distribuição diamétrica das populações nas três áreas inventariadas (IN = Ingaí, IU = Ibituruna e LU = Luminárias), entre 2000 ( ) e 2005 ( ).

Figure 2 – Diameter distribution of population in three areas surveys (IN = Ingaí, IU = Ibituruna and LU = Luminárias), between 2000 ( ) and 2005 ( ).

Continua...

To be continued...

IN IU LU

Machaerium stipitatum (DC.) Vogel Copaifera langsdorffii Desf.

Cupania vernalis Cambess.

Luehea grandiflora Mart. & Zucc.

0 50 100 150 200 250

5 < 10 10 < 20 20 < 40 40 < 80

Classes diamétricas (cm)

Nú m er o d e in di v íd uo s

0 2 4 6 8 10

5 < 10 10 < 20 20 < 40 40 < 80

Classes diamétricas (cm)

Nú m er o de i n d iv íd u os

0 5 10 15 20 25 30 35

5 < 10 10 < 20 20 < 40 40 < 80

Classes diamétricas (cm)

Nú m er o d e in di v íd uo s

0 10 20 30 40 50

5 < 10 10 < 20 20 < 40 40 < 80

Classes diamétricas (cm)

Nú m er o de i n d iv íd u os

0 5 10 15 20

5 < 10 10 < 20 20 < 40 40 < 80

Classes diamétricas (cm)

Núm er o de i ndi ví du os

0 10 20 30 40 50

5 < 10 10 < 20 20 < 40 40 < 80

Classes diamétricas (cm)

Nú m er o de i n d iv íd u os

0 5 10 15

5 < 10 10 < 20 20 < 40 40 < 80

Classes diamétricas (cm)

Nú m er o d e in di ví d u os

0 5 10

5 < 10 10 < 20 20 < 40 40 < 80

Classes diamétricas (cm)

Nú m er o d e in di ví d u os

0 2 4 6 8

5 < 10 10 < 20 20 < 40 40 < 80

Classes diamétricas (cm)

Nú m er o d e in d iv íd uo s

0 3 6 9

5 < 10 10 < 20 20 < 40 40 < 80

Classes diamétricas (cm)

Nú m er o d e in di v íd uo s

0 3 6 9 12 15 18

5 < 10 10 < 20 20 < 40 40 < 80

Classes diamétricas (cm)

Nú m er o de i nd iv íd u o s

0 10 20 30 40 50 60 70

5 < 10 10 < 20 20 < 40 40 < 80

Classes diamétricas (cm)

Nú m er o d e in d iv íd uo s

Carvalho et al (2009)

Estudo de espécies arbóreas em FES

(16)

Revista de Geografia. Recife: UFPE DCG/NAPA, v. 26, n^o 2, mai/ago. 2009.

147 3). A população de C. bahianus não apresentou redução drástica no início da estação seca (Fig. 2), porém, em D. coronata, ocorreu uma diminuição brusca na densidade no início da estação seca (Fig. 3). No conjunto dos microhabitats, bem como em cada um separadamente, as maiores densidades foram registradas no período chuvoso e as menores no período seco.

Figura 2. Densidades mensais da população de Cryptanthus bahianus (ind.35m

^-2

) e incremento populacional (r) ind. (ind.mês)

¹

Opções mais interessantes:

-‐ Comparação entre hábitats diferentes

-‐ Comparação entre espécies com diferentes estratégias de vida

-‐ Relação com mudanças climáQcas

Segundo N. Gotelli,: "medem

tudo sem seguir um plano"...

(18)

Diferentes formas de estudar dinâmica

3 -‐ Modelos matemáQcos

Ideia geral:

-‐ Propor cenários simples -‐ Gerar previsões testáveis

-‐ Variar parâmetros importantes

alligatorparasites.wordpress.com

(19)

Hal Caswell: "Por que experimentos são mais aceitos que modelos?

Não são simpliﬁcações da mesma forma?

(20)

DO SIMPLES AO MAIS COMPLEXO

(21)

Modelo de Crescimento Exponencial

r é a taxa intrínseca de crescimento (sem limites)

r = b -‐ d

(22)

Modelo de Crescimento Exponencial

Se r > 0, a população aumenta sem limites

Quanto maior a população (N), mais rapidamente ela cresce

(23)

Quanto maior o r , mais rapidamente a população cresce

Natur e Educ a7 on

(24)

Modelo de Crescimento Exponencial

Exemplos reais (?):

Silvertown & Charlesworth (2001)

Ou apenas uma fase inicial?

(25)

Modelo de Crescimento Exponencial

Premissas:

-‐ População fechada

-‐ Taxas de natalidade e mortalidade constantes

-‐ Ausência de estrutura na população -‐ Crescimento connnuo

(26)

Complicando: E se as populações Qverem algum Qpo de regulação?

Taxas vitais

podem variar

(27)

Alguns fatores que podem afetar as taxas vitais de plantas:

-‐ Interações com consumidores (predadores, herbívoros, patógenos) -‐ Interação com mutualistas (polinizadores, dispersores)

-‐ Interações compeQQvas (intra ou interespecíﬁcas) -‐ Variações genéQcas

-‐ Condições abióQcas (solo, clima, luz, etc) *

* Afetam, mas, em geral, não regulam

(28)

Regulação Populacional

Base para a teoria da evolução

blog.tepapa.govt.nz

(29)

Dependência da densidade

Um dos conceitos ecológicos mais anQgos

"Balanço da natureza"

Condição essencial para a persistência de populações!

(30)

K

Modelo de Crescimento LogísQco

K = Capacidade suporte do ambiente

À medida que N se aproxima de K, a taxa de crescimento diminui

(31)

Modelo de Crescimento LogísQco

Modelo dependente da densidade!

para N = 300 (0,80)

para N = 1350

(0,10)

(32)

K pode alterar r de duas formas:

-‐ diminuindo a taxa de natalidade (b) -‐ aumentando a taxa de mortalidade (d)

r = b -‐ d

Lembrando que

Interações compeQQvas ou de "predação" podem atuar

(33)

MODELO JANZEN -‐ CONNELL

Maior quanQdade de sementes próximas à planta mãe

Maior densidade gera maior

COMPETIÇÃO intraespecíﬁca e maior probabilidade de transmissão de PATÓGENOS

Maior proximidade à planta mãe gera maior chance de PREDAÇÃO e

ATAQUE DE PATÓGENOS

(34)

Box 1 The Janzen-Connell effect and its assumptions

The Janzen-Connell mechanism relies on assumptions about the relationship between seed (or seedling) density and the probability of individual recruitment, and the relationship between seed dispersal and distance from the parent plant. As shown in (a) the relationship between recruitment and density may be density independent, compensating or overcompensating. Seed dispersal is typically leptokurtic (b), so that most seeds land immediately beneath the parent tree. When this leptokurtic dispersal is combined with the density responses in (a), the net density of recruits depends on the form of density dependence as shown in (c). The Janzen-Connell mechanism is based on the prediction that when density dependence is overcompensating, recruitment fails beneath a parent tree. On the other hand, if density dependence is compensating, absent or undercompensating (intermediate between compensating or absent) then the highest densities of recruits occur immediately beneath the adults (c). The Janzen-Connell effect is a powerful mechanism: to illustrate this (d) shows the effect in operation in a simple model (described by Pacala 1997). In this model, there is a series of sites, each of which is occupied by an adult tree. Following the death of an adult, an empty site is occupied by another tree, the new occupier being determined by a simple lottery in which the probability of any species occupying being proportional to the number of seeds it disperses. To mimic the Janzen- Connell effect, the probability of recruitment of species i into a site formerly occupied by species i is reduced by a factor v. v = 1 corresponds to no density dependence (equivalent to a neutral model), whereas when v = 0 density dependence is completely overcompensating. The model assumes that a fraction of seed (m) disperses globally (varied between 0.01 and 0.9, indicated by the numbers above the lines in d), whereas the rest stays in the natal site. As shown, in (d) diversity is always maximized when density dependence is overcompensating. Moreover, when most seed lands in the parental site (global dispersal is 0.5 or less) the relationship is nonlinear so that the increases in diversity as a consequence of density dependence are greatest when v is small. This emphasizes that overcompensating density dependence is potentially an extremely powerful force, particularly when dispersal is low, exactly as envisaged in the original model (models were run for 1000 patches, with simulations lasting 5 · 10

⁵

generations. 30% of individuals died in each generation and the model was initiated with 50 identical species at time 0).

Density of seeds

7 6 5 4 3 2

1 0.0 0.2 0.4 0.6 0.8 1.0

Distance from parent

Density of recruits (log scale) Density of recruits (log scale) Density of seeds Relative species ric hness

v, reduction of recruitment in conspecific sites Overcompensating

NDD (v = 0)

No NDD (v = 1) Overcompensating

NDD Compensating

NDD No NDD

No NDD

Compensating NDD

Overcompensating NDD

m = 0.9

(a)

(c)

(b)

(d)

m = 0.5

m = 0.2

m = 0.1

m = 0.05 m = 0.01

Letter Pathogens cause overcompensating dynamics 1263

! 2010 Blackwell Publishing Ltd/CNRS

Precisa haver "sobrecompensação"

No modelo Janzen-‐Connell não basta haver regulação

É um modelo voltado para explicar coexistência em comunidades

Bagchi et al. ( 2010)

A redução na densidade de coespecíﬁcos próximos à planta mãe, propicia o

estabelecimento de outras espécies abaixo da copa

(35)

Modelo de Crescimento LogísQco

Premissas:

-‐ População fechada

-‐ Ausência de estrutura na população

-‐ Crescimento connnuo

(36)

Populações Estruturadas -‐ Modelos Matriciais

Marrero-‐Gomez et al.(2007)

Mecanismo básico de funcionamento já trabalhado em aula

(37)

Populações Estruturadas -‐ Modelos Matriciais

EsQmar a estrutura estável etária/tamanhos = Autovetor dominante EsQmar a taxa de crescimento = Autovalor dominante ( λ )

Prever o crescimento da população

Importância:

(38)

Relembrando alguns pontos importantes:

Matriz de Leslie

(baseada em idades) Matriz de Le{ovitch (baseada em estágios)

Diagonal principal

somente com zeros

(39)

Relembrando alguns pontos importantes:

"Todos os estudos demográﬁcos sofrem com o problema de que os dados coletados a par;r de poucos anos podem ser a<picos"

Silvertown & Charlestown (2006)

Principalmente para plantas de

vida longa

arvoresbrasil.nom.br

Lembra algo?

(40)

Importância de Parcelas Permanentes CTFS -‐ Center for Tropical Forest Science

Primeira Parcela CTFS

Ilha de Barro Colorado, Panamá (desde 1980) Muitos estudos populacionais importantes!

Foto: www.aqua-firma.co.uk/editorfiles/Image/Panama

(41)

Populações Estruturadas -‐ Modelos Matriciais Simples

Premissas:

-‐ Populações fechadas

-‐ Probabilidades de transição constantes -‐ Ausência de estrutura genéQca

(42)

Modiﬁcações nos valores de probabilidades afetando lambda ( λ ) λ = 1.259

Em árvores, maiores elasQcidades associadas à classe adulta

Análises de Perturbação -‐ Sensibilidade e ElasQcidade

(43)

Uma análise interessante!

Somar as elasQcidades dentro de cada um dos três principais processos

F = Fecundidade

S = Sobrevivência (L) G = Crescimento

Proporção que cada processo representa ou ainda

Proporção de cada estágio dentro de um dado processo

(44)

Ordenação triangular das elasQcidades de F -‐ G -‐ S

Silvertown et al. (1996) Ecology

F

G S

(45)

534 MIGUEL FRANCO AND JONATHAN SILVERTOWN Ecology, Vol. 85, No. 2

FIG. 1. The distribution of 102 species of perennial plants in elasticity space, as defined by the vital rates survival (S), growth (G), and fecundity (F). (a) Distribution of proportional values of elasticity. (b)–(f) Rescaled elasticity values for each of five groups of plants: (b) semelparous plants, (c) iteroparous herbs from open habitats, (d) iteroparous forest herbs, (e) shrubs, and (f) trees.

complex life cycles, not all of the papers contained enough information to decompose the matrix data into their component vital rates. Therefore, although we in- corporated a substantial number of new studies, we had to drop some of the species presented in previous anal- yses (e.g., Franco and Silvertown 1996). The results presented here come from 102 species listed in the Appendix. Projection analyses were conducted with the program STAGECOACH (Cochran and Ellner 1992).

This program was also used to calculate other life his- tory variables as in Franco and Silvertown (1996). The intrinsic rate of increase (r) was calculated as the nat- ural logarithm of

⌅

, the dominant eigenvalue of the population matrix for each species. Life span (L) is the expected age at death, conditional on passing through stage 1 (Cochran and Ellner’s Eq. 6). Age at sexual maturity (

⇤

) is the average age at which an individual enters a stage class with positive fecundity (Cochran and Ellner’s Eq. 15). Two measures of generation time, A˜, the mean age of parents of offspring produced at stable stage distribution (Cochran and Ellner’s Eq. 26), and

⌃

, the mean age at which members of a cohort produce offspring (Cochran and Ellner’s Eq. 27), were calculated. This was done because they measure slight- ly different things, but also because values for some species were computable by one measure and not the other. Finally, the net reproductive rate (R

₀

) is the av-

erage number of offspring produced by an individual over its life span (Cochran and Ellner’s Eq. 18). In cases where more than one type of recruit occurred (i.e., in species with clonal growth), all these life his- tory indices were taken for the average ‘‘newborn equivalent,’’ as weighted by the relative reproductive value of the different types of offspring in STAGE- COACH (Cochran and Ellner 1992). Additionally, us- ing the spectrum of eigenvalues for each matrix (spe- cies) we calculated the damping ratio (

⇥

), a measure of the speed with which the population converges to stability, and the period of oscillation (P

_i

, where i cor- responded to the highest possible complex eigenvalue), the average duration of an oscillation as the population converges to equilibrium. These correspond to equa- tions 4.90 and 4.99 of Caswell (2001). Not all matrices yielded complex eigenvalues, and therefore some spe- cies lack P

_i

Franco & Silvertown (2004)

Semélparas Herbáceas de ambientes abertos

Herbáceas de ﬂorestas Arbustos Árvores

(46)

Os processos estão relacionados à longevidade das plantas

February 2004 COMPARATIVE DEMOGRAPHY OF PLANTS 537

FIG. 4. The relationship between each of the elasticities of (a) survival, (b) growth, and (c) fecundity and life span for 102 species of perennial plants.

space (Fig. 1b–f) are all remarkably similar to the original distributions of the groups plotted using matrix element elasticities by Silvertown et al. (1993). The match between the two analyses is all the more re- markable because only 52 species out of the total of 120 analyzed so far were present in both the original dataset and the current one, and four of these have new data (see the Appendix). The similarity of the two sets of distributions demonstrates that, although matrix elasticities are technically compounds of vital rates, the matrix regions that were originally designated as representing growth, stasis, and fecundity were appropri- ately named for practical purposes. It is evident from this that the elasticities of distinct matrix regions, as defined by Silvertown et al. (1993), are largely determined by contributions from specific vital rates.

Notwithstanding the agreement between element and vital rate elasticities, the latter are to be preferred because they strictly correspond to the fundamental demographic processes that matrix element elasticities only approximate. Another reason for the preference is that matrix element elasticities are influenced by the number and breadth of size classes used in a population model (Enright et al. 1995), while vital rate elasticities are more robust to such details of matrix construction.

As mentioned in Introduction, Zuidema and Zagt (in Zuidema 2000) found that, in contrast to the elasticity of matrix elements, the elasticity of vital rates was rather insensitive to changes in the number of categories (matrix size) employed.

It is important to bear in mind that whichever type of elasticity analysis is used, estimates of demographic parameters will always be highly dependent upon the ecological conditions, for example the successional sta- tus, under which the estimates were obtained (Silver- town et al. 1996, Silva Matos et al. 1999). This problem suggests that standardization may be useful before species are compared. One possible method of standardization would be to confine comparisons only to those species represented by populations at equilibrium (i.e.,

⇥ 1 or r 0). However, this would ignore the fact that equilibrium is not a typical state for the populations of some species, particularly short-lived ones, and such a comparison would therefore be biased against certain life history types. In the present data set, only 44 of the 102 species fall within the bounds 0.95⌅ ⇥ ⌅1.05 and these are mainly woody (nine shrubs and 20 trees).

Standardization by this method would severely bias the data set and defeat the object of comparing species by excluding all eight semelparous perennial species, most (22 out of 31 species) iteroparous herbs of open habitats, and half the forest herbs and shrubs (seven out of 13 and nine out of 18 species, respectively).

Correlates of vital rate elasticities

As is to be expected, elasticities of vital rates correlate with life history and population parameters. Lon- gevity, age at first reproduction, and generation time all increase along an arc that runs from the F vertex to the S vertex, passing through the center of the triangle (Fig. 2a–d). These patterns reflect the changes in plant life history that occur with succession from pioneer to climax communities (Silvertown and Franco 1993). Population model properties also correlate with vital rate elasticities, but in a more varied manner. The intrinsic rate of natural increase (r) is highest at the point F G 0.5, S ⇤ 0 and decreases toward S ⇤ 1 (Fig. 3a). By contrast, the net reproductive rate (R₀) is highest near the center of the triangle (Fig. 3d). The damping ratio ( ), which measures how quickly a population’s size structure converges on equilibrium, is high for short-lived species at theGandFvertices and decreases toward the center of the triangle and the S vertex. (Fig. 3b). The period of oscillation is lowest

As is to be expected, elasticities of vital rates correlate with life history and population parameters. Lon- gevity, age at first reproduction, and generation time all increase along an arc that runs from the F vertex to the S vertex, passing through the center of the triangle (Fig. 2a–d). These patterns reflect the changes in plant life history that occur with succession from pioneer to climax communities (Silvertown and Franco 1993). Population model properties also correlate with vital rate elasticities, but in a more varied manner. The intrinsic rate of natural increase (r) is highest at the point F G 0.5, S ⇤ 0 and decreases toward S ⇤ 1 (Fig. 3a). By contrast, the net reproductive rate (R0) is highest near the center of the triangle (Fig. 3d). The damping ratio ( ), which measures how quickly a population’s size structure converges on equilibrium, is high for short-lived species at theGandFvertices and decreases toward the center of the triangle and the S vertex. (Fig. 3b). The period of oscillation is lowest

As is to be expected, elasticities of vital rates correlate with life history and population parameters. Lon- gevity, age at first reproduction, and generation time all increase along an arc that runs from the F vertex to the S vertex, passing through the center of the triangle (Fig. 2a–d). These patterns reflect the changes in plant life history that occur with succession from pioneer to climax communities (Silvertown and Franco 1993). Population model properties also correlate with vital rate elasticities, but in a more varied manner. The intrinsic rate of natural increase (r) is highest at the point F G 0.5,S ⇤ 0 and decreases toward S⇤ 1 (Fig. 3a). By contrast, the net reproductive rate (R₀) is highest near the center of the triangle (Fig. 3d). The damping ratio ( ), which measures how quickly a population’s size structure converges on equilibrium, is high for short-lived species at theGandFvertices and decreases toward the center of the triangle and the S vertex. (Fig. 3b). The period of oscillation is lowest

F G

S

Requer interpretação cuidadosa e dentro de

grupos similares

(47)

1 -‐ Dependência da densidade

Adicionando complexidade a modelos matriciais simples

Toda a população Apenas uma classe

3 -‐ EstocasQcidade demográﬁca -‐ Populações pequenas 2 -‐ EstocasQcidade ambiental Toda a população

Apenas uma classe

(48)

Analisando duas ou mais matrizes

4 -‐ Metapopulações

1 -‐ Genets + Ramets -‐ Matrizes de Goodman 2 -‐ Variação Temporal

3 -‐ Variação Espacial

LTRE ^-‐ Life Table Response Experiment

(49)

conditions and/or experimental treatments allows managers to evaluate the efficacy of specific management actions and to project what will happen if a certain management strategy is implemented (Song, 1996). However PVA models must be used with caution, because they are just models, or ‘‘carica- tures of reality’’ (Beissinger and Westphal, 1998). Accordingly, one must be aware of the limitations of the models, especially when the results are to be used for decisions on practical species conservation and management. In the case of the model presented here, it is necessary to point out that all data comes from a single monitoring plot and this lack of replication does not allow us to discern local from environmental variability.

However, we were forced to restrict our monitoring to a single location, in order to avoid endangering the species by our own activities. In addition, comparisons between the native and introduced populations were performed for only one year, and relevant vital rates such as the survival of mature adults were not compared. However, we believe that our comparisons of the demographic structure, fruit production and seedling mortality were sufficient to suggest that the dynamics of the natural and planted populations were quite similar. We also assume that herbivores are not a significant factor, because we did not observe any damage that could be attributed to introduced (rabbits, mouflons) or natural herbivores (lizards, insects, etc.), and all observed deaths in the field were caused by summer drought or natural senescence.

In PVA’s, demographic responses to variable environments can be analyzed by prospective or retrospective analyses.

Sensitivity or elasticity analyses are prospective and quantify the change in population growth rate given a specified change in one or more elements of the matrix. Retrospective analyses, by life table response experiments, can be used to deter- mine life-history stages or demographic transitions that contributed to differences between populations observed during the observation period (Horvitz et al., 1997; Caswell, 2000).

In this paper we resorted principally to prospective analyses because they are the most suitable approach to predict how expected levels of stochasticity will interact with conservation measures to influence the future population growth rate of threatened or endangered species (Menges, 1990; Heppell et al., 1994). The retrospective analyses used in this paper do not clearly coincide with the classical approach. Here, we mainly used it to get an idea of the most likely historical fluc- tuations in population size.

Elasticity analysis revealed that the most critical stage in the life cycle ofH. juliaeis the survival of mature reproductive plants, which showed the highest elasticity (31%) in the average matrix. The survival of this stage in natural conditions was 90.8%, and did not show much variation between good and bad years. For management reasons, we periodically vis- ited the natural populations from 1985 onwards, and the planted population from 1989 onwards, when the individuals were three years old. Our field observations indicated that large reproductive plants generally died of senility after 14 years. In contrast, juvenile recruitment was highly variable, with very high values (4.88) in good, and low values (0) in

1.0 0.8 0.6 0.4 0.2 0

0 0.2

0.4 0.6

0.8

1.0 0

0.2

0.4

0.6

0.8

1.0 L

F G

1 2

3 54

6

97 8

92-93 93-94

94-95 95-96

96-97

97-98

98-99 99-00

00-01

P > 350 mm

P < 350 mm

Fig. 5 – Triangular ordination diagram representing the position of the nine matrices forHelianthemum juliaebetween 1992 and 2002 with respect to their relative contribution (=summed elasticities) of fecundity (F), Growth (G) and survival (L) to the population growth rate,k. The matrices have been chronologically numbered from 1, 1992–1993 to 9, 2001–2002. Shaded areas enclose matrices that correspond to two precipitation classes,P< 350 mm,P> 350 mm.

B I O L O G I C A L C O N S E R V A T I O N 1 3 6 ( 2 0 0 7 ) 5 5 2–5 6 2 559

Marrero-‐Gomez et al.(2007) Estudo com matrizes temporais de Helianthemum juliae e

relação com precipitação

(50)

Crescimento conrnuo -‐ Modelos de Projeção Integral

Não divide os indivíduos em classes/estágios

Easterling et al. (2000) -‐ Ecology

MPI

MM

Aconitum noveboracense

(51)

Modelos de Projeção Integral

the integral projection model (IPM) in which individuals are characterized by a continuous variablexsuch as size. The state of the population given byn(x,t), such that the number of individuals with sizes betweenaand bisRb

a n(x,t)dx. Instead of the matrixM, the IPM has a projection kernelK(y,x), so that

n(y,tþ1)¼ Z^S

s

K(y,x)n(x,t)dx,

wheresandSare the minimum and maximum possible sizes. The integration is the continuous version of equation 4, adding up all the contributions to sizeyat timetþ1 by individuals of sizex at timet. Providing some technical conditions are met (see Ellner and Rees, 2006, for details), the IPM behaves essentially like a

matrix model, and so the results described above carry over.

Constructing the projection kernel K(y,x) is straightforward using the regressions shown in figure 3. For an individual of sizexto become sizey, it must (1) grow from x toy, (2) survive, and (3) not flower (flowering is fatal in monocarpic plants like Platte thistle). These probabilities are calculated from the fitted relationships in figures 3A, 3B, and 3C, respectively. The use of regression models to construct the projection kernel brings some advantages: (1) accepted statistical approaches can be used for selecting an ap- propriate regression model; and (2) additional variables characterizing individuals’ states can be included by adding explanatory variables rather than having to select a single best state variable. For example, in some thistles the probability of flowering depends on both an

A. B.

C. D.

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.5

0 1.0 2.0 1.5 2.5 3.0

Root crown diameter year t mm (log scale)

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Root crown diameter mm (log scale)

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.6

0.8

0.4

0.2

0 1.0

Root crown diameter mm (log scale)

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Root crown diameter mm (log scale) 0.2

0.4

0 0.6 0.8 1.0

200 400

0 600 800

Root crown diameter year t+1 mm (log scale) Probability of survivalSeed production

Figure 3. Size structured demographic rates for Platte thistle, Cirsium canescens. (A) Growth (as characterized by plant size in successive years), (B) survival , (C) the probability of flowering, and (D) seed production all vary continuously with size and can be de scribed by simple regression models. (Redrawn from Rose et al.,

2005) In panels B and C, the data were divided into 20 equal sized categories, and the plotted points are fractions within each cate gory, but the logistic regression models (plotted as curves) were fitted to the binary values (e.g., flowering or not flowering) for each individual.

Tópicos importantes da deﬁnição de População:

Dinâmica Populacional de Plantas

Disciplina BIE 0320

Ecologia de Populações e Comunidades Vegetais

2015

Tópicos importantes da deﬁnição de População:

-­‐ Mesma espécie -­‐ Mesmo local

-­‐ Mesmo tempo (?)

Estrutura Populacional Quais aspectos?

-­‐ Distribuição de idades

-­‐ Distribuição de tamanhos -­‐ Distribuição de estágios -­‐ Razão sexual

-­‐ Estrutura genéQca

-­‐ Distribuição espacial

Dinâmica Populacional Taxas vitais

-­‐ Nascimento -­‐ Mortalidade -­‐ Imigração -­‐ Emigração

+ Crescimento

1 -­‐ Deﬁnir e demarcar área

Como se faz na práQca?

Para populações de herbáceas parece rela7vamente simples

Mas nem sempre...

Como se faz na práQca?

1 -­‐ Deﬁnir e demarcar área

Em ﬂorestas

2 -­‐ Contar indivíduos e monitorar ao longo do tempo

Como se faz na práQca?

Nesse caso, sem marcar e acompanhar cada indivíduo

2 -­‐ Contar indivíduos e monitorar ao longo do tempo

Como se faz na práQca?

Nesse caso, marcando e acompanhando cada indivíduo

 































































Como se faz na práQca?

Diferentes formas de estudar dinâmica

1 -­‐ Inferir dinâmica a parQr de estrutura

Ideia geral: Diferença entre classes = probabilidade de transição

Premissa perigosa: Estrutura atual representa a estrutura estável

Figura 5: Classes de diâmetro de Ocotea pulchella. Classes Éxas de 2 cm. 4-3,1 a 5,0 cm;

6-5,1 a 7,0 cm; 8-7,1 a 9,0 cm; . . .; 42-41,1 a 43,0 cm; e, 44-43,1 a 45,0 cm.

Figura 6: Classes de diâmetro de Anadenanthera falcata. Classes Éxas de 2 cm. 4-3,1 a 5,0 cm; 6-5,1 a 7,0 cm; 8-7,1 a 9,0 cm; . . . ; 84-73,1 a 85,0 cm; e, 86-85,1 a 87,0 cm.

62

Interpretação convencional:

População em crescimento ("J inverQdo")

População em declínio

Si lv a & S oar es 1 99 9

Porém...

Condit e t al . ( 19 98 )

502

viduals). However, the result can also be viewed in the

slope

against observed

-‐ Mesma espécie -‐ Mesmo local

-‐ Mesmo tempo (?)

-‐ Distribuição de idades

-‐ Distribuição de tamanhos -‐ Distribuição de estágios -‐ Razão sexual

-‐ Estrutura genéQca

-‐ Distribuição espacial

-‐ Nascimento -‐ Mortalidade -‐ Imigração -‐ Emigração

1 -‐ Deﬁnir e demarcar área

1 -‐ Deﬁnir e demarcar área

2 -‐ Contar indivíduos e monitorar ao longo do tempo

2 -‐ Contar indivíduos e monitorar ao longo do tempo

1 -‐ Inferir dinâmica a parQr de estrutura

Não foi encontrada ^(*) uma relação inversa entre inclinação e taxa de crescimento ( λ ) para plantas lenhosas em BCI (216 spp.)

Valores negaQvos indicam maior decaimento -‐ "J inverQdo"

2 -‐ Descrição das mudanças ao longo do tempo